| Title: | Adaptive Nature-Inspired Algorithms for Hybrid Genetic Optimization |
|---|---|
| Description: | The Genetic Algorithm (GA) is a type of optimization method of Evolutionary Algorithms. It uses the biologically inspired operators such as mutation, crossover, selection and replacement.Because of their global search and robustness abilities, GAs have been widely utilized in machine learning, expert systems, data science, engineering, life sciences and many other areas of research and business. However, the regular GAs need the techniques to improve their efficiency in computing time and performance in finding global optimum using some adaptation and hybridization strategies. The adaptive GAs (AGA) increase the convergence speed and success of regular GAs by setting the parameters crossover and mutation probabilities dynamically. The hybrid GAs combine the exploration strength of a stochastic GAs with the exact convergence ability of any type of deterministic local search algorithms such as simulated-annealing, in addition to other nature-inspired algorithms such as ant colony optimization, particle swarm optimization etc. The package 'adana' includes a rich working environment with its many functions that make possible to build and work regular GA, adaptive GA, hybrid GA and hybrid adaptive GA for any kind of optimization problems. Cebeci, Z. (2021, ISBN: 9786254397448). |
| Authors: | Zeynel Cebeci [aut, cre], Erkut Tekeli [aut], Cagatay Cebeci [aut] |
| Maintainer: | Erkut Tekeli <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1.0 |
| Built: | 2024-12-23 06:24:18 UTC |
| Source: | CRAN |
The package adana provides the functions related to the hyrid adaptive genetic algorithms for solving optimization problems.
The Genetic Algorithm (GA) is a type of optimization method of Evolutionary Algorithms. It uses the biologically inspired operators such as mutation, crossover, selection and replacement.Because of their global search and robustness abilities, GAs have been widely utilized in machine learning, expert systems, data science, engineering, life sciences and many other areas of research and business. However, the regular GAs need the techniques to improve their efficiences in computing time and performance in finding global optimum using some adaptation and hybridization strategies. The adaptive GAs (AGA) increase the convergence speed and success of regular GAs by setting the parameters crossover and mutation probabilities dynamically. The hybrid GAs combine the exploration strength of a stochastic GAs with the exact convergence ability of any type of deterministic local search algorithms such as simulated-annealing, in addition to other nature-inspired algorithms such as ant colony optimization, particle swarm optimization etc. The package 'adana' includes a rich working environment with its many functions that make possible to build and work regular GA, adaptive GA, hybrid GA and hybrid adaptive GA for any kind of optimization problems.
Zeynel Cebeci, Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari [Genetic Algorithms and Optimization Applications with R], 535 p. Nobel Academic Publishing. Ankara
The adana function is a GA function that can be used for any single-objective optimization problem.
adana(gatype = "gga", objective = "max", maxiter = 100, initfunc = initbin, fitfunc, selfunc = seltour, crossfunc = px1, mutfunc = bitmut, replace = elitism, adapfunc = NULL, hgafunc = NULL, monitorfunc = NULL, n = 100, m = 8, lb = rep(0, 8), ub = rep(1, 8), nmode = "real", type = 1, permset = 0:9, prevpop = NULL, selt = 2, selbc = 0.5, selc = 2, selk = 1.005, sells = 1.5, selns = 0.5, selps = 0.5, sels = 1.5, selt0 = 50, selw = 2, reptype = FALSE, cxpc = 0.9, cxpc2 = 0.8, cxon = 2, cxk = 2, cxps = 0.5, cxa = 0, cxb = 0.15, cxealfa = 1, cxalfa = 0.5, mutpm = 0.05, mutpm2 = 0.2, mutb = 2, mutpow = 2, mutq = 0.5, mutmy = c(), mutsdy = c(), adapa = 0.75, adapb = 0.5, adapc = 0.1, adapd = 0.1, hgastep = 10, hgans = 1, hgaftype = "w", reps = 1, repk = 10, lambda = 1, tercrit = c(1), abdif = 1e-06, bestdif = 1e-06, objval = 0, optdif = 1e-06, rmcnt = 10, rmdif = 1e-06, phidif = 1e-06, rangedif = 1e-06, meandif = 1e-06, sddif = 1e-06, mincv = 0.001, simlev = 0.95, maxtime = 60, keepbest = TRUE, parfile = NULL, verbose = FALSE, ...)adana(gatype = "gga", objective = "max", maxiter = 100, initfunc = initbin, fitfunc, selfunc = seltour, crossfunc = px1, mutfunc = bitmut, replace = elitism, adapfunc = NULL, hgafunc = NULL, monitorfunc = NULL, n = 100, m = 8, lb = rep(0, 8), ub = rep(1, 8), nmode = "real", type = 1, permset = 0:9, prevpop = NULL, selt = 2, selbc = 0.5, selc = 2, selk = 1.005, sells = 1.5, selns = 0.5, selps = 0.5, sels = 1.5, selt0 = 50, selw = 2, reptype = FALSE, cxpc = 0.9, cxpc2 = 0.8, cxon = 2, cxk = 2, cxps = 0.5, cxa = 0, cxb = 0.15, cxealfa = 1, cxalfa = 0.5, mutpm = 0.05, mutpm2 = 0.2, mutb = 2, mutpow = 2, mutq = 0.5, mutmy = c(), mutsdy = c(), adapa = 0.75, adapb = 0.5, adapc = 0.1, adapd = 0.1, hgastep = 10, hgans = 1, hgaftype = "w", reps = 1, repk = 10, lambda = 1, tercrit = c(1), abdif = 1e-06, bestdif = 1e-06, objval = 0, optdif = 1e-06, rmcnt = 10, rmdif = 1e-06, phidif = 1e-06, rangedif = 1e-06, meandif = 1e-06, sddif = 1e-06, mincv = 0.001, simlev = 0.95, maxtime = 60, keepbest = TRUE, parfile = NULL, verbose = FALSE, ...)
gatype |
Type of GA.
Default value is "gga" |
objective |
Type of optimization.
Default value is "max" |
maxiter |
Maximum generation number Default value is 100 |
initfunc |
Name of fitness function.
Default value is "initbin" |
fitfunc |
Fitness function |
selfunc |
Name of the selection function Default value is "seltour" |
crossfunc |
Name of the crossover function Default value is "px1" |
mutfunc |
Name of the mutation function Default value is "bitmut" |
replace |
Name of the replacement function Default value is "elitism" |
adapfunc |
Name of the adaptation function |
hgafunc |
The name of the function that will do the hybridization. |
monitorfunc |
Monitoring function |
n |
Population size |
m |
Length of chromosome |
lb |
A vector containing lower bounds for variables in value-coded problems |
ub |
A vector containing upper bounds for variables in value-coded problems |
nmode |
Value mode for initiating value-coding problems
Default value is "real" |
type |
Integer indicating the type of initialization matrix.
|
permset |
A vector containing the ordinal values to be used in permutation-coded initialization. Default value is 0:9 |
prevpop |
A matrix containing previously prepared chromosomes during initialization. |
selt |
The tournament size for the seltour and seltour2 functions. Default value is 2. |
selbc |
The base parameter for the selers function. Default value is 0.5. |
selc |
Scale parameter for selsscale and selsscale2 functions Default value is 2. |
selk |
Power parameter for selpscale function Default value is 1.005. |
sells |
Scale parameter for sellscale function Default value is 1.5. |
selns |
Polynomal coefficient for selnlrs function Default value is 0.5. |
selps |
Cut-point threshold value for seltrunc function. Default value is 0.5. |
sels |
Selection pressure for sellrs, sellrs3 and selrscale2 functions. Default value is 1.5. |
selt0 |
The starting temperature for selboltour function. Default value is 50. |
selw |
Window size for selwscale function. Default value is 2. |
reptype |
TRUE value is entered for the sampling with replacement when the seltour and seltour2 are used. Default value is FALSE. |
cxpc |
Crossover ratio Default value is 0.9. |
cxpc2 |
Adapted crossover ratio for the leitingzhi function. |
cxon |
Number of offspring per mating in crossover. Default value is 2. |
cxk |
Number of cut-points for multi-point crossover. Default value is 2. |
cxps |
Probability threshold value for hux, ux, ux2, dc crossovers. Default value is 0.5. |
cxa |
Location Parameter for lapx crossover Default value is 0. |
cxb |
Scale Parameter for lapx crossover Default value is 0.15 |
cxealfa |
The random alpha value for sax, wax, ebx crosses. It is determined dynamically, but for some controlled studies, a fixed value can be assigned. |
cxalfa |
The random alpha value for sax, wax, ebx crosses. It is determined dynamically, but for some controlled studies, a fixed value can be assigned. |
mutpm |
Mutation rate Default value is 0.05 |
mutpm2 |
Adaptive mutation rate |
mutb |
The exponent value used to avoid uniformity in unimut and nunimut2. Default value is 0.5 |
mutpow |
The exponent value for powmut and powmut2 functions. Default value is 2. |
mutq |
A number. Value of q for bsearchmut1 Default value is 0.5 |
mutmy |
A vector. Vector of means of genes |
mutsdy |
A vector. Vector of standard deviations of genes |
adapa |
Adaptation threshold a for leitingzhi function Default value is 0.5 |
adapb |
Adaptation threshold b for leitingzhi function Default value is 0.75 |
adapc |
Crossover adaptation threshold for adana3 function Default value is 0.2 |
adapd |
Mutation adaptation threshold for adana3 function Default value is 0.05 |
hgastep |
In a hybrid GA implementation, it is an integer indicating how many generations the hybrid optimization algorithm will be called. Default value is 10 |
hgans |
Number of individuals to be transferred to the Optim. Default value is 2 |
hgaftype |
Types of fitness to transfer.
Default value is "w" |
reps |
The number of the best individuals to be selected when elitism is applied. Default value is 1. |
repk |
The selection pressure parameter for the Round Robin function. Default value is 10. |
lambda |
Total number of offspring in replacement algorithms in steady-state replacement type GAs Default value is 1. |
tercrit |
A vector for termination criterion Default value is (1,13). |
abdif |
It is an approach difference value used by the termination criterion 6. Default value is 1e-06. |
bestdif |
The approach value to the global optimum value. Default value is 1e-06. |
objval |
Global optimum. Used by some termination criterion. This criterion is used if the global optimum of the problem is known. |
optdif |
It is an approach difference value used by the termination criterion 3. Default value is 1e-06. |
rmcnt |
k value used by the termination criterion 5. Default value is 10. |
rmdif |
It is an approach difference value used by the termination criterion 5. Default value is 1e-06. |
phidif |
It is an approach difference value used by the termination criterion 10. Default value is 1e-06. |
rangedif |
It is an approach difference value used by the termination criterion 8. Default value is 1e-06. |
meandif |
It is an approach difference value used by the termination criterion 4. Default value is 1e-06. |
sddif |
It is an approach difference value used by the termination criterion 7. Default value is 1e-06. |
mincv |
Minimum coefficient of variance used by the termination criterion 9. Default value is 0.001. |
simlev |
It is an approach difference value used by the termination criterion 7. Default value is 0.99. |
maxtime |
It is maximum runtime (minute) value used by the termination criterion 12. Default value is 60. |
keepbest |
If the keepbest parameter is TRUE, the best solution value, chromosome, and generation number are saved in the list named bestsol. Default value is TRUE. |
parfile |
The name of the file where the parameter values are defined if any. Default value is NULL. |
verbose |
TRUE is assigned to display the statistics of fitness values obtained at the end of the loop in the GA study. Default value is FALSE. |
... |
additional arguments to be passed to the |
adana function is a genetic algorithm function that can be used for all kinds of single-objective optimization problems. The adana function, unlike other GA packages, not only has adaptive GA functions, but also offers specially developed deterministic and self-adaptive techniques called adana1, adana2, and adana3, and is easily hybridized with other optimization methods inspired by nature. Besides, the adana function supports the use of monitors to monitor the progress of the GA run. In addition to containing many crossover and mutation operators, it is coded with a plug-and-play approach so that the user can add custom operator functions that he has developed.
The initialization population is created by using the name of the initialization function and other parameters passed to initfunc with the initialize function. The fit values of individuals in the population are calculated using fitfunc, which is passed to the evaluate function before each iteration. Then, the termination conditions are checked according to the criteria specified in the termination criteria (tercrit) argument via the terminate function. When the termination condition is not met, adana GA continues to run and searches for the best solution. If the keepbest argument is TRUE, the best solution value, chromosome, and generation number are saved in the list named bestsol.
Since the adana function allows adaptive GA studies, from which it is named, it runs a function that is passed with the adapfunc argument and contains the code of the adaptation algorithm. This adaptation function returns the crossover and mutation rates by recalculating. Thus, it strengthens the GA with its exploitation and exploration adaptations.
In order to determine the individuals to be selected for the mating pool, the selection process is done with the selfunc selection function transferred to the select function.
The crossover of selected individuals is executed with the crossover operator in the crossfunc argument passed to the cross function.
Mutation operations are performed with the mutation operator function assigned to mutfunc by the mutate function.
Finally, for GA, replacement is performed by passing the parent population and the offspring population to the replace function.
Hybridization with other optimization techniques can also be done before an iteration of the GA is complete. For this, the hybridization function passed to the hgafunc argument is used. Other parameters that need the optimization technique called in the hybridization function call, are also passed.
Progress made in each GA generation can be monitored visually with a monitor function. For this, the monitor function passed to the monitorfunc argument is used.
In GA implementations, if the required parameters for R functions that perform selection, crossover, mutation, renewal, and other operations are not entered in the function call, their default values are used. The user can change these parameters during the function call to suit the problem. However, there are many parameters used by the adana function and the functions it calls. It may be more practical to use the parameters by saving them to a file. The parfile argument can be used for this purpose.
genfits |
A matrix containing statistics for generations. |
initpop |
A matrix containing the initial population |
finalpop |
A matrix containing the final population |
bestsol |
Value of the best solution |
objective |
Objective of the optimization, min or max |
tcode |
Termination code |
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
GA Operators:
initialize,
evaluate,
terminate,
select,
cross,
mutate
Initialize Functions:
initbin,
initval,
initperm,
initnorm
Selection Functions:
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers,
seltrunc
Crossover Functions:
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
Mutation Functions:
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
Replacement Functions:
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
Adaptation Functions:
fixpcmut,
ilmdhc,
adana1,
adana2,
adana3,
leitingzhi
Hybridization Functions:
hgaoptim,
hgaoptimx,
hgaroi
# Preparing data material = c("knife", "tin", "potato", "coffee", "sleeping bag", "rope", "compass") weigth = c(1, 5, 10, 1, 7, 5, 1) point = c(10, 20, 15, 2, 30, 10, 30) kspdata = data.frame(material, weigth, point) capacity = 100 # Fitness Function kspfit2 = function(x, ...) { tpoint = x %*% kspdata$point tweigth = x %*% kspdata$weigth G1 = tweigth-capacity fitval = tpoint-max(0,G1)^2 return(fitval) } # Run GA n = 20 m = nrow(kspdata) niter = 100 kspGGA = adana(n=n, m=m, maxiter=niter, objective="max", gatype="gga", initfunc=initbin, fitfunc=kspfit2, selfunc=seltour, crossfunc=kpx, mutfunc=bitmut, replace=elitism, selt=2, reps=4, repk=5, cxon=2, cxk=3, cxpc=0.8, mutpm=0.05, tercrit=c(1), keepbest=TRUE, verbose=TRUE, monitorfunc=monprogress) head(kspGGA$finalpop) # Display Final Population head(kspGGA$genfits) # Display Fitness Values According to Generations bestsol(kspGGA) # Display Best Solution kspdata[kspGGA$bestsol$chromosome == 1, ] # Display Best Chromosome# Preparing data material = c("knife", "tin", "potato", "coffee", "sleeping bag", "rope", "compass") weigth = c(1, 5, 10, 1, 7, 5, 1) point = c(10, 20, 15, 2, 30, 10, 30) kspdata = data.frame(material, weigth, point) capacity = 100 # Fitness Function kspfit2 = function(x, ...) { tpoint = x %*% kspdata$point tweigth = x %*% kspdata$weigth G1 = tweigth-capacity fitval = tpoint-max(0,G1)^2 return(fitval) } # Run GA n = 20 m = nrow(kspdata) niter = 100 kspGGA = adana(n=n, m=m, maxiter=niter, objective="max", gatype="gga", initfunc=initbin, fitfunc=kspfit2, selfunc=seltour, crossfunc=kpx, mutfunc=bitmut, replace=elitism, selt=2, reps=4, repk=5, cxon=2, cxk=3, cxpc=0.8, mutpm=0.05, tercrit=c(1), keepbest=TRUE, verbose=TRUE, monitorfunc=monprogress) head(kspGGA$finalpop) # Display Final Population head(kspGGA$genfits) # Display Fitness Values According to Generations bestsol(kspGGA) # Display Best Solution kspdata[kspGGA$bestsol$chromosome == 1, ] # Display Best Chromosome
Adana-1 is an adaptation function that calculates the mutation rates to be applied in generations by sine wave modeling (Cebeci, 2021).
adana1(g, gmax, ...)adana1(g, gmax, ...)
g |
Current generation |
gmax |
Maximum generation |
... |
Further arguments passed to or from other methods. |
pc |
Crossover rate |
pm |
Mutation rate |
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
fixpcmut,
ilmdhc,
adana2,
leitingzhi,
adana3
gmax <- 1000 g <- c(1, 10, 50, 100, 250, 500, 750, gmax) adana1(g=g, gmax=gmax)gmax <- 1000 g <- c(1, 10, 50, 100, 250, 500, 750, gmax) adana1(g=g, gmax=gmax)
Adana-2 is an adaptation function that calculates the mutation rates to be applied in generations by square root modeling (Cebeci, 2021).
adana2(g, gmax, ...)adana2(g, gmax, ...)
g |
Current generation |
gmax |
Maximum generation |
... |
Further arguments passed to or from other methods. |
pc |
Crossover rate |
pm |
Mutation rate |
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
fixpcmut,
ilmdhc,
adana1,
leitingzhi,
adana3
gmax <- 1000 g <- c(1, 10, 50, 100, 250, 500, 750, gmax) adana1(g=g, gmax=gmax)gmax <- 1000 g <- c(1, 10, 50, 100, 250, 500, 750, gmax) adana1(g=g, gmax=gmax)
This adaptation function proposed by Cebeci (2021) is an adaptation function that takes into account the cooperation of individuals.
adana3(fitvals, g, gmax, cxpc, mutpm, adapc, adapd, ...)adana3(fitvals, g, gmax, cxpc, mutpm, adapc, adapd, ...)
fitvals |
A vector. Fitness values of current generation |
g |
Current generation |
gmax |
Maximum generation |
cxpc |
Crossover rate. 0 <= cxpc <= 1 |
mutpm |
Mutation rate. 0 <= mutpm <= 1 |
adapc |
Adaptation threshold for crossover rate. 0 <= adapa <= 1. default is 0.05 |
adapd |
Adaptation threshold for mutation rate. 0 <= adapb <= 1. default is 0.05 |
... |
Further arguments passed to or from other methods. |
pc |
Crossover rate |
pm |
Mutation rate |
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
fixpcmut,
ilmdhc,
adana1,
adana2,
leitingzhi
The Asymmetric Two-Point Crossover (ATC) operator relies on the two-point crossover being implemented differently for Parent1 and Parent2 (Yuan, 2002). Offspring2 is generated by a standard two-point crossover. However, in the generation of Offspring1, the part between the cut points is taken from Parent2, while the other parts are completed from Parent1.
atc(x1, x2, cxon, ...)atc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Yuan B. (2002). Deterministic crowding, recombination and self-similarity. In Proc. of the 2002 Cong. on Evolutionary Computation (Cat. No. 02TH8600) (Vol. 2, pp. 1516-1521). IEEE.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) atc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) atc(parent1, parent2)
The AX operator calculates the simple arithmetic mean of the parental chromosomes. Therefore, it is a single-output operator and generates a single offspring (Gwiazda, 2006).
ax(x1, x2, cxon, ...)ax(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Gwiazda T.D. (2006). Genetic Algorithms Reference. Vol. I: Crossover for Single-Objective Numerical Optimization Problems. Tomaszgwiadze E-books, Poland.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) ax(parent1, parent2, cxon=1)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) ax(parent1, parent2, cxon=1)
Display best solution from result of GA
bestsol(garesult)bestsol(garesult)
garesult |
GA result object |
Display chromosome, fitness value and generation number of best solution.
Zeynel Cebeci & Erkut Tekeli
The function bin2gray converts a binary coded number to gray coded integer.
bin2gray(bin)bin2gray(bin)
bin |
A binary coded number. |
The bin2gray function works as a compliment of the gray2bin function.
Returns the gray coded integer equivalent of the input number.
Zeynel Cebeci & Erkut Tekeli
bin = c(1,0,1,1) bin2gray(bin) # returns 1110 bin = c(1,0,1,0) bin2gray(bin) # returns 1111bin = c(1,0,1,1) bin2gray(bin) # returns 1110 bin = c(1,0,1,0) bin2gray(bin) # returns 1111
The function bin2int converts a binary coded number to integer.
bin2int(bin)bin2int(bin)
bin |
A binary coded number. |
The bin2int function works as a compliment of the int2bin function.
Returns the integer equivalent of the input number.
Zeynel Cebeci & Erkut Tekeli
x <- c(1,1,1,1,1,0,1,0,0) bin2int(x) # returns 500x <- c(1,1,1,1,1,0,1,0,0) bin2int(x) # returns 500
The Bit Flip Mutation operator converts the bit at a randomly selected point to its allele.
This operator is used on binary encoded chromosomes.
bitmut(y, ...)bitmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(1,1,0,1,0,1,0,1,0,0) bitmut(offspring)offspring = c(1,1,0,1,0,1,0,1,0,0) bitmut(offspring)
Eshelman and Schaffer (1993) proposed an algorithm called Blended- Crossover (BLX-) by introducing the concept of interval scheme to be applied in real-valued problems (Takahashi & Kita, 2001).
blxa(x1, x2, cxon, ...)blxa(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Eshelman, L.J. and Schaffer, J.D. (1993). Real-coded genetic algorithms and interval schemata. In Foundations of Genetic Algorithms, Vol. 2, pp. 187-202, Elsevier.
Takahashi, M. and Kita, H. (2001). A crossover operator using independent component analysis for real-coded genetic algorithms. In Proc. of the 2001 Cong. on Evolutionary Computation (IEEE Cat.No. 01TH8546), Vol. 1, pp. 643-649. IEEE.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
ebeveyn1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) ebeveyn2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) blxa(ebeveyn1, ebeveyn2, cxon=3)ebeveyn1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) ebeveyn2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) blxa(ebeveyn1, ebeveyn2, cxon=3)
Blended crossover- is another version of the Blended crossover- operator.
blxab(x1, x2, cxon, ...)blxab(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) blxab(parent1, parent2)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) blxab(parent1, parent2)
The Boundary Mutation operator is a mutation operator that changes the value of a randomly selected gene in the chromosome with the upper or lower limit value for that gene.
This operator is used for value encoded (integer or real number) chromosomes.
boundmut(y, lb, ub, ...)boundmut(y, lb, ub, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) boundmut(offspring, lb=lb, ub=ub)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) boundmut(offspring, lb=lb, ub=ub)
Boundary Search Mutation-1 is an algorithm based on probing the boundaries of the convenience region in constraint processing for NLP optimization (Michalewicz & Schoenauer, 1996). Two genes are randomly selected from the chromosome and one of them is multiplied by a random factor at the q value, while the other gene is multiplied by .
This operator is used for value encoded (integer or real number) chromosomes.
bsearchmut1(y, mutq, ...)bsearchmut1(y, mutq, ...)
y |
A vector. Chromosome of the offspring |
mutq |
A number. Value of q |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
A vector. The numbers of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1-32.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(8, 6, 4, 1, 3) #set.seed(12) bsearchmut1(offspring) mutq = 0.5 #set.seed(12) bsearchmut1(offspring, mutq=mutq)offspring = c(8, 6, 4, 1, 3) #set.seed(12) bsearchmut1(offspring) mutq = 0.5 #set.seed(12) bsearchmut1(offspring, mutq=mutq)
Boundary Search Mutation-2 is an algorithm based on searching the convenience region boundaries in constraint processing for NLP optimization (Michalewicz & Schoenauer, 1996). Two genes are randomly selected from the chromosome and one is multiplied by the random value p, while the other gene is multiplied by the q value calculated using p.
This operator is used for value encoded (integer or real number) chromosomes.
bsearchmut2(y, ...)bsearchmut2(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
A vector. The numbers of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1-32.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(8, 6, 4, 1, 3) bsearchmut2(offspring)offspring = c(8, 6, 4, 1, 3) bsearchmut2(offspring)
In the parent chromosomes, the randomly selected value between the minimum and maximum values of each gene is assigned as the value of that gene in the offspring chromosome (Herrera et.al, 1998).
bx(x1, x2, cxon, ...)bx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Herrera, F., Lozano, M. and Verdegay J.L. (1998). Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis. Artificial Intelligence Review, 12(4), 265-319.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) bx(parent1, parent2)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) bx(parent1, parent2)
The function CalcM calculates the number of bits in the binary representation of the integer vector
calcM(ub, ...)calcM(ub, ...)
ub |
A vector containing upper bounds |
... |
Further arguments passed to or from other methods. |
This function uses the upper bounds of the integer vector to calculate the number of bits in the binary representation of an integer vector.
A vector of the numbers of bits for binary representation of an integer vector.
Zeynel Cebeci & Erkut Tekeli
ub = c(10, 10, 10) calcM(ub)ub = c(10, 10, 10) calcM(ub)
Count-preserving Crossover (CPC) is an operator that assumes the same number of chromosomes equal to 1 in each chromosome in the initial population and tries to preserve this number (Hartley & Konstam, 1993; Gwiazda 2006).
cpc(x1, x2, cxon, ...)cpc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Hartley S.J. and Konstam A.H. (1993). Using genetic algorithms to generates Steiner triple systems. In Proc. of the 1993 ACM Conf. on Computer Science (pp. 366-371).
Gwiazda T.D. (2006). Genetic Algorithms Reference. Vol. I: Crossover for Single-Objective Numerical Optimization Problems. Tomaszgwiadze E-books, Poland.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) cpc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) cpc(parent1, parent2)
It is a wrapper function that calls crossover operators from a single function.
cross(crossfunc, matpool, cxon, cxpc, gatype, ...)cross(crossfunc, matpool, cxon, cxpc, gatype, ...)
crossfunc |
The name of the crossover operator |
matpool |
A matrix. Mating pool containing selected individuals. |
cxon |
Number of offspring to be generated as a result of crossover |
cxpc |
Crossover Ratio. Default value is 0.95 |
gatype |
Indicates the GA type. "gga" is assigned for generational refresh, and "ssga" for steady-state refresh. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
genpop = initbin(12,8) #Initial population m = ncol(genpop)-2 #Number of Gene sumx = function(x, ...) (sum(x)) #Fitness Function fitvals = evaluate(fitfunc=sumx, genpop[,1:m]) #Fitness Values genpop[,"fitval"] = fitvals selidx = select(selfunc=selrws, fitvals) #Selection of Parents matpool = genpop[selidx,] #Mating Pool offsprings = cross(crossfunc=px1, matpool=matpool, #Crossing cxon=2, cxpc=0.8, gatype="gga") offsprings offsprings = cross(crossfunc=kpx, matpool=matpool, cxon=2, cxpc=0.8, gatype="ssga", cxps=0.5, cxk=2) offspringsgenpop = initbin(12,8) #Initial population m = ncol(genpop)-2 #Number of Gene sumx = function(x, ...) (sum(x)) #Fitness Function fitvals = evaluate(fitfunc=sumx, genpop[,1:m]) #Fitness Values genpop[,"fitval"] = fitvals selidx = select(selfunc=selrws, fitvals) #Selection of Parents matpool = genpop[selidx,] #Mating Pool offsprings = cross(crossfunc=px1, matpool=matpool, #Crossing cxon=2, cxpc=0.8, gatype="gga") offsprings offsprings = cross(crossfunc=kpx, matpool=matpool, cxon=2, cxpc=0.8, gatype="ssga", cxps=0.5, cxk=2) offsprings
The Cycle Crossover (CX) is an algorithm that considers the gene order in the parental chromosomes (Oliver et.al., 1987).
cx(x1, x2, cxon, ...)cx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Oliver, I.M., Smith, D. and Holland J.R. (1987). Study of the permutation crossover operators on the traveler salesman problem. In Grefenstette, J.J. (ed). Genetic Algorithms and Their Applications, Proc. of the 2nd Int. Conf. Hillsdale, New Jersey: Lawrence Erlbaum, pp. 224-230.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
icx,
smc
parent1 =c(9, 8, 2, 1, 7, 4, 5, 0, 6, 3) parent2 =c(1, 2, 3, 4, 5, 6, 7, 8, 9, 0) cx(parent1, parent2)parent1 =c(9, 8, 2, 1, 7, 4, 5, 0, 6, 3) parent2 =c(1, 2, 3, 4, 5, 6, 7, 8, 9, 0) cx(parent1, parent2)
The Discrete Crossover (DC) operator is an operator that swaps parent genes if a randomly selected value in the range [0,1] for each gene in the chromosome is greater than or equal to a given threshold value, and does not change if it is less than the threshold value.
dc(x1, x2, cxon, cxps, ...)dc(x1, x2, cxon, cxps, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxps |
Threshold value. 0 <= cxps <= 1 |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) dc(parent1, parent2, cxps=0.6)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) dc(parent1, parent2, cxps=0.6)
The function decode converts a binary number with m digits to a real number between the lower and upper bound.
decode(bin, lb, ub, m)decode(bin, lb, ub, m)
bin |
A binary number |
lb |
Lower bound of real number |
ub |
Upper bound of real number |
m |
Number of the digits of output value. |
This function converts a binary number with m digits to its real equivalent expressed in the range [lb, ub].
Returns the real equivalent of the input number.
Zeynel Cebeci & Erkut Tekeli
x = c(0,1,0,0,0,0,1,1) decode(x, lb=50, ub=250, m=8)x = c(0,1,0,0,0,0,1,1) decode(x, lb=50, ub=250, m=8)
The function decode4int converts each element in a given binary vector to a integer number.
decode4int(x, M, ...)decode4int(x, M, ...)
x |
A vector containing binary numbers |
M |
A vector containing the number of bits of each binary in the x. |
... |
Further arguments passed to or from other methods. |
This function converts each element in the binary vector passed with the x argument to an integer. The M argument refers to the number of bits of each binary in the x vector.
A vector of integer for input binary vector
Zeynel Cebeci & Erkut Tekeli
binmat = c(0,0,1,1,1,0,0,1,0,0,1,0) M = c(4,4,4) intmat = decode4int(binmat, M=M) intmatbinmat = c(0,0,1,1,1,0,0,1,0,0,1,0) M = c(4,4,4) intmat = decode4int(binmat, M=M) intmat
The decodepop function generates a real-valued population from a population encoded with binary representation.
decodepop(x, lb, ub, m, ...)decodepop(x, lb, ub, m, ...)
x |
A vector containing binary numbers |
lb |
A vector containing lower bounds for variables |
ub |
A vector containing upper bounds for variables |
m |
Length for each variable |
... |
Further arguments passed to or from other methods. |
A real-valued matrix
Zeynel Cebeci & Erkut Tekeli
lb = c(2.5, -2, 0) ub = c(4.3, 2, 1.5) eps = c(0.1, 1, 0.01) #d = nchar(sub('^+','',sub("\.",'',eps)))-1 d = grep('.', strsplit(as.character(eps), '')[[1]])-1 x = round(runif(5, lb[1],ub[1]),d[1]) y = round(runif(5, lb[2],ub[2]),d[2]) w = round(runif(5, lb[3],ub[3]),d[3]) pop = cbind(x, y, w) pop encpop = encodepop(pop, lb=lb, ub=ub, eps=eps) pop = encpop$binmat m = encpop$m decpop = decodepop(pop, lb=lb, ub=ub, m=m) decpop for(j in 1:ncol(decpop)) decpop[,j]=round(decpop[,j], d[j]) decpoplb = c(2.5, -2, 0) ub = c(4.3, 2, 1.5) eps = c(0.1, 1, 0.01) #d = nchar(sub('^+','',sub("\.",'',eps)))-1 d = grep('.', strsplit(as.character(eps), '')[[1]])-1 x = round(runif(5, lb[1],ub[1]),d[1]) y = round(runif(5, lb[2],ub[2]),d[2]) w = round(runif(5, lb[3],ub[3]),d[3]) pop = cbind(x, y, w) pop encpop = encodepop(pop, lb=lb, ub=ub, eps=eps) pop = encpop$binmat m = encpop$m decpop = decodepop(pop, lb=lb, ub=ub, m=m) decpop for(j in 1:ncol(decpop)) decpop[,j]=round(decpop[,j], d[j]) decpop
Disrespectful Crossover (DISC) is an operator that breaks down similarities or reinforces differences in parental chromosomes (Watson & Pollack, 2000).
disc(x1, x2, cxon, ...)disc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Watson R.A. and Pollack J.B. (2000). Recombination without respect: Schema combination and disruption in genetic algorithm crossover. In Proc. of the 2nd Annual Conf. on Genetic and Evolutionary Computation (pp. 112-119).
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) disc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) disc(parent1, parent2)
The Displacement mutation cuts the genes between two randomly determined cut-points from the chromosome as a subset and then inserts them, starting from a randomly selected location (Michalewicz, 1992).
This operator is used in problems with permutation encoding.
dismut(y, ...)dismut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutrange |
A vector. The numbers of begining and ending of the mutated genes. |
r |
The number of insertation location. |
Zeynel Cebeci & Erkut Tekeli
Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs. Berlin-Heidelberg: Springer Verlag.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
invswapmut,
insswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) dismut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) dismut(offspring)
Extended Box Crossover (EBX) was proposed by Yoon and Kim (2012) as the more advanced form of Box Crossover (BX). In the EBX operator, the minimum and maximum values are weighted by an alpha factor.
ebx(x1, x2, lb, ub, cxon, cxalfa, ...)ebx(x1, x2, lb, ub, cxon, cxalfa, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
lb |
A vector. Lower bounds of each gene in the chromosomes. |
ub |
A vector. Upper bounds of each gene in the chromosomes. |
cxon |
Number of offspring to be generated as a result of crossover |
cxalfa |
A vector. Alpha value for each gene in the chromosomes. If no value is entered, they are randomly selected by the function in the range [0,1]. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Yoon, Y. and Kim, Y.H. (2012). The roles of crossover and mutation in real-coded genetic algorithms. In Bioinspired Computational Algorithms anf Their Applications (ed. S. Gao), London: INTECH Open Acces Publisher. pp. 65-82.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
lb = c(0, 0, 0, 0, 0, 0) ub = c(2, 3, 1, 2, 4, 3) parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) ebx(parent1, parent2, lb, ub)lb = c(0, 0, 0, 0, 0, 0) ub = c(2, 3, 1, 2, 4, 3) parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) ebx(parent1, parent2, lb, ub)
Linkage Crossover (LC) is an operator based on the repositioning of a randomly selected fragment from one of the parents, starting from a randomly selected location in the offspring chromosome (Harik & Goldberg, 1997). It is also called Exchange Crossover (EC).
eclc(x1, x2, cxon, ...)eclc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Harik, G.D. and Goldberg, D.E. (1997). Learning linkage. Foundation of Genetic Algorithms Ch. 4, Morgan-Kaufmann. pp. 247-262.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) eclc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) eclc(parent1, parent2)
The reproduction of individuals with the highest fitness is called elitism. The elitism operator copies a certain number of individuals into the new population. Other individuals are selected from among the offspring in proportion to their fitness values.
elitism(parpop, offpop, reps, ...)elitism(parpop, offpop, reps, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
reps |
Number of elite individuals |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
With the Extended-Line Crossover (ELX) operator, offspring are generated on a line determined by the variable values in the parental chromosomes. ELX identifies the possible line from which offspring can be generated.
elx(x1, x2, lb, ub, cxon, cxealfa, ...)elx(x1, x2, lb, ub, cxon, cxealfa, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
lb |
A vector. Lower bounds of each gene in the chromosomes. |
ub |
A vector. Upper bounds of each gene in the chromosomes. |
cxon |
Number of offspring to be generated as a result of crossover |
cxealfa |
A number. Expansion rate |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
lb = c(0, 0, 0, 0, 0, 0) ub = c(2, 3, 1, 2, 4, 3) parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) elx(parent1, parent2, lb, ub, cxealfa=1000)lb = c(0, 0, 0, 0, 0, 0) ub = c(2, 3, 1, 2, 4, 3) parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) elx(parent1, parent2, lb, ub, cxealfa=1000)
The function encode converts a real number to a binary number with m digits between the given lower bound and upper bound.
encode(real, lb, ub, m)encode(real, lb, ub, m)
real |
A real number |
lb |
Lower bound of real number |
ub |
Upper bound of real number |
m |
Number of the digits of output value. |
This function converts a real number to its binary equivalent expressed in m digits in the range [lb, ub].
Returns the binary equivalent of the input number.
Zeynel Cebeci & Erkut Tekeli
x = 102.5 encode(x, lb=50, ub=250, m=8)x = 102.5 encode(x, lb=50, ub=250, m=8)
The function encode4int converts each element in a given integer vector to a binary number.
encode4int(x, M, ...)encode4int(x, M, ...)
x |
A vector containing integer numbers |
M |
A vector containing the number of bits in the binary representation of each integer variable. |
... |
Further arguments passed to or from other methods. |
This function converts each element in the integer vector passed with the x argument to a binary number. The M argument refers to the number of bits in the binary representation of each integer variable.
A vector of binary representation of input vector
Zeynel Cebeci & Erkut Tekeli
n = 5 lb = c(0, 0, 0) ub = c(10, 10, 10) set.seed(1) intmat = matrix(round(runif(3*n, lb, ub)), nr=n, nc=3) colnames(intmat) = paste0("v",1:3) head(intmat) M = calcM(ub) M binmat = matrix(NA, nrow=n, ncol=sum(M)) for(i in 1:n) binmat[i,] = encode4int(intmat[i,], M=M) head(binmat)n = 5 lb = c(0, 0, 0) ub = c(10, 10, 10) set.seed(1) intmat = matrix(round(runif(3*n, lb, ub)), nr=n, nc=3) colnames(intmat) = paste0("v",1:3) head(intmat) M = calcM(ub) M binmat = matrix(NA, nrow=n, ncol=sum(M)) for(i in 1:n) binmat[i,] = encode4int(intmat[i,], M=M) head(binmat)
The encodepop function generates a population encoded with binary representation from a real-valued population given as a matrix.
encodepop(x, lb, ub, eps, ...)encodepop(x, lb, ub, eps, ...)
x |
A vector containing real numbers |
lb |
A vector containing lower bounds for variables |
ub |
A vector containing upper bounds for variables |
eps |
Sensitivity vector containing desired sensitivity values for each variable |
... |
Further arguments passed to or from other methods. |
binmat |
A binary coded matrix as counterpart of real-valued input matrix |
m |
A vector containing bit length of each variable |
Zeynel Cebeci & Erkut Tekeli
lb = c(2.5, -2, 0) ub = c(4.3, 2, 1.5) eps = c(0.1, 1, 0.01) #d = nchar(sub('^+','',sub("\.",'',eps)))-1 d = grep('.', strsplit(as.character(eps), '')[[1]])-1 x = round(runif(5, lb[1],ub[1]),d[1]) y = round(runif(5, lb[2],ub[2]),d[2]) w = round(runif(5, lb[3],ub[3]),d[3]) pop = cbind(x, y, w) pop encpop = encodepop(pop, lb, ub, eps) head(encpop$binmat[,1:10]) m = encpop$m mlb = c(2.5, -2, 0) ub = c(4.3, 2, 1.5) eps = c(0.1, 1, 0.01) #d = nchar(sub('^+','',sub("\.",'',eps)))-1 d = grep('.', strsplit(as.character(eps), '')[[1]])-1 x = round(runif(5, lb[1],ub[1]),d[1]) y = round(runif(5, lb[2],ub[2]),d[2]) w = round(runif(5, lb[3],ub[3]),d[3]) pop = cbind(x, y, w) pop encpop = encodepop(pop, lb, ub, eps) head(encpop$binmat[,1:10]) m = encpop$m m
The Edge Recombination Crossover (ERX) operator ignores outbound directions, that is, it evaluates a chromosome with an undirected edge loop (Whitley et.al., 1989). This operator is based on the concept of neighborhood, as the main idea is to prioritize the edges common to both parents when creating offspring.
erx(x1, x2, cxon, ...)erx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Whitley, L.D., Starkweather, T. and D'Ann, F. (1989). Scheduling problems and traveling salesman: the genetic edge recombination operator. In Proc. of ICGA, Vol. 89, pp. 133-40.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 3, 5, 6, 4, 2, 8, 7) parent2 = c(1, 4, 2, 3, 6, 5, 7, 8) erx(parent1, parent2, cxon=2)parent1 = c(1, 3, 5, 6, 4, 2, 8, 7) parent2 = c(1, 4, 2, 3, 6, 5, 7, 8) erx(parent1, parent2, cxon=2)
Calculates the fitness value of a population using the fitness function given with the fitfunc argument.
evaluate(fitfunc, population, objective, ...)evaluate(fitfunc, population, objective, ...)
fitfunc |
Fitness function |
population |
Population matrix |
objective |
“max” or “min” |
... |
Further arguments passed to or from other methods. |
A vector of fitness values for each induvidual in population.
Zeynel Cebeci & Erkut Tekeli
population = initbin() head(population, 5) m = ncol(population)-2 fitvals = evaluate(maxone, population[,1:m], objective="max") head(fitvals, 5)population = initbin() head(population, 5) m = ncol(population)-2 fitvals = evaluate(maxone, population[,1:m], objective="max") head(fitvals, 5)
This function finds the peaks and valleys on the curve of user-defined functions with one variable. The function also plots the function curve that can be used to demonstrate the points for local optima and global optimum in a optimization problem.
findoptima(x, type="max", pflag=TRUE)findoptima(x, type="max", pflag=TRUE)
x |
a vector of variable |
type |
Either “max” (the default) or “min”. The peaks are
found when |
pflag |
if this is TRUE, the first and last values are also checked. |
The findoptima function finds all the peaks and valleys in a given function curve. The points can be colorized with different colors. See the example below.
Returns a vector of indices of the peaks or valleys on the function curve.
Zeynel Cebeci & Erkut Tekeli
Cebeci Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari. Ankara:Nobel Akademik Yayincilik
fx <- function(x) -sin(x)-sin(2*x)-cos(3*x) + 3 x <- seq(-2*pi, 2*pi, by=0.001) curve(fx, x) cr <- curve(fx, x, lwd=2) xy <- cbind(cr$x, cr$y) peaks <- findoptima(cr$y, type = "max") valleys <- findoptima(cr$y, type = "min") ## Finds peaks and valleys peaks <- findoptima(cr$y, type="max") valleys <- findoptima(cr$y, type="min") ## Plotting the function curve and local optima and global optimum points(xy[peaks,], pch=19, cex=1.2, col=2) points(xy[valleys,], pch=18, cex=1.2, col=4) gmin <- valleys[which.min(xy[valleys,2])] gmax <- peaks[which.min(xy[valleys,2])] points(xy[gmax,1], xy[gmax,2], pch=19, cex=2, col=2) points(xy[gmin,1], xy[gmin,2], pch=18, cex=2, col=4) text(xy[gmax,1], xy[gmax,2], labels="Glob.Max", pos=2, cex=0.8, col=1) text(xy[gmin,1], xy[gmin,2], labels="Glob.Min", pos=2, cex=0.8, col=1)fx <- function(x) -sin(x)-sin(2*x)-cos(3*x) + 3 x <- seq(-2*pi, 2*pi, by=0.001) curve(fx, x) cr <- curve(fx, x, lwd=2) xy <- cbind(cr$x, cr$y) peaks <- findoptima(cr$y, type = "max") valleys <- findoptima(cr$y, type = "min") ## Finds peaks and valleys peaks <- findoptima(cr$y, type="max") valleys <- findoptima(cr$y, type="min") ## Plotting the function curve and local optima and global optimum points(xy[peaks,], pch=19, cex=1.2, col=2) points(xy[valleys,], pch=18, cex=1.2, col=4) gmin <- valleys[which.min(xy[valleys,2])] gmax <- peaks[which.min(xy[valleys,2])] points(xy[gmax,1], xy[gmax,2], pch=19, cex=2, col=2) points(xy[gmin,1], xy[gmin,2], pch=18, cex=2, col=4) text(xy[gmax,1], xy[gmax,2], labels="Glob.Max", pos=2, cex=0.8, col=1) text(xy[gmin,1], xy[gmin,2], labels="Glob.Min", pos=2, cex=0.8, col=1)
The function is used when the crossover and mutation rates are not changed throughout the GA run.
fixpcmut(cxpc, mutpm, ...)fixpcmut(cxpc, mutpm, ...)
cxpc |
Crossover rate |
mutpm |
Mutation rate |
... |
Further arguments passed to or from other methods. |
pc |
Crossover rate |
pm |
Mutation rate |
Zeynel Cebeci & Erkut Tekeli
ilmdhc,
adana1,
adana2,
leitingzhi,
adana3
Gauss Mutation is an operator made by adding randomly selected values from a normal distribution with a mean of 0 and a standard deviation of sigma to a randomly selected gene in the chromosome (Michalewicz, 1995; Back et.al., 1991; Fogel, 1995).
This operator is used for value encoded (integer or real number) chromosomes.
gaussmut(y, mutsdy, ...)gaussmut(y, mutsdy, ...)
y |
A vector. Chromosome of the offspring |
mutsdy |
A vector. Vector of standard deviations of genes |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
Michalewicz, Z. (1995). Genetic algorithms, numerical optimizations and constraints. In Proc. of the 6th. Int. Conf. on Genetic Algorithms, pp. 151-158. Morgan Kaufmann.
Back, T., Hoffmeister, F. and Schwefel, H.F. (1991). A survey of elolution strategies. In Proc. of the 4th. Int. Conf. on Genetic Algorithms (eds. R.K. Belew and L.B. Booker), pp. 2-9. Morgan Kaufmann.
Fogel D.B. (1995). Evolutionary computation. Toward a new philosophy of machine intellegence. Piscataway, NJ: IEEE Press.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
mutsdy = c(1, 1.5, 1.01, 0.4, 1.5, 1.2) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) gaussmut(offspring)mutsdy = c(1, 1.5, 1.01, 0.4, 1.5, 1.2) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) gaussmut(offspring)
Gauss Mutation-2 is an operator by adding a randomly selected value from the standard normal distribution to a randomly selected gene in the chromosome.
This operator is used for value encoded (integer or real number) chromosomes.
gaussmut2(y, ...)gaussmut2(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) gaussmut2(offspring)offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) gaussmut2(offspring)
GM is an operator made by adding randomly selected values from a normal distribution with mean and standard deviation of MU and SIGMA, respectively, to a randomly selected gene in the chromosome.
This operator is used for value encoded (integer or real number) chromosomes.
gaussmut3(y, mutmy, mutsdy, ...)gaussmut3(y, mutmy, mutsdy, ...)
y |
A vector. Chromosome of the offspring |
mutmy |
A vector. Vector of means of genes |
mutsdy |
A vector. Vector of standard deviations of genes |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
mutmy = c(5, 5, 2, 4, 3, 4) mutsdy = c(1, 1.5, 1.01, 0.4, 1.5, 1.2) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) gaussmut(offspring, mutmy=mutmy, mutsdy=mutsdy)mutmy = c(5, 5, 2, 4, 3, 4) mutsdy = c(1, 1.5, 1.01, 0.4, 1.5, 1.2) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) gaussmut(offspring, mutmy=mutmy, mutsdy=mutsdy)
Geometric Crossover is used to search for applicable region boundaries in constraint processing in NLP problems (Michalewicz & Schoenauer, 1996). It generates one offspring per each cross.
geomx(x1, x2, cxon, ...)geomx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary Algorithms for constrained parameter optimization problems. Evoltionary Computation, 4(1), 1-32.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) geomx(parent1, parent2)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) geomx(parent1, parent2)
The function gray2bin converts gray coded integer to a binary coded number.
gray2bin(gray)gray2bin(gray)
gray |
A gray coded number. |
The gray2bin function works as a compliment of the bin2gray function.
Returns the binary coded integer equivalent of the input number.
Zeynel Cebeci & Erkut Tekeli
gray = c(1,1,1,0) gray2bin(gray) # returns 1011 gray = c(1,1,1,1) gray2bin(gray) # returns 1010gray = c(1,1,1,0) gray2bin(gray) # returns 1011 gray = c(1,1,1,1) gray2bin(gray) # returns 1010
The function gray2bin2 converts a gray-coded integer to a binary-coded number. The conversion function is performed according to the algorithm given by Chakraborty and Janikov (2003).
gray2bin2(gray)gray2bin2(gray)
gray |
A gray coded number. |
To convert gray coded numbers to binary numbers, a conversion function is defined using the algorithm given by Chakraborty and Janikov (2003). This function is a generic function that does not use the xor operator.
Returns the binary coded integer equivalent of the input number.
Zeynel Cebeci & Erkut Tekeli
Chakraborty, U.K., and Janikow C.Z. (2003). An analysis of Gray versus binary encoding in genetic search. Information Sciences, 156 (3-4), 253-269.
gray = c(1,1,1,0) gray2bin2(gray) # returns 1011 gray = c(1,1,1,1) gray2bin2(gray) # returns 1010gray = c(1,1,1,0) gray2bin2(gray) # returns 1011 gray = c(1,1,1,1) gray2bin2(gray) # returns 1010
All members of the current population are deleted, the new population is created entirely from offspring.
grdelall(parpop, offpop)grdelall(parpop, offpop)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
The Mu+Lamda replacement is based on the selection of the fittest parents and offspring as individuals of the new generation population (Smith et.al., 1999; Jenkins et.al., 2019).
grmuplambda(parpop, offpop, ...)grmuplambda(parpop, offpop, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
Smith, A.E. and Vavak F. (1999). Replacement strategies in steady state genetic algorithms: Static environments. Foundations of Genetic Algorithms. pp. 499-505.
Jenkins, A., Gupta, V., Myrick, A. and Lenoir, M. (2019). Variations of Genetic Algorithms. arXiv preprint arXiv:1911.00490.
grdelall,
elitism,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
Parents and offspring are ranked separately according to their compatibility among themselves. Then offspring with the best fitness value is replaced by parent with the worst fitness value.
grmuplambda2(parpop, offpop, lambda, ...)grmuplambda2(parpop, offpop, lambda, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
lambda |
Number of individuals renewed in the population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
After the offspring are ranked according to their fitness values, the best fit offspring are replaced by parents randomly selected from the current parent population.
grmuplambda3(parpop, offpop, lambda, ...)grmuplambda3(parpop, offpop, lambda, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
lambda |
Number of individuals renewed in the population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
In the current population, randomly selected parents are replaced by randomly selected offspring.
grmuplambda4(parpop, offpop, lambda, ...)grmuplambda4(parpop, offpop, lambda, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
lambda |
Number of individuals renewed in the population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuvlambda,
grrobin,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
In this renewal strategy, after the offspring are ranked according to their fitness values, the number of the population of the offspring with the best fitness value is replaced by the parents (Schwefel, 1981). To use this renewal algorithm, it is necessary to produce many more offspring than the population count.
grmuvlambda(parpop, offpop, ...)grmuvlambda(parpop, offpop, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grrobin,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
The parent and offspring populations are combined. Then, each individual in the combined population is compared with k randomly selected individuals. In these double tournaments, if an individual has higher fitness than the individual they are compared to, +1 point is obtained. The new population is created from the individuals with the highest score.
grrobin(parpop, offpop, repk, ...)grrobin(parpop, offpop, repk, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
repk |
Number of Comparisons |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
ssrmup1,
ssrgenitor,
ssrfamtour,
ssrx
The Heuristic Crossover (HC) operator is a conditional operator (Herrera et.al, 1998; Umbarkar & Sheth, 2005). A random r value is generated in the range [0,1]. Then if Parent2's fitness value is greater than or equal to Parent1's fitness value, the difference between them is weighted by r and added to Parent2. It is subtracted in minimization problems. This operator produces a single offspring, but due to the random value of r, repeated offspring may result in different offspring.
hc(x1, x2, fitfunc, cxon, ...)hc(x1, x2, fitfunc, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
fitfunc |
Fitness Function |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Herrera, F., Lozano, M. and Verdegay, J.L. (1998). Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis. Artificial Intellegence Review, 12(4), 265-319 Umbarkar, A.J. and Sheth P.D. (2015). Crossover operators in genetic algorithms: A riview, ICTACT Journal on Soft Computing, 6(1), 1083-1092.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) hc(parent1, parent2, fitfunc)fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) hc(parent1, parent2, fitfunc)
This function allows GA to hybridize with methods in the optim general-purpose optimization function for n-variable problems in R's basic stats package (R Core Team, 2021).
hgaoptim(genpop, fitfunc, hgaparams, hgaftype, hgans, ...)hgaoptim(genpop, fitfunc, hgaparams, hgaftype, hgans, ...)
genpop |
A matrix of individuals in the current population and their fitness values. |
fitfunc |
Fitness function |
hgaparams |
A list of parameters defined for use by the Optim function. |
hgaftype |
Types of fitness to transfer.
|
hgans |
Number of individuals to be transferred to the Optim. |
... |
Further arguments passed to or from other methods. |
A matrix containing the updated population.
Zeynel Cebeci & Erkut Tekeli
R Core Team. (2021). R: A language and environmental for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
hgaparams = list(method="Nelder-Mead", poptim=0.05, pressel=0.5, control = list(fnscale=1, maxit=100)) n = 5 # Size of population m = 2 # Number of variables lb = c(-5.12, -5.12) # Lower bounds for sample data ub = c(5.12, 5.12) # Upper bounds for sample data genpop = initval(n, m, lb=lb, ub=ub) # Sample population fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 fitvals = evaluate(fitfunc, genpop[,1:m]) genpop[,"fitval"]=fitvals genpop newpop = hgaoptim(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3) newpophgaparams = list(method="Nelder-Mead", poptim=0.05, pressel=0.5, control = list(fnscale=1, maxit=100)) n = 5 # Size of population m = 2 # Number of variables lb = c(-5.12, -5.12) # Lower bounds for sample data ub = c(5.12, 5.12) # Upper bounds for sample data genpop = initval(n, m, lb=lb, ub=ub) # Sample population fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 fitvals = evaluate(fitfunc, genpop[,1:m]) genpop[,"fitval"]=fitvals genpop newpop = hgaoptim(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3) newpop
This function allows GA to hybridize with methods in the optimx package (Nash & Varadhan, 2011; Nash, 2014).
hgaoptimx(genpop, fitfunc, hgaparams, hgaftype, hgans, ...)hgaoptimx(genpop, fitfunc, hgaparams, hgaftype, hgans, ...)
genpop |
A matrix of individuals in the current population and their fitness values. |
fitfunc |
Fitness function |
hgaparams |
A list of parameters defined for use by the Optim function. |
hgaftype |
Types of fitness to transfer.
|
hgans |
Number of individuals to be transferred to the Optim. |
... |
Further arguments passed to or from other methods. |
A matrix containing the updated population.
Zeynel Cebeci & Erkut Tekeli
Nash, J.C. and Varadhan, R. (2011). Unified optimization algorithms to aid software system users: optimx for R. Journal of Statistical Software, 43(9), 1-14. URL http://www.jstatsoft.org/v43/i09. Nash, J.C. (2014). On best practice optimization methods in R. Journal of Statistical Software, 60(2), 1-14. URL http://www.jstatsoft.org/v60/i02.
n = 5 # Size of population m = 2 # Number of Variables lb = c(-5.12, -5.12) # Lower bounds of sample data ub = c(5.12, 5.12) # Upper bounds of sample data hgaparams = list(method="L-BFGS-B", poptim=0.05, pressel=0.5, lower=lb, upper=ub, control=list(maximize=FALSE, maxit=100)) genpop = initval(n, m, lb=lb, ub=ub) # Sample population fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 fitvals = evaluate(fitfunc, genpop[,1:m]) genpop[,"fitval"]=fitvals genpop genpop = hgaoptimx(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3) genpopn = 5 # Size of population m = 2 # Number of Variables lb = c(-5.12, -5.12) # Lower bounds of sample data ub = c(5.12, 5.12) # Upper bounds of sample data hgaparams = list(method="L-BFGS-B", poptim=0.05, pressel=0.5, lower=lb, upper=ub, control=list(maximize=FALSE, maxit=100)) genpop = initval(n, m, lb=lb, ub=ub) # Sample population fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 fitvals = evaluate(fitfunc, genpop[,1:m]) genpop[,"fitval"]=fitvals genpop genpop = hgaoptimx(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3) genpop
This function allows GA to hybridize with methods in the ROI package (Theussl et.al., 2020).
hgaroi(genpop, fitfunc, hgaparams, hgaftype, hgans, ...)hgaroi(genpop, fitfunc, hgaparams, hgaftype, hgans, ...)
genpop |
A matrix of individuals in the current population and their fitness values. |
fitfunc |
Fitness function |
hgaparams |
A list of parameters defined for use by the Optim function. |
hgaftype |
Types of fitness to transfer.
|
hgans |
Number of individuals to be transferred to the Optim. |
... |
Further arguments passed to or from other methods. |
A matrix containing the updated population.
Zeynel Cebeci & Erkut Tekeli
Theussl, S., Schwendinger, F. and Hornik, K. (2020). ROI: An extensible R optimization infrastructure. Journal of Statistical Software, 94(15), 1-64.
n = 5 # Size of population m = 2 # Number of variable lb = c(-5.12, -5.12) # Lower bounds of sample data ub = c(5.12, 5.12) # Upper bounds of sample data hgaparams = list(method="L-BFGS-B", poptim=0.05, pressel=0.5, lower=lb, upper=ub, control=list(maxit=100)) genpop = initval(n, m, lb=lb, ub=ub) # Sample population fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 fitvals = evaluate(fitfunc, genpop[,1:m]) genpop[,"fitval"]=fitvals genpop genpop = hgaroi(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3) genpopn = 5 # Size of population m = 2 # Number of variable lb = c(-5.12, -5.12) # Lower bounds of sample data ub = c(5.12, 5.12) # Upper bounds of sample data hgaparams = list(method="L-BFGS-B", poptim=0.05, pressel=0.5, lower=lb, upper=ub, control=list(maxit=100)) genpop = initval(n, m, lb=lb, ub=ub) # Sample population fitfunc = function(x, ...) 2*(x[1]-1)^2 + 5*(x[2]-2)^2 + 10 fitvals = evaluate(fitfunc, genpop[,1:m]) genpop[,"fitval"]=fitvals genpop genpop = hgaroi(genpop, fitfunc, hgaparams, hgaftype="r", hgans=3) genpop
"Heuristic Uniform Crossover" is an algorithm that works by detecting genes that differ to control the level of disruption in Parental chromosomes (De Jong & Spears, 1991).
hux(x1, x2, cxon, cxps, ...)hux(x1, x2, cxon, cxps, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxps |
It determines the rate of gene exchange between the chromosomes of the parents. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
De Jong, K.A. and Spears, W. (1991). On the virtues of parameterized uniform crossover. In Proc. of the 4th Int. Conf. on Genetic Algorithms. Morgan Kaufman Publishers.
cross,
px1,
kpx,
sc,
rsc,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) hux(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) hux(parent1, parent2)
ICX is based on a deterministic algorithm that can produce up to 2 offspring (Hussain et.al., 2018).
icx(x1, x2, cxon, ...)icx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Hussain, A., Muhammad, Y.S. and Sajid, M.N. (2018). An improved genetic algorithm crossover operator for traveling salesman problem. Turkish Journal of Mathematics and Computer Science, 9, 1-13.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
smc
parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) icx(parent1, parent2)parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) icx(parent1, parent2)
ILM/DHC is an adaptive function with an increasing low mutation rate (ILM) and a decreasing high crossover rate (DHC) as the generation progresses (Hassanat et.al., 2019).
ilmdhc(g, gmax, ...)ilmdhc(g, gmax, ...)
g |
Current generation |
gmax |
Maximum generation |
... |
Further arguments passed to or from other methods. |
pc |
Crossover rate |
pm |
Mutation rate |
Zeynel Cebeci & Erkut Tekeli
Hassanat, A., Almohammadi, K., Alkafaween, E., Abunawas, E., Hammouri, A. and Prasath, V.B. (2019). Choosing mutation and crossover ratios for genetic algorithm: A review with a new dynamic approach. Information, 10(12), 390.
fixpcmut,
adana1,
adana2,
leitingzhi,
adana3
N = 50 gmax = 1000 g = c(1, 10, 50, 100, 250, 500, 750, gmax) pc = ilmdhc(g=g, gmax=gmax)$pc pc nc = round(pc*N) nc pm = ilmdhc(g=g, gmax=gmax)$pm pm nm = round(pm*N) nm nm = ifelse (!nm, 1, nm) nm plot(pm, type="l", col=4, lwd=2, lty=1, xaxt="n", ylab="Ratio", xlab="Generation") lines(pc, type="l", col=2, lwd=2, lty=2) legend("top", inset=.02, c("pm","pc"), col=c(4,2), lty=c(1,2), horiz=TRUE, cex=0.8) axis(1, at=1:length(g),labels=g, col.axis="red", las=2)N = 50 gmax = 1000 g = c(1, 10, 50, 100, 250, 500, 750, gmax) pc = ilmdhc(g=g, gmax=gmax)$pc pc nc = round(pc*N) nc pm = ilmdhc(g=g, gmax=gmax)$pm pm nm = round(pm*N) nm nm = ifelse (!nm, 1, nm) nm plot(pm, type="l", col=4, lwd=2, lty=1, xaxt="n", ylab="Ratio", xlab="Generation") lines(pc, type="l", col=2, lwd=2, lty=2) legend("top", inset=.02, c("pm","pc"), col=c(4,2), lty=c(1,2), horiz=TRUE, cex=0.8) axis(1, at=1:length(g),labels=g, col.axis="red", las=2)
The initbin function is an initialization function that can be used for binary encoding. It generates an initial population of population size n and chromosome length m.
initbin(n, m, prevpop, type, ...)initbin(n, m, prevpop, type, ...)
n |
Population size |
m |
Chromosome length |
prevpop |
Matrix of solutions used in heuristic and hybrid initialization |
type |
Type of output matrix |
... |
Further arguments passed to or from other methods. |
The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes
chromosomes of initial population and additional two empty columns for generation number and fitness values.
Zeynel Cebeci & Erkut Tekeli
initval,
initperm,
initnorm,
initialize
n = 20 #Population size (number of chromosemes) m = 5 #Number of gene (chromosome length) population = initbin(n, m) head(population, 4) tail(population, 4)n = 20 #Population size (number of chromosemes) m = 5 #Number of gene (chromosome length) population = initbin(n, m) head(population, 4) tail(population, 4)
The initialize function is a function that wraps various initialization functions.
initialize(initfunc, n, m, type, ...)initialize(initfunc, n, m, type, ...)
initfunc |
Initialization function |
n |
Population size |
m |
Chromosome length (number of variables) |
type |
Type of output matrix |
... |
Further arguments passed to or from other methods. |
The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes
chromosomes of initial population and additional two empty columns for generation number and fitness values.
Zeynel Cebeci & Erkut Tekeli
initbin,
initval,
initperm,
initnorm
initpop = initialize(initfunc=initbin, n=6, m=4) initpopinitpop = initialize(initfunc=initbin, n=6, m=4) initpop
The pmean and psd arguments of this function represent the mean and standard deviation of a normally distributed population, respectively. Using these parameters, the function generates a random initial population with n individuals and m variables.~
initnorm(n, m, pmean, psd, type, ...)initnorm(n, m, pmean, psd, type, ...)
n |
Population size |
m |
Chromosome length (number of variables) |
pmean |
Mean of normal distribution |
psd |
Standard deviation of normal distribution |
type |
Type of output matrix |
... |
Further arguments passed to or from other methods. |
The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes
chromosomes of initial population and additional two empty columns for generation number and fitness values.
Zeynel Cebeci & Erkut Tekeli
initbin,
initval,
initperm,
initialize
initpop = initialize(initfunc=initnorm, n=20, m=5, pmean=50, psd=5, type=2) head(initpop,3)initpop = initialize(initfunc=initnorm, n=20, m=5, pmean=50, psd=5, type=2) head(initpop,3)
This function generates an initial population when each variable of the chromosomes is desired to be encoded on a rank scale or permutation.
initperm(n, permset, prevpop, type, ...)initperm(n, permset, prevpop, type, ...)
n |
Population size |
permset |
A vector of permutation set |
prevpop |
Matrix of solutions used in heuristic and hybrid initialization |
type |
Type of output matrix |
... |
Further arguments passed to or from other methods. |
Unlike other initialization function inputs, the initperm function has an argument called permset. This argument is a vector containing permutation set values. The permutation set can contain numbers or letters. In the initial population, each variable randomly takes any value from this set, but there cannot be two of the same value in a chromosome.
The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes
chromosomes of initial population and additional two empty columns for generation number and fitness values.
Zeynel Cebeci & Erkut Tekeli
initbin,
initval,
initnorm,
initialize
n = 20 #Population size (number of chromosemes) m = 6 #number of Variables lb = c(10, 2, 5, 100, 50, 25) ub = c(40, 8, 20, 500, 250, 90) population = initval(n, m, lb=lb, ub=ub, nmode="integer") tail(population, 3)n = 20 #Population size (number of chromosemes) m = 6 #number of Variables lb = c(10, 2, 5, 100, 50, 25) ub = c(40, 8, 20, 500, 250, 90) population = initval(n, m, lb=lb, ub=ub, nmode="integer") tail(population, 3)
Initialize the population with integer or real numbers
initval(n, m, prevpop, lb, ub, nmode="real", type, ...)initval(n, m, prevpop, lb, ub, nmode="real", type, ...)
n |
Population size |
m |
Chromosome length (number of variables) |
prevpop |
Matrix of solutions used in heuristic and hybrid initialization |
lb |
Lower bound of each variables |
ub |
Upper bound of each variables |
nmode |
Type of variables (“integer” or “real”) |
type |
Type of output matrix |
... |
Further arguments passed to or from other methods. |
With this function, populations are initialized with integer and/or real numbers depending on the GA problem. In this case, the value type must be known. Furthermore, the lower and upper bound values for each variable must be known. If desired, heuristic or mixed initialization can be done with the prevpop argument.
The output matrix includes only chromosomes of initial population when type=2, otherwise The output matrix includes
chromosomes of initial population and additional two empty columns for generation number and fitness values.
Zeynel Cebeci & Erkut Tekeli
initbin,
initperm,
initnorm,
initialize
n = 15 #Population size (number of chromosemes) m = 4 #number of Variables population = initval(n, m) head(population, 3) tail(population, 3)n = 15 #Population size (number of chromosemes) m = 4 #number of Variables population = initval(n, m) head(population, 3) tail(population, 3)
SM is inserted back in a different place into the chromosome by removing a randomly selected gene from the chromosome.
This operator is used in problems with permutation encoding.
insmut(y, ...)insmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
mutpoint |
The number of inserted location of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) insmut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) insmut(offspring)
It is a mutation operator that combines insertion and inversion mutation.
This operator is used in problems with permutation encoding.
insswapmut(y, ...)insswapmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
A vector. The numbers of begining and ending of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) insswapmut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) insswapmut(offspring)
The function int2bin converts integers to binary coded numbers.
int2bin(int, m)int2bin(int, m)
int |
Input number (integer) |
m |
Number of the digits of output value. |
Returns the binary coded number of the integer number given in the input.
Zeynel Cebeci & Erkut Tekeli
int2bin(250) # returns 11111010 int2bin(250, 9) # returns 011111010int2bin(250) # returns 11111010 int2bin(250, 9) # returns 011111010
It is a mutation operator that combines displacement and inversion mutation.
This operator is used in problems with permutation encoding.
invdismut(y, ...)invdismut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutrange |
A vector. The numbers of begining and ending of the mutated genes. |
r |
The number of insertation location. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) invdismut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) invdismut(offspring)
Inversion Mutation selects a subset of genes and inverses the genes in the subset (Hollad, 1975; Fogel, 1990).
This operator is used in problems with permutation or binary encoding.
invmut(y, ...)invmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutrange |
A vector. The numbers of begining and ending of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
Holland, J. (1975). Adaptation in Naturel and Articial Systems, Ann Arbor: University of Michigan Press.
Fogel D.B. (1995). Evolutionary computation. Toward a new philosophy of machine intellegence. Piscataway, NJ: IEEE Press.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) invmut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) invmut(offspring)
It is a mutation operator that combines swap and inversion mutation.
This operator is used in problems with permutation encoding.
invswapmut(y, ...)invswapmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
A vector. The numbers of begining and ending of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
insswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) invswapmut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) invswapmut(offspring)
In the k-PX cross, the parent chromosomes are cut from two or more points and transferred to the offspring, providing more diversity.
kpx(x1, x2, cxon, cxk, ...)kpx(x1, x2, cxon, cxk, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxk |
Number of cut points |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) kpx(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) kpx(parent1, parent2)
Laplace Crossover (LAPX) is a crossover operator that uses a location parameter and a scaling parameter (Krishnamoorthy, 2006; Deep et.al., 2009).
lapx(x1, x2, cxon, cxa, cxb, ...)lapx(x1, x2, cxon, cxa, cxb, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxa |
Location Parameter |
cxb |
Scale Parameter. ( |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC
Deep, K., Singh, K.P., Kansal, M.L. and Mohan, C. (2009). A real-coded genetic algorithm for solving integer and mixed integer optimization problems. Applied Mathematics and Computation, 212(2): 505-518.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) lapx(parent1, parent2, cxon=3)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) lapx(parent1, parent2, cxon=3)
New offspring are generated by applying an arithmetic mean on the parents' chromosomes with a different random weight for each gene.
lax(x1, x2, cxon, ...)lax(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) lax(parent1, parent2, cxon=3)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) lax(parent1, parent2, cxon=3)
This adaptation function proposed by Lei & Tingzhi (1994) is an adaptation function that takes into account the cooperation of individuals.
leitingzhi(fitvals, cxpc, cxpc2, mutpm, mutpm2, adapa, adapb, ...)leitingzhi(fitvals, cxpc, cxpc2, mutpm, mutpm2, adapa, adapb, ...)
fitvals |
A vector. Fitness values of current generation |
cxpc |
Crossover rate for adaptation. 0 <= cxpc <= 1. default is 0.9 |
cxpc2 |
Crossover rate for adaptation. 0 <= cxpc2 <= 1. default is 0.5 |
mutpm |
Mutation rate for adaptation. 0 <= mutpm <= 1. default is 0.05 |
mutpm2 |
Mutation rate for adaptation. 0 <= mutpm2 <= 1. default is 0.2 |
adapa |
Adaptation threshold for average of fitness values. 0 <= adapa <= 1. default is 0.7 |
adapb |
Adaptation threshold for minimum of fitness values. 0.5 <= adapb <= 1. default is 0.5 |
... |
Further arguments passed to or from other methods. |
pc |
Crossover rate |
pm |
Mutation rate |
Zeynel Cebeci & Erkut Tekeli
Lei, W. and Tingzhi, S. (2004). An improved adaptive genetic algorithm and its application to image segmentation. In Proc. of 5th Int. Conf. on Artificial Neural Network and Genetic Algorithms, pp. 112-119.
fixpcmut,
ilmdhc,
adana1,
adana2,
adana3
Fitness function that calculates the number of 1s in each individual
maxone(x, ...)maxone(x, ...)
x |
A vector |
... |
Further arguments passed to or from other methods. |
Number of 1s
Zeynel Cebeci & Erkut Tekeli
C2 = c(1, 1, 1, 0, 1, 0, 0, 0) maxone(C2) C3 = c(1, 1, 1, 1, 1, 1, 1, 1) maxone(C3)C2 = c(1, 1, 1, 0, 1, 0, 0, 0) maxone(C2) C3 = c(1, 1, 1, 1, 1, 1, 1, 1) maxone(C3)
Fitness function that calculates the number of 1s in each individual
maxone1(x, ...)maxone1(x, ...)
x |
A vector |
... |
Further arguments passed to or from other methods. |
Number of 1s
Zeynel Cebeci & Erkut Tekeli
C2 = c(1, 1, 1, 0, 1, 0, 0, 0) maxone1(C2) C3 = c(1, 1, 1, 1, 1, 1, 1, 1) maxone1(C3)C2 = c(1, 1, 1, 0, 1, 0, 0, 0) maxone1(C2) C3 = c(1, 1, 1, 1, 1, 1, 1, 1) maxone1(C3)
Calculates the sum of each row of a matrix or data frame.
maxone2(x, ...)maxone2(x, ...)
x |
A matrix or a data frame |
... |
Further arguments passed to or from other methods. |
A vector includes sum of each row in a matrix or data frame
Zeynel Cebeci & Erkut Tekeli
binmat = matrix(nrow=5, ncol=8, byrow=TRUE, c( 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 )) rownames(binmat) = paste0("C",1:5) maxone2(binmat)binmat = matrix(nrow=5, ncol=8, byrow=TRUE, c( 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 )) rownames(binmat) = paste0("C",1:5) maxone2(binmat)
Calculates the inverse of the sum of each row of a matrix or data frame.
minone(x, ...)minone(x, ...)
x |
A matrix or a data frame |
... |
Further arguments passed to or from other methods. |
A vector includes the inverse of the sum of each row in a matrix or data frame
Zeynel Cebeci & Erkut Tekeli
binmat = matrix(nrow=5, ncol=8, byrow=TRUE, c( 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 )) rownames(binmat) = paste0("C",1:5) minone(binmat)binmat = matrix(nrow=5, ncol=8, byrow=TRUE, c( 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 )) rownames(binmat) = paste0("C",1:5) minone(binmat)
Monprogress function performs by creating a line plot of the best fitness value found across generations.
monprogress(g, genfits, objective, ...)monprogress(g, genfits, objective, ...)
g |
Generation number |
genfits |
A matrix for fitness values |
objective |
Type of optimization. "min" or "max" |
... |
Further arguments passed to or from other methods. |
No return value, called for the side effect of drawing a plot.
Zeynel Cebeci & Erkut Tekeli
n = 100 genfits = matrix(NA, nrow=n, ncol=5) genfits[1,3] = 50 objective = "max" for(i in 1:(n-1)){ g=i monprogress(g=g, genfits=genfits, objective=objective) genfits[g+1, 3] = genfits[g, 3] + runif(1, -2, 5) }n = 100 genfits = matrix(NA, nrow=n, ncol=5) genfits[1,3] = 50 objective = "max" for(i in 1:(n-1)){ g=i monprogress(g=g, genfits=genfits, objective=objective) genfits[g+1, 3] = genfits[g, 3] + runif(1, -2, 5) }
Modified Partially Mapped Crossover (MPMX) is a crossover operator for permutation encoded chromosomes. Each of the offspring uses sequencing information partially determined by each of their parents. Two different cut points are randomly determined. The part outside of the two cut points is replaced. Pieces between the two cut points are complemented from the original parental genes. However, if the same genes are found among the copied genes, they are changed.
mpmx(x1, x2, cxon, ...)mpmx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9) parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0) mpmx(parent1, parent2)parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9) parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0) mpmx(parent1, parent2)
The Maximal Preservative Crossover (MPX) operator is an operator that tries to preserve good edges but ensure adequate gene exchange between parents (Muhlenbein et.al., 1988).
mpx(x1, x2, cxon, ...)mpx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Muhlenbein, H., Gorges-Schleuter, M. and Kramer, O. (1988). Evolution algorithms in combinatorial optimization. Parallel Computing, 7(1), 65-85.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9) parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0) mpx(parent1, parent2)parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9) parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0) mpx(parent1, parent2)
With mutation, the chromosomes of individuals are randomly changed and sent to the next generation.
mutate(mutfunc, population, mutpm, gatype, ...)mutate(mutfunc, population, mutpm, gatype, ...)
mutfunc |
The name of the mutation operator |
population |
A matrix. Population of offspring to be mutated |
mutpm |
Mutation Rate |
gatype |
Indicates the GA type. "gga" is assigned for generational refresh, and "ssga" for steady-state refresh. |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the mutated offsprings
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offsprings=initbin(25,5) offsprings[,"fitval"] = evaluate(maxone, offsprings[,1:(ncol(offsprings)-2)]) head(offsprings, 4) # mutant individual may be further ahead. mutatedpop = mutate(mutfunc=bitmut, population=offsprings, mutpm=0.1, gatype="gga") mutatedpop[,"fitval"] = evaluate(maxone, mutatedpop[,1:(ncol(mutatedpop)-2)]) head(mutatedpop, 4)offsprings=initbin(25,5) offsprings[,"fitval"] = evaluate(maxone, offsprings[,1:(ncol(offsprings)-2)]) head(offsprings, 4) # mutant individual may be further ahead. mutatedpop = mutate(mutfunc=bitmut, population=offsprings, mutpm=0.1, gatype="gga") mutatedpop[,"fitval"] = evaluate(maxone, mutatedpop[,1:(ncol(mutatedpop)-2)]) head(mutatedpop, 4)
This crossover function copies parent1 and parent2 to offspring1 and offspring2, respectively. A vector of length m is then randomly generated for each parent, containing the values 0 and 1. Elements in this vector are then compared for each gene location. If the element at the ith position of the first vector is equal to that of the second vector, no change is made. However, if the first is 0 and the second is 1, the ith gene of Parent2 is copied as the ith gene of Offspring1. If the ith elements of the vectors are 1 and 0, the i th gene of Parent1 is copied as the i th gene of Offspring2 (Louis & Rawlins, 1991).
mx(x1, x2, cxon, ...)mx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Louis S.J. and Rawlins G.J. (1991). Designer Genetic Algorithms: Genetic Algorithms in Structure Design. In 4th Int. Conf. on Genetic Algorithms. (pp. 53-60)
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) mx(parent1, parent2, cxon=3)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) mx(parent1, parent2, cxon=3)
The nunimut operator is a mutation operator that adjusts for generations by reducing the mutation severity according to genetic progression (Michalewicz, 1994).
This operator is used for value encoded (integer or real number) chromosomes.
nunimut(y, lb, ub, g, gmax, mutb, ...)nunimut(y, lb, ub, g, gmax, mutb, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
g |
Current generation number. |
gmax |
Maximum generation number. |
mutb |
An exponent parameter that sets non-uniformity |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
Michalewicz, . (1994).
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) nunimut(offspring, lb=lb, ub=ub, g=1, gmax=100, mutb=0.5) set.seed(12) nunimut(offspring, lb=lb, ub=ub, g=50, gmax=100, mutb=0.5)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) nunimut(offspring, lb=lb, ub=ub, g=1, gmax=100, mutb=0.5) set.seed(12) nunimut(offspring, lb=lb, ub=ub, g=50, gmax=100, mutb=0.5)
This operator is an adaptive mutation operator that increases the probability of the mutation severity approaching 0 as the number of generations increases.
This operator is used for value encoded (integer or real number) chromosomes.
nunimut2(y, lb, ub, g, gmax, mutb, ...)nunimut2(y, lb, ub, g, gmax, mutb, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
g |
Current generation number. |
gmax |
Maximum generation number. |
mutb |
An exponent parameter that sets non-uniformity |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) nunimut2(offspring, lb=lb, ub=ub, g=1, gmax=100, mutb=0.5) set.seed(12) nunimut2(offspring, lb=lb, ub=ub, g=50, gmax=100, mutb=0.5)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) nunimut2(offspring, lb=lb, ub=ub, g=1, gmax=100, mutb=0.5) set.seed(12) nunimut2(offspring, lb=lb, ub=ub, g=50, gmax=100, mutb=0.5)
Order Crossover (OX) is a crossover operator for permutation encoded chromosomes. It is a different variant of PMX and it receives a part of the offspring chromosome from Parent1 and the remaining part from Parent2 in a certain sequence (Davis, 1985).
ox(x1, x2, cxon, ...)ox(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Davis, L. (1985). Appliying adaptive algorithms to epistatic domains. In Proc. of the Int. Joint Conf. on Artificial Intellegence, Vol. 85, pp. 162-164.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) ox(parent1, parent2)parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) ox(parent1, parent2)
Order-based crossover (OX2) is a crossover operator for permutation encoded chromosomes. It is an operator that forces the order of several randomly selected positions in one parent to the other parent (Syswerda, 1991).
ox2(x1, x2, cxon, cxoxk, ...)ox2(x1, x2, cxon, cxoxk, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxoxk |
Number of genes to be changed |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Sysweda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 2, 3, 4, 5, 6, 7, 8) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) ox2(parent1, parent2)parent1 = c(1, 2, 3, 4, 5, 6, 7, 8) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) ox2(parent1, parent2)
The Position-Based Crossover (PBX) operator inserts a different number of randomly selected genes in one parent into the same position in Offspring1, then rounds off the other genes in sequence according to their positions in the other parent (Syswerda, 1991). Other offspring are generated similarly if desired or necessary. PBX is an operator that tries to ensure diversity in recombination while taking care to preserve position.
pbx(x1, x2, cxon, ...)pbx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Syswerda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx2,
cx,
icx,
smc
parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) pbx(parent1, parent2, cxon=2)parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) pbx(parent1, parent2, cxon=2)
The Position-Based Crossover (PBX) operator inserts a different number of randomly selected genes in one parent into the same position in Offspring1, then rounds off the other genes in sequence according to their positions in the other parent (Syswerda, 1991). Other offspring are generated similarly if desired or necessary. PBX is an operator that tries to ensure diversity in recombination while taking care to preserve position.
pbx2(x1, x2, cxon, ...)pbx2(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Syswerda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
cx,
icx,
smc
ebeveyn1 = c(3, 4, 8, 2, 7, 1, 6, 5) ebeveyn2 = c(4, 2, 5, 1, 6, 8, 3, 7) pbx2(ebeveyn1, ebeveyn2, cxon=2)ebeveyn1 = c(3, 4, 8, 2, 7, 1, 6, 5) ebeveyn2 = c(4, 2, 5, 1, 6, 8, 3, 7) pbx2(ebeveyn1, ebeveyn2, cxon=2)
Fitness statistics graph by GA generations
plotfitness(genfits, options)plotfitness(genfits, options)
genfits |
A matrix. Best fitness of each generation |
options |
A vector. Statistics to be plotted.
|
No return value, called for the side effect of drawing a plot.
Zeynel Cebeci & Erkut Tekeli
Partially Mapped Crossover (PMX) is the most commonly used crossover operator for permutation encoded chromosomes. Each of the offspring uses sequencing information partially determined by each of their parents (Goldberg & Lingle, 1985). Two different cut points are randomly determined. The part between the two cut points is replaced. Pieces outside of the two cut points are complemented from the original parental genes. However, if the same genes are found among the copied genes, they are changed.
pmx(x1, x2, cxon, ...)pmx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Goldberg, D.E. and Lingle, R. (1985). Alleles, loci, and the traveling salesman problem. In Proc. of an international conference on genetic algorithms and their applications. Vol. 154, pp. 154-159. Carnegie-Mellon University, Pittsburgh, PA.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) pmx(parent1, parent2, cxon=2)parent1 = c(3, 4, 8, 2, 7, 1, 6, 5) parent2 = c(4, 2, 5, 1, 6, 8, 3, 7) pmx(parent1, parent2, cxon=2)
Power Mutation is an operator that generates a mutation in a random gene at a certain power of a random number.
This operator is used for value encoded (integer or real number) chromosomes.
powmut(y, lb, ub, mutpow, ...)powmut(y, lb, ub, mutpow, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
mutpow |
An exponent parameter |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) powmut(offspring, lb=lb, ub=ub, mutpow=3)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) powmut(offspring, lb=lb, ub=ub, mutpow=3)
Power Mutation is an operator that generates a mutation in a random gene at a certain power of a random number. In this operator, a different exponent parameter can be given for each gene.
This operator is used for value encoded (integer or real number) chromosomes.
powmut2(y, lb, ub, mutpow, ...)powmut2(y, lb, ub, mutpow, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
mutpow |
A vector of exponent parameter |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) mutpow = c(3, 0.5, 0.5, 2, 3, 1) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) powmut2(offspring, lb=lb, ub=ub, mutpow=mutpow)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) mutpow = c(3, 0.5, 0.5, 2, 3, 1) offspring = c(8, 6, 4, 1, 3, 7) set.seed(12) powmut2(offspring, lb=lb, ub=ub, mutpow=mutpow)
One-point crossover is where randomly selected parent chromosomes from the mating pool are cut at one point and then recombine to generate off-springs.
px1(x1, x2, cxon, ...)px1(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) px1(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) px1(parent1, parent2)
The Random Resetting Mutation operator replaces the value of a randomly selected gene with a randomly selected value between the allowed limits for that gene.
This operator is used for value encoded (integer or real number) chromosomes.
randmut(y, lb, ub, ...)randmut(y, lb, ub, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut(offspring, lb, ub)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut(offspring, lb, ub)
For each gene, if a random number is less than the mutation rate, the gene's value is modified by adding a random value selected from the normal distribution with a mean of zero and a standard deviation of 0.1x(ub-lb).
This operator is used for value encoded (integer or real number) chromosomes.
randmut2(y, lb, ub, mutpm, ...)randmut2(y, lb, ub, mutpm, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
mutpm |
Mutation rate |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
mutate,
bitmut,
randmut,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c( 2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut2(offspring, lb=lb, ub=ub, mutpm=0.1)lb = c( 2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut2(offspring, lb=lb, ub=ub, mutpm=0.1)
For each gene, if a random number is less than the mutation rate, the gene's mean value is zero and its standard deviation is |ub-lb| The random value selected from the normal distribution is changed by adding it (Yoon & Kim, 2012).
This operator is used for value encoded (integer or real number) chromosomes.
randmut3(y, lb, ub, mutpm, ...)randmut3(y, lb, ub, mutpm, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
mutpm |
Mutation rate |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
Yoon, Y. and Kim, Y.H. (2012). The roles of crossover and mutation in real-coded genetic algorithms. In Bioinspired Computational Algorithms and Their Applications (ed. S. Gao). London: INTECH Open Access Publisher. pp. 65-82.
mutate,
bitmut,
randmut,
randmut2,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut3(offspring, lb=lb, ub=ub, mutpm=0.1)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut3(offspring, lb=lb, ub=ub, mutpm=0.1)
An alternative random mutation operator proposed by Wijayaningrum et.al. (2017).
This operator is used for value encoded (integer or real number) chromosomes.
randmut4(y, lb, ub,...)randmut4(y, lb, ub,...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
Wijayaningrum, V.N., Starkweather, T. and D'ann, F. (2017). Scheduling problemsand traveling salesman: The genetic edge recombination operators. In Proc. of ICGA, Vol. 89, pp. 133-40.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut4(offspring, lb=lb, ub=ub)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) randmut4(offspring, lb=lb, ub=ub)
The Randomized And/Or Crossover (RAOC) operator processes parental chromosomes with AND/OR. According to the value of a randomly selected number, one of the offspring is determined by AND and the other is determined by the OR operation.
raoc(x1, x2, cxon, ...)raoc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) raoc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) raoc(parent1, parent2)
It is a crossover function that transfers genes that are equal at a particular locus on the parent chromosomes to the offspring as they are while transferring the different ones randomly (Radcliffe, 1991).
rrc(x1, x2, cxon, ...)rrc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Radcliffe N.J. (1991). Forma analysis and Random Restpectful Recombination. In 4th Int. Conf. on Genetic Algorithms. Vol. 91, pp. 222-229.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) rrc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) rrc(parent1, parent2)
Minimizes undesirable crossover results when parents have the same or many identical genes (Booker, 1987).
rsc(x1, x2, cxon, ...)rsc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Booker L.B. (1987). Improving Search in Genetic Algorithms, in Genetic Algorithms and Simulated Anneling, Morgan Kaufmann Publishing.
cross,
px1,
kpx,
sc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) rsc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) rsc(parent1, parent2)
The Single Arithmetic Crossover (SAX) operator calculates the arithmetic mean by multiplying the parts of the Parents after a randomly determined breakpoint by a random value. Other elements remain the same.
sax(x1, x2, cxon, cxalfa, ...)sax(x1, x2, cxon, cxalfa, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxalfa |
Alpha value. If no value is entered, it is randomly selected by the function in the range [0,1]. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) sax(parent1, parent2)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) sax(parent1, parent2)
After the SC operator determines a random cut point, it randomly shuffles both parental chromosomes and performs a single-point crossover.
sc(x1, x2, cxon, ...)sc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) sc(parent1, parent2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) sc(parent1, parent2)
In the Boltzman tournament, the initial selection pressure is low. Therefore, every individual, whether low or high fitness value, has a chance to be selected. In the following generations, the selection pressure gradually increases. In other words, individuals with high fitness value are forced to be selected.
selboltour(fitvals, ns, selt0, selg, selgmax, ...)selboltour(fitvals, ns, selt0, selg, selgmax, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selt0 |
Number, Initial temperature |
selg |
Current generation number |
selgmax |
Maximum generation number |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6, -1, 2, 4, 5) # Fitness Values cnames = paste0("C",1:length(fitvals)) # Chromosome Names matpool = selboltour(fitvals, selt0=100, selg=5, selgmax=100) cat(cnames[matpool],"\n") matpool = selboltour(fitvals, selt0=100, selg=95, selgmax=100) cat(cnames[matpool],"\n")fitvals = c(6, -1, 2, 4, 5) # Fitness Values cnames = paste0("C",1:length(fitvals)) # Chromosome Names matpool = selboltour(fitvals, selt0=100, selg=5, selgmax=100) cat(cnames[matpool],"\n") matpool = selboltour(fitvals, selt0=100, selg=95, selgmax=100) cat(cnames[matpool],"\n")
Deterministic Selection is similar to Remainder Stochastic Selection. The expected value of each individual in the mating pool is calculated. Individuals are copied directly into the mating pool by the exact number of expected values. Then, sorting is done according to the fraction part of the expected values. In this case, the individuals with the highest fractions go to the top of the list to be selected. The number of individuals required to complete the mating pool to population size is selected by going from the beginning of the list to the end.
seldet(fitvals, ns, ...)seldet(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = seldet(fitvals) cat("Selected chromosomes: ", cnames[matpool], "\n")fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = seldet(fitvals) cat("Selected chromosomes: ", cnames[matpool], "\n")
The select function is a function that wraps all parent selection algorithms. It is coded for call purposes from adana main function.
select(selfunc, fitvals, ns, selb, selbc, selc, selk, sells, selns, selps, sels, selt, selt0, selw, selg, selgmax, fmin, reptype, ...)select(selfunc, fitvals, ns, selb, selbc, selc, selk, sells, selns, selps, sels, selt, selt0, selw, selg, selgmax, fmin, reptype, ...)
selfunc |
Name of selection function |
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selb |
Exponent coefficent, ( |
selbc |
Base of exponent |
selc |
Scaling parameter |
selk |
Power factor |
sells |
Scaling factor |
selns |
Number of Selection pressure |
selps |
Percentage of Selection, ( |
sels |
Selection pressure, ( |
selt |
Number of tournament size |
selt0 |
Number, Initial temperature |
selw |
Number, Window Size |
selg |
Current generation number |
selgmax |
Maximum generation number |
fmin |
The number to subtract from all fitness values. |
reptype |
Type of Sampling, |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Cebeci, Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari, 535 p. Ankara:Nobel Akademik Yayincilik.
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers,
seltrunc
# Create population population = initialize(initfunc=initbin, n=10, m=8) head(population, 5) # Calculate fitness values m = ncol(population)-2 fitvals = evaluate(maxone, population[,1:m]) population[,"fitval"] = fitvals head(population, 5) # Select parents by RWS selidx = select(selfunc=selrws, fitvals=fitvals) matpool = population[selidx,] head(matpool, 5) # Selected chromosomes table(rownames(matpool))# Create population population = initialize(initfunc=initbin, n=10, m=8) head(population, 5) # Calculate fitness values m = ncol(population)-2 fitvals = evaluate(maxone, population[,1:m]) population[,"fitval"] = fitvals head(population, 5) # Select parents by RWS selidx = select(selfunc=selrws, fitvals=fitvals) matpool = population[selidx,] head(matpool, 5) # Selected chromosomes table(rownames(matpool))
The Exponantial Ranking Selection operator is a selection operator that uses probabilities obtained by exponentially weighting the ordinal numbers of individuals.
selers(fitvals, ns, selbc, ...)selers(fitvals, ns, selbc, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selbc |
Base of exponent |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs
fitvals = c(6, -1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selers(fitvals, selbc=0.1) cat(cnames[matpool],"\n") matpool = selers(fitvals, selbc=0.8) cat(cnames[matpool],"\n")fitvals = c(6, -1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selers(fitvals, selbc=0.1) cat(cnames[matpool],"\n") matpool = selers(fitvals, selbc=0.8) cat(cnames[matpool],"\n")
The Exponent Scaling operator is the selection operator in which the fitness values are scaled by the simulated annealing method.
selescale(fitvals, ns, selb, ...)selescale(fitvals, ns, selb, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selb |
Exponent coefficent, ( |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selescale(fitvals, selb=0.1) cat(cnames[matpool],"\n") matpool = selescale(fitvals, selb=2) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selescale(fitvals, selb=0.1) cat(cnames[matpool],"\n") matpool = selescale(fitvals, selb=2) cat(cnames[matpool],"\n")
The Linear Ranking Selection operator selects via probabilities obtained using ordered numbers according to their fitness values (Pohlheim, 2020).
sellrs(fitvals, ns, sels, ...)sellrs(fitvals, ns, sels, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
sels |
Selection pressure, ( |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Pohlheim, H. (2020). Tutorial for "GEATbx: Genetic and Evolutionary Algorithms Toolbox for use with MATLAB", Version 3.30, URL http://www.geatbx.com/ver_3_3/algindex-02html#P181_11564.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) # Fitness Values cnames = paste0("C",1:length(fitvals)) # Chromosome Names matpool = sellrs(fitvals) cat(cnames[matpool],"\n") matpool = sellrs(fitvals, sels=2) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) # Fitness Values cnames = paste0("C",1:length(fitvals)) # Chromosome Names matpool = sellrs(fitvals) cat(cnames[matpool],"\n") matpool = sellrs(fitvals, sels=2) cat(cnames[matpool],"\n")
The Linear Ranking Selection-2 operator selects via probabilities obtained using ordered numbers according to their fitness values. Selection pressure is not applied in this algorithm (Scrucca, 2013).
sellrs2(fitvals, ns, ...)sellrs2(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Scrucca, L. (2013). GA: A package for Genetic Algorithms in R. Journal of Statistical Software, 53(4), 1-37.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = sellrs2(fitvals) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = sellrs2(fitvals) cat(cnames[matpool],"\n")
The LRS operator selects through probabilities obtained using ordered numbers according to their fitness values. In this algorithm, the selection pressure can be adjusted with the s parameter.
sellrs3(fitvals, ns, sels, ...)sellrs3(fitvals, ns, sels, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
sels |
Selection pressure, ( |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = sellrs3(fitvals) cat(cnames[matpool],"\n") matpool = sellrs3(fitvals, sels=2) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = sellrs3(fitvals) cat(cnames[matpool],"\n") matpool = sellrs3(fitvals, sels=2) cat(cnames[matpool],"\n")
The Fitness Linear Scaling operator scales the fitness values using a linear regression model and performs the selection (Louis, 2019).
sellscale(fitvals, ns, sells, ...)sellscale(fitvals, ns, sells, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
sells |
Scaling factor |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Louis, S.J. (2019). Scaling in Genetic Algorithms. URL https://www.cse.unr.edu/~sushil/class/gas/notes/scaling.pdf
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = sellscale(fitvals) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = sellscale(fitvals) cat(cnames[matpool],"\n")
The Nonlinear Ranking Selection is a nonlinear selection method that applies higher selection pressure than the Linear Ranking Selection (Pholheim, 1995).
selnlrs(fitvals, ns, selns, ...)selnlrs(fitvals, ns, selns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selns |
Number of Selection pressure |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Pholheim, H. (1995). Ein genetischer algorithmus mit mehrfachpopulationen zur numerischen optimierung. at-Automatisierungstechnik, 43(3), 127-135.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selnlrs(fitvals) cat(cnames[matpool],"\n") matpool = selnlrs(fitvals, selns=0.1) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selnlrs(fitvals) cat(cnames[matpool],"\n") matpool = selnlrs(fitvals, selns=0.1) cat(cnames[matpool],"\n")
the Power-law Scaling is a selection method in which the kth power of the fit values is used as the scaled fit values (Gillies, 1985).
selpscale(fitvals, ns, selk, ...)selpscale(fitvals, ns, selk, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selk |
Power factor |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Gillies, A.M. (1985). Machine learning procedures for generating image domain feature detectors. PhD thesis, University of Michigan, Ann Arbor.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selpscale(fitvals, selk=1.1) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selpscale(fitvals, selk=1.1) cat(cnames[matpool],"\n")
Random selection is the process of selecting parents completely randomly from the current population, regardless of the individual's fitness values.
selrand(fitvals, ns, ...)selrand(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
Random selection is done by simple random sampling method with replacement. Each individual has an equal chance (p = 1/n) of being selected.
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
seltrunc,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers
fitvals = c(6, -1, 2, 4, 5) # Fitness values cnames = paste0("C",1:length(fitvals)) # Chromose names matpool = selrand(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")fitvals = c(6, -1, 2, 4, 5) # Fitness values cnames = paste0("C",1:length(fitvals)) # Chromose names matpool = selrand(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")
The Rank Scaling is a selection method in which fitness values are scaled according to their ordinal number.
selrscale(fitvals, ns, ...)selrscale(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selrscale(fitvals) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selrscale(fitvals) cat(cnames[matpool],"\n")
The Rank Scaling-2 is a selection method in which fitness values are scaled according to their ordinal number. Selection pressure can be adjusted by the user.
selrscale2(fitvals, ns, sels, ...)selrscale2(fitvals, ns, sels, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
sels |
Scaling factor, ( |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selrscale2(fitvals) cat(cnames[matpool],"\n") matpool = selrscale2(fitvals, sels=2) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selrscale2(fitvals) cat(cnames[matpool],"\n") matpool = selrscale2(fitvals, sels=2) cat(cnames[matpool],"\n")
The fitness probability of individuals is multiplied by the population size to calculate the number of times the individual will reproduce in the mating pool, ie the expected number of copies. The expected number of copies is a fractional number. An exact fraction of the expected number of copies of the individual is sent to the mating pool. It is also determined whether it can go back to the mating pool for the fraction part (Brindle, 1981).
selrss(fitvals, ns, ...)selrss(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Brindle, A. (1981). Genetic algorithms for function optimization. PhD thesis, University of Alberta.
select,
selrand,
selrswrp,
selrws,
selrws2 ,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selrss(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selrss(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")
Random selection is made by simple random sampling method with replacements, based on the fitness values of individuals. Each individual has the chance to be selected proportionally to their fitness value.
selrswrp(fitvals, ns, ...)selrswrp(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
seltrunc,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers
fitvals = c(6, 1, 2, 4, 5) # Fitness Values cnames = paste0("C",1:length(fitvals)) # Chromosome names matpool = selrswrp(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")fitvals = c(6, 1, 2, 4, 5) # Fitness Values cnames = paste0("C",1:length(fitvals)) # Chromosome names matpool = selrswrp(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")
This function provides the opportunity to take more than one place in the mating pool in proportion to the fitness value of each individual.
selrws(fitvals, ns, ...)selrws(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
seltrunc,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers
fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selrws(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selrws(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")
This function provides the opportunity to take more than one place in the mating pool in proportion to the fitness value of each individual.
selrws2(fitvals, ns, ...)selrws2(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
seltrunc,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers
fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selrws(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selrws(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")
Sigma Scaling is based on the mean rather than the worst fitness value as in Window Scaling. In Sigma Scaling, an individual's fitness is a function of the population mean and population standard deviation (Forrest, 1985; Goldberg, 1989).
selsscale(fitvals, ns, selc, ...)selsscale(fitvals, ns, selc, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selc |
Scaling parameter |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Forrest, S. (1985). Documentation of prisoner's dilemma and norms programs that use the genetic algorithm. Technical report, University of Michigan.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selsscale(fitvals, selc=2) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selsscale(fitvals, selc=2) cat(cnames[matpool],"\n")
Sigma Scaling is based on the mean rather than the worst fitness value as in Window Scaling. In Sigma Scaling, an individual's fitness is a function of the population mean and population standard deviation. In this approach, if the scaled value is less than zero, it is set to zero.
selsscale2(fitvals, ns, selc, ...)selsscale2(fitvals, ns, selc, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selc |
Scaling parameter |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selsscale2(fitvals) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) cnames = paste0("C",1:length(fitvals)) matpool = selsscale2(fitvals) cat(cnames[matpool],"\n")
The Stochastic Universal Selection is the Roulette Wheel Selection method with multiple winning points.
selsus(fitvals, ns, ...)selsus(fitvals, ns, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selsus(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")fitvals = c(6, 1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = selsus(fitvals) cat("Selected Chromosomes: ", cnames[matpool], "\n")
The best one is selected in the group consisting of t individuals selected by random sampling with or without replacement from the current population (Smith et.al, 1991).
seltour(fitvals, ns, selt, reptype, ...)seltour(fitvals, ns, selt, reptype, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selt |
Number of tournament size |
reptype |
Type of Sampling, |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Smith, R.E., Goldberg, D.E. and Earickson, J.A. (1991). SGA-C: A C-language implementation of a simple gewnetic algorithm. Technical report 91002, Illinois Genetic Algorithms Laboratory, Urbana, IL, USA.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour2
selt = 2 # Size of tournament fitvals = c(6, -1, 2, 4, 5) # Fitness values cnames = paste0("C",1:length(fitvals)) # Chromosome names matpool = seltour(fitvals, selt=selt) cat(cnames[matpool],"\n")selt = 2 # Size of tournament fitvals = c(6, -1, 2, 4, 5) # Fitness values cnames = paste0("C",1:length(fitvals)) # Chromosome names matpool = seltour(fitvals, selt=selt) cat(cnames[matpool],"\n")
Each individual is given a chance to participate in the tournament at least once in selection by tournament in this function. For this reason, individuals participating in the tournament cannot participate in another tournament, but after the tournament of all individuals is completed, they can get a chance to participate in another tournament (Nicolau, 2009).
seltour2(fitvals, ns, selt, reptype, ...)seltour2(fitvals, ns, selt, reptype, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selt |
Number of tournament size |
reptype |
Type of Sampling, |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
Nicolau, M. (2009). Application of a simple binary genetic algorithm to a noiseless testbed benchmark. In Proc. genetic and Evolutionary Computation Conf. (GECCO), Montreal, Canada.
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers,
seltrunc,
select
selt = 2 # Size of tournament fitvals = c(6, -1, 2, 4, 5) # Fitness values cnames = paste0("C",1:length(fitvals)) # Chromosome names matpool = seltour2(fitvals, selt=selt) cat(cnames[matpool],"\n")selt = 2 # Size of tournament fitvals = c(6, -1, 2, 4, 5) # Fitness values cnames = paste0("C",1:length(fitvals)) # Chromosome names matpool = seltour2(fitvals, selt=selt) cat(cnames[matpool],"\n")
Individuals in the population are ranked according to their fitness value and individuals with higher fitness value than a determined threshold value are included in the mating pool.
seltrunc(fitvals, ns, selps, ...)seltrunc(fitvals, ns, selps, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
selps |
Percentage of Selection, ( |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selrss,
selsus,
seldet,
selwscale,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2,
selboltour,
sellrs,
sellrs2,
sellrs3,
selnlrs,
selers
fitvals = c(6, -1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = seltrunc(fitvals, selps=0.60) cat(cnames[matpool],"\n")fitvals = c(6, -1, 2, 4, 5) cnames = paste0("C",1:length(fitvals)) matpool = seltrunc(fitvals, selps=0.60) cat(cnames[matpool],"\n")
Window Scaling is a method based on subtracting the worst fitness value from the other fitness values. In this case, since the scaled values of the worst fit individuals will be 0, these individuals will not be given a chance to be selected.
selwscale(fitvals, ns, fmin, ...)selwscale(fitvals, ns, fmin, ...)
fitvals |
Vector of fitness values belonging to individuals |
ns |
Number of individuals to be selected |
fmin |
The number to subtract from all fitness values. |
... |
Further arguments passed to or from other methods. |
The indices of randomly selected individuals are returned.
Zeynel Cebeci & Erkut Tekeli
select,
selrand,
selrswrp,
selrws,
selrws2,
selsus,
seldet,
selrss,
selsscale,
selsscale2,
sellscale,
selrscale,
selrscale2,
selpscale,
selescale,
seltour,
seltour2
fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) fmin = min(fitvals) cnames = paste0("C",1:length(fitvals)) matpool = selwscale(fitvals, fmin=fmin) cat(cnames[matpool],"\n") fitvals = fitvals[matpool] fitvals matpool = selwscale(fitvals, fmin=fmin) cat(cnames[matpool],"\n") fitvals = fitvals[matpool] fitvals fmin = min(fitvals) matpool = selwscale(fitvals, fmin=fmin) cat(cnames[matpool],"\n")fitvals = c(6.1, 3.5, 6.2, 4.4, 5.2) fmin = min(fitvals) cnames = paste0("C",1:length(fitvals)) matpool = selwscale(fitvals, fmin=fmin) cat(cnames[matpool],"\n") fitvals = fitvals[matpool] fitvals matpool = selwscale(fitvals, fmin=fmin) cat(cnames[matpool],"\n") fitvals = fitvals[matpool] fitvals fmin = min(fitvals) matpool = selwscale(fitvals, fmin=fmin) cat(cnames[matpool],"\n")
The show function provides access to user-defined visualization functions.
show(monitorfunc, g, genfits, objective, x, ...)show(monitorfunc, g, genfits, objective, x, ...)
monitorfunc |
Monitoring function |
g |
Generation number |
genfits |
A matrix for fitness values |
objective |
Type of optimization. "min" or "max" |
x |
... |
... |
Further arguments passed to or from other methods. |
NA
Zeynel Cebeci & Erkut Tekeli
n = 100 genfits = matrix(NA, nrow=n, ncol=5) genfits[1,3] = 50 objective = "max" monitorfunc = monprogress for(i in 1:(n-1)){ g=i show(monitorfunc, g=g, genfits=genfits, objective=objective, x=NULL) genfits[g+1, 3] = genfits[g, 3] + runif(1, -2, 5) }n = 100 genfits = matrix(NA, nrow=n, ncol=5) genfits[1,3] = 50 objective = "max" monitorfunc = monprogress for(i in 1:(n-1)){ g=i show(monitorfunc, g=g, genfits=genfits, objective=objective, x=NULL) genfits[g+1, 3] = genfits[g, 3] + runif(1, -2, 5) }
Shuffle Mutation works by randomly shuffling the values in a randomly selected subset of the chromosome (Syswerda, 1991).
This operator is used in problems with permutation encoding.
shufmut(y, ...)shufmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutrange |
A vector. The numbers of begining and ending of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
Syswerda, G. (1991). Schedule optimization using genetic algorithms. Handbook of Genetic Algorithms.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) shufmut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) shufmut(offspring)
The proposed algorithm with the name of SMC is a simple algorithm that works deterministic and alternatively (Kumar & Panneerselvam, 2017).
smc(x1, x2, cxon, ...)smc(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Varun Kumar, S.G. and Panneerselvam R. (2017). A Study of Crossover Operators for Genetic Algorithms to Solve VRP and its Variants and New Sinusoidal Motion Crossover Operator. International Journal of Computational Intelligence Research. Vol 13, Number 7, pp. 1717-1733
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx
parent1 = c(1, 2, 3, 4, 5, 6, 7, 8) parent2 = c(4, 6, 7, 3, 2, 1, 8, 6) smc(parent1, parent2)parent1 = c(1, 2, 3, 4, 5, 6, 7, 8) parent2 = c(4, 6, 7, 3, 2, 1, 8, 6) smc(parent1, parent2)
Sphere Crossover is an operator performed by applying Sphere equality to parent chromosomes. It generates one offspring per each cross.
spherex(x1, x2, cxon, ...)spherex(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) spherex(parent1, parent2)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) spherex(parent1, parent2)
The two most compatible between the two parents and their offspring are added to the new generation population, while those with low fitness are discarded (Sivanandam et.al., 2007).
ssrfamtour(parpop, offpop, reppars, ...)ssrfamtour(parpop, offpop, reppars, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
reppars |
A vector. Indices of the parents |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
Sivanandam et.al., (2007).
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrgenitor,
ssrx
The offspring obtained by mating two randomly selected parents from the mating pool is placed in the place of the worst individual in the current population (Whitley, 1988).
ssrgenitor(parpop, offpop, ...)ssrgenitor(parpop, offpop, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
Whitley, L.D. (1988). GENITOR: A different genetic algorithm. In Proc. of the Rocky Mountain conf. on artificial intellegence, pp. 118-130.
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrfamtour,
ssrx
Two randomly selected parents from the mating pool are mated to produce one or more offspring. The fit value of an individual randomly selected from the population is compared with the offspring with the highest fitness value. If the fitness value of the offspring is higher, the offspring is replaced with the individual.
ssrmup1(parpop, offpop, ...)ssrmup1(parpop, offpop, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrgenitor,
ssrfamtour,
ssrx
The offspring with the best fitness value takes the place of an individual randomly selected from among the individuals excluding their parents and the individual with the worst fitness value in the population.
ssrx(parpop, offpop, reppars, ...)ssrx(parpop, offpop, reppars, ...)
parpop |
A matrix. Parent population |
offpop |
A matrix. Offspring population |
reppars |
A vector. Indices of the parents |
... |
Further arguments passed to or from other methods. |
A matrix. Population of the new generation.
Zeynel Cebeci & Erkut Tekeli
grdelall,
elitism,
grmuplambda,
grmuplambda2,
grmuplambda3,
grmuplambda4,
grmuvlambda,
grrobin,
ssrmup1,
ssrgenitor,
ssrfamtour
SM is the reciprocal exchange of the values of two randomly selected genes on the chromosome (Banzhaf, 1990).
This operator is used in problems with permutation or binary encoding.
swapmut(y, ...)swapmut(y, ...)
y |
A vector. Chromosome of the offspring |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
A vector. The numbers of the mutated genes. |
Zeynel Cebeci & Erkut Tekeli
Banzhaf, W. (1990). The "molecular" traveling salesman. Biological Cybernetics, 64(1), 7-14.
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
unimut,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) swapmut(offspring)offspring = c(1, 2, 3, 4, 5, 6, 7, 8, 9) swapmut(offspring)
The function of terminating the genetic algorithm
terminate(tercrit, maxiter, objective, t, genfits, fitvals, objval, optdif, rmcnt, rmdif, abdif, mincv, sddif, rangedif, simlev, phidif, meandif, bestdif, stime, maxtime)terminate(tercrit, maxiter, objective, t, genfits, fitvals, objval, optdif, rmcnt, rmdif, abdif, mincv, sddif, rangedif, simlev, phidif, meandif, bestdif, stime, maxtime)
tercrit |
A vector. Indications of termination criteria. |
maxiter |
Maximum iteration |
objective |
????? |
t |
Generation number |
genfits |
A matrix. Best fitness of each generation |
fitvals |
Fitness values of current generation |
objval |
Global optimum value |
optdif |
Difference from global optimum value |
rmcnt |
k value for minimum difference of the mean of the last k best fitness values. |
rmdif |
The minimum difference between the mean of the last k best fitness values and the best fitness value in the current generation. |
abdif |
Minimum difference between best fitness value and mean of fitness values |
mincv |
Minimum coefficient of variance |
sddif |
The minimum difference between the last two standard deviations. |
rangedif |
Minimum and maximum difference (range of change) |
simlev |
Similarity percentage of fitness values |
phidif |
Phi convergence |
meandif |
The minimum difference between the last two fitness values |
bestdif |
Percentage of difference between the last two best fitness values |
stime |
System time saved before starting GA |
maxtime |
Maximum running time |
Termination criterion
0 : No termination
1 : Maximum iteration
2 : Reaching the global optimum value
3 : Converging the global optimum
4 : The minimum difference between the last two fitness values
5 : Percentage of difference between the last two best fitness values
6 : Minimum difference of the mean of the last k best fitness values
7 : Minimum difference between best fitness value and mean of fitness values
8 : The minimum difference between the last two standard deviations.
9 : Minimum and maximum difference (range of change)
10: Minimum coefficient of variance
11: Phi convergence
12: Similarity percentage of fitness values
13: Maximum running time
Zeynel Cebeci & Erkut Tekeli
The Random Resetting Mutation operator replaces the value of a randomly selected gene with a randomly selected value between the allowed limits for that gene (Michalewicz, 1994).
This operator is used for value encoded (integer or real number) chromosomes.
unimut(y, lb, ub, ...)unimut(y, lb, ub, ...)
y |
A vector. Chromosome of the offspring |
lb |
A vector. Lower bounds of genes |
ub |
A vector. Upper bounds of genes |
... |
Further arguments passed to or from other methods. |
mutant |
A vector. Chromosome of the offspring |
mutgen |
The number of the mutated gene. |
Zeynel Cebeci & Erkut Tekeli
Michalewicz, . (1994).
mutate,
bitmut,
randmut,
randmut2,
randmut3,
randmut4,
boundmut,
nunimut,
nunimut2,
powmut,
powmut2,
gaussmut,
gaussmut2,
gaussmut3,
bsearchmut1,
bsearchmut2,
swapmut,
invmut,
shufmut,
insmut,
dismut,
invswapmut,
insswapmut,
invdismut
lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) unimut(offspring, lb, ub)lb = c(2, 1, 3, 1, 0, 4) ub = c(10, 15, 8, 5, 6, 9) offspring = c(8, 6, 4, 1, 3, 7) unimut(offspring, lb, ub)
Uniform Partial Mapped Crossover (UPMX) is a crossover operator for permutation encoded chromosomes. Parent1 is cloned into Offspring1. A random point v1 is chosen. The gene at point v1 in Parent2 is determined. The v2 point carrying this gene is determined in Offspring1. The genes at v1 and v2 are swapped. These processes are repeated k times (Migkikh et.al., 1996).
upmx(x1, x2, cxon, ...)upmx(x1, x2, cxon, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Migkikh, V.V., Topchy, A.A., Kureichick, V.M. and Tetelbaum, A.Y. (1996). Combined Genetic and local search algorithm for the quadratic assignment problem. In Proc. of IC on Evolutionary Computation and Its Applications, EvCA, 96, 335-341.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9) parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0) upmx(parent1, parent2)parent1 = c(0, 8, 4, 5, 6, 7, 1, 2, 3, 9) parent2 = c(6, 7, 1, 2, 4, 8, 3, 5, 9, 0) upmx(parent1, parent2)
In a uniform crossover, the number of crossover points is not fixed and evaluates each gene independently (De Jong & Spears, 1991). In other words, it generalizes multi-point crossover as each gene locus is viewed as a potential crossover point.
ux(x1, x2, cxon, cxps, ...)ux(x1, x2, cxon, cxps, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxps |
It determines the rate of gene exchange between the chromosomes of the parents. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
De Jong, K.A. and Spears, W. (1991). On the virtues of parameterized uniform crossover. In Proc. of the 4th Int. Conf. on Genetic Algorithms. Morgan Kaufman Publishers.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) ux(parent1, parent2, cxon=3)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) ux(parent1, parent2, cxon=3)
In a uniform crossover, the number of crossover points is not fixed and evaluates each gene independently (De Jong & Spears, 1991). In other words, it generalizes multi-point crossover as each gene locus is viewed as a potential crossover point.
ux2(x1, x2, cxon, cxps, ...)ux2(x1, x2, cxon, cxps, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxps |
It determines the rate of gene exchange between the chromosomes of the parents. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
De Jong, K.A. and Spears, W. (1991). On the virtues of parameterized uniform crossover. In Proc. of the 4th Int. Conf. on Genetic Algorithms. Morgan Kaufman Publishers.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
wax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) ux2(parent1, parent2, cxon=2)parent1 = c(1, 0, 1, 0, 1, 1, 1, 0) parent2 = c(1, 1, 1, 0, 1, 0, 0, 1) ux2(parent1, parent2, cxon=2)
New offspring are produced by applying an arithmetic mean to all of the parents' chromosomes. (Davis, 1985; Back et.al, 1991; Michalewicz & Janikov, 1991; Michalewicz, 1992; Michalewicz, 1995).
wax(x1, x2, cxon, cxalfa, ...)wax(x1, x2, cxon, cxalfa, ...)
x1 |
A vector. It contains the chromosomal information of parent-1. |
x2 |
A vector. It contains the chromosomal information of parent-2. |
cxon |
Number of offspring to be generated as a result of crossover |
cxalfa |
Alpha value. If no value is entered, it is randomly selected by the function in the range [0,1]. |
... |
Further arguments passed to or from other methods. |
A matrix containing the generated offsprings.
Zeynel Cebeci & Erkut Tekeli
Davis, L. (1985). Aplaying adaptive algorithms to epistatics domains. In Proc. of the Int. Joint Conf. on Artificial Intellengence, Vol. 85, pp. 162-164.
Back, T., Hoffmeister, F. and Schwefel, H.P. (1991). A survey of evolution strategies. In Proc. of the 4th Int. Conf. on Genetic Algorithms, pp. 2-9. Morgan Kaufmann.
Michalewicz, Z. and Janikov, S.J. (1991). Genetic algorithms for numerical optimization. Statistics and Computing, 1(2), 75-91.
Michalewicz, Z. (1992). Genetic algorithms + data structures = evolution programs. Berlin-Heidelberg: Springer Verlag.
Michalewicz, Z. (1995). Genetic algorithms, numerical optimization and constraints. In Proc. of the 4th Int. Conf. on Genetic Algorithms. pp. 151-158. Morgan Kaufmann.
cross,
px1,
kpx,
sc,
rsc,
hux,
ux,
ux2,
mx,
rrc,
disc,
atc,
cpc,
eclc,
raoc,
dc,
ax,
hc,
sax,
lax,
bx,
ebx,
blxa,
blxab,
lapx,
elx,
geomx,
spherex,
pmx,
mpmx,
upmx,
ox,
ox2,
mpx,
erx,
pbx,
pbx2,
cx,
icx,
smc
parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) wax(parent1, parent2)parent1 = c(1.1, 1.6, 0.0, 1.1, 1.4, 1.2) parent2 = c(1.2, 0.0, 0.0, 1.5, 1.2, 1.4) wax(parent1, parent2)