| Title: | Gradient-Free Optimization Algorithm for Single and Multi-Objective Problems |
|---|---|
| Description: | An implementation of the Jaya optimization algorithm for both single-objective and multi-objective problems. Jaya is a population-based, gradient-free optimization algorithm capable of solving constrained and unconstrained optimization problems without hyperparameters. This package includes features such as multi-objective Pareto optimization, adaptive population adjustment, and early stopping. For further details, see R.V. Rao (2016) <doi:10.5267/j.ijiec.2015.8.004>. |
| Authors: | Neeraj Bokde [aut, cre]
|
| Maintainer: | Neeraj Bokde <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.0.3 |
| Built: | 2024-11-19 03:57:34 UTC |
| Source: | CRAN |
Implements the Jaya optimization algorithm for single-objective optimization. The algorithm minimizes or maximizes the given objective function over specified bounds.
jaya( fun = NULL, lower, upper, popSize = 50, maxiter, n_var, seed = NULL, suggestions = data.frame(), opt = "minimize", objectives = NULL, constraints = list(), early_stopping = FALSE, tolerance = 1e-06, patience = 10, adaptive_pop = FALSE, min_popSize = 20, max_popSize = 100, parallel = FALSE, cores = NULL )jaya( fun = NULL, lower, upper, popSize = 50, maxiter, n_var, seed = NULL, suggestions = data.frame(), opt = "minimize", objectives = NULL, constraints = list(), early_stopping = FALSE, tolerance = 1e-06, patience = 10, adaptive_pop = FALSE, min_popSize = 20, max_popSize = 100, parallel = FALSE, cores = NULL )
fun |
Objective function to be minimized or maximized (single-objective). |
lower |
Vector of lower bounds for the decision variables. |
upper |
Vector of upper bounds for the decision variables. |
popSize |
Size of the population for the optimization process. |
maxiter |
Maximum number of iterations. |
n_var |
Number of decision variables. |
seed |
Optional random seed for reproducibility. |
suggestions |
Optional data frame of initial population suggestions. |
opt |
Specify whether to "minimize" or "maximize" the objective function. |
objectives |
(optional) A list of functions for multi-objective optimization. |
constraints |
(optional) A list of constraints as functions returning <= 0 for feasibility. |
early_stopping |
Logical. If TRUE, stops optimization early based on tolerance and patience. |
tolerance |
Numeric. Tolerance for early stopping. |
patience |
Integer. Number of iterations to wait for improvement before stopping early. |
adaptive_pop |
Logical. If TRUE, enables adaptive population size adjustment. |
min_popSize |
Integer. Minimum population size for adaptive adjustment. |
max_popSize |
Integer. Maximum population size for adaptive adjustment. |
parallel |
Logical. If TRUE, enables parallel computation for evaluating population. |
cores |
Integer. Number of cores to use for parallel computation. Defaults to all available cores minus one. |
A list containing the following: - 'Best': The best solution found (variable values and objective function value). - 'Iterations': Best objective function values at each iteration.
# Example: Single-objective optimization sphere_function <- function(x) sum(x^2) result <- jaya( fun = sphere_function, lower = rep(-5, 3), upper = rep(5, 3), popSize = 20, maxiter = 50, n_var = 3, opt = "minimize" ) print(summary(result)) plot(result)# Example: Single-objective optimization sphere_function <- function(x) sum(x^2) result <- jaya( fun = sphere_function, lower = rep(-5, 3), upper = rep(5, 3), popSize = 20, maxiter = 50, n_var = 3, opt = "minimize" ) print(summary(result)) plot(result)
Implements the Jaya optimization algorithm for multi-objective optimization. This algorithm supports non-dominated sorting and handles constraints and adaptive population sizes.
jaya_multi( objectives, lower, upper, popSize = 50, maxiter, n_var, seed = NULL, suggestions = data.frame(), constraints = list(), adaptive_pop = FALSE, min_popSize = 20, max_popSize = 100, early_stopping = FALSE, tolerance = 1e-06, patience = 10 )jaya_multi( objectives, lower, upper, popSize = 50, maxiter, n_var, seed = NULL, suggestions = data.frame(), constraints = list(), adaptive_pop = FALSE, min_popSize = 20, max_popSize = 100, early_stopping = FALSE, tolerance = 1e-06, patience = 10 )
objectives |
A list of objective functions to optimize. |
lower |
Numeric vector specifying the lower bounds for variables. |
upper |
Numeric vector specifying the upper bounds for variables. |
popSize |
Population size. Default is 50. |
maxiter |
Maximum number of iterations. |
n_var |
Number of variables. |
seed |
Random seed for reproducibility. Default is 'NULL'. |
suggestions |
Data frame of initial suggestions for starting population. Default is an empty data frame. |
constraints |
A list of constraint functions. Each constraint should return a non-positive value if satisfied. |
adaptive_pop |
Logical. Whether to adapt population size during optimization. Default is 'FALSE'. |
min_popSize |
Minimum population size if adaptive population is enabled. Default is 20. |
max_popSize |
Maximum population size if adaptive population is enabled. Default is 100. |
early_stopping |
Logical. Whether to stop early if no improvement is observed. Default is 'FALSE'. |
tolerance |
Numeric tolerance for early stopping. Default is 1e-6. |
patience |
Number of iterations to wait for improvement before stopping. Default is 10. |
A list containing: - 'Pareto_Front': A data frame of non-dominated solutions with decision variables and their corresponding objective values. - 'Solutions': The final population including decision variables and their objective values.
# Example: Multi-objective optimization sphere_function_1 <- function(x) sum(x^2) sphere_function_2 <- function(x) sum((x - 2)^2) result <- jaya_multi( objectives = list(sphere_function_1, sphere_function_2), lower = rep(-5, 3), upper = rep(5, 3), popSize = 20, maxiter = 50, n_var = 3 ) print(summary(result))# Example: Multi-objective optimization sphere_function_1 <- function(x) sum(x^2) sphere_function_2 <- function(x) sum((x - 2)^2) result <- jaya_multi( objectives = list(sphere_function_1, sphere_function_2), lower = rep(-5, 3), upper = rep(5, 3), popSize = 20, maxiter = 50, n_var = 3 ) print(summary(result))
Generates pairwise 2D plots for all combinations of objectives in the Pareto front. This function visualizes trade-offs between different objectives.
plot_jaya_multi_pairwise(x, objectives = NULL, ...)plot_jaya_multi_pairwise(x, objectives = NULL, ...)
x |
An object of class |
objectives |
A vector of objective column names to include in the pairwise plots.
If |
... |
Additional graphical parameters passed to the |
The function automatically detects objectives in the Pareto front if not specified. It creates pairwise plots for all possible combinations of objectives.
# Example usage of plot_jaya_multi_pairwise # Define sample multi-objective optimization problem objective1 <- function(x) sum(x^2) objective2 <- function(x) sum(abs(x)) objective3 <- function(x) sum(x^3) objective4 <- function(x) sum(x^4) objectives <- list(objective1, objective2, objective3, objective4) lower_bounds <- c(-5, -5, -5) upper_bounds <- c(5, 5, 5) # Run multi-objective optimization using jaya_multi set.seed(42) multi_result <- jaya_multi( objectives = objectives, lower = lower_bounds, upper = upper_bounds, popSize = 50, maxiter = 100, n_var = length(lower_bounds) ) # Pairwise plot of objectives plot_jaya_multi_pairwise(multi_result)# Example usage of plot_jaya_multi_pairwise # Define sample multi-objective optimization problem objective1 <- function(x) sum(x^2) objective2 <- function(x) sum(abs(x)) objective3 <- function(x) sum(x^3) objective4 <- function(x) sum(x^4) objectives <- list(objective1, objective2, objective3, objective4) lower_bounds <- c(-5, -5, -5) upper_bounds <- c(5, 5, 5) # Run multi-objective optimization using jaya_multi set.seed(42) multi_result <- jaya_multi( objectives = objectives, lower = lower_bounds, upper = upper_bounds, popSize = 50, maxiter = 100, n_var = length(lower_bounds) ) # Pairwise plot of objectives plot_jaya_multi_pairwise(multi_result)
This function generates plots for single-objective optimization results from the Jaya algorithm. It visualizes the best objective function value against the number of iterations.
## S3 method for class 'jaya' plot(x, ...)## S3 method for class 'jaya' plot(x, ...)
x |
An object of class |
... |
Additional graphical parameters passed to the |
This function supports plotting results for single-objective optimization.
It creates a plot of the best objective function value observed across iterations.
Ensure that the input object is from the jaya function.
# Example: Single-objective optimization sphere_function <- function(x) sum(x^2) lower_bounds <- rep(-5, 3) upper_bounds <- rep(5, 3) pop_size <- 20 max_iterations <- 50 num_variables <- length(lower_bounds) # Run optimization single_result <- jaya( fun = sphere_function, lower = lower_bounds, upper = upper_bounds, popSize = pop_size, maxiter = max_iterations, n_var = num_variables, opt = "minimize" ) # Plot the result plot(single_result)# Example: Single-objective optimization sphere_function <- function(x) sum(x^2) lower_bounds <- rep(-5, 3) upper_bounds <- rep(5, 3) pop_size <- 20 max_iterations <- 50 num_variables <- length(lower_bounds) # Run optimization single_result <- jaya( fun = sphere_function, lower = lower_bounds, upper = upper_bounds, popSize = pop_size, maxiter = max_iterations, n_var = num_variables, opt = "minimize" ) # Plot the result plot(single_result)
Provides a summary of optimization results for both single-objective and multi-objective cases. Displays key parameters, limits, and results such as the best solution for single-objective optimization or the Pareto front for multi-objective optimization.
## S3 method for class 'jaya' summary(object, ...)## S3 method for class 'jaya' summary(object, ...)
object |
An object of class |
... |
Additional arguments (currently unused). |
- For single-objective optimization, the summary includes the best solution and the associated function value. - For multi-objective optimization, the summary displays the objectives, decision variable limits, and the first few entries of the Pareto front. - Automatically handles missing or incomplete attributes gracefully.
# Single-objective optimization example sphere_function <- function(x) sum(x^2) single_result <- jaya( fun = sphere_function, lower = c(-5, -5, -5), upper = c(5, 5, 5), popSize = 20, maxiter = 50, n_var = 3, opt = "minimize" ) summary(single_result) # Multi-objective optimization example objective1 <- function(x) sum(x^2) objective2 <- function(x) sum(abs(x)) multi_result <- jaya_multi( objectives = list(objective1, objective2), lower = c(-5, -5, -5), upper = c(5, 5, 5), popSize = 50, maxiter = 100, n_var = 3 ) summary(multi_result)# Single-objective optimization example sphere_function <- function(x) sum(x^2) single_result <- jaya( fun = sphere_function, lower = c(-5, -5, -5), upper = c(5, 5, 5), popSize = 20, maxiter = 50, n_var = 3, opt = "minimize" ) summary(single_result) # Multi-objective optimization example objective1 <- function(x) sum(x^2) objective2 <- function(x) sum(abs(x)) multi_result <- jaya_multi( objectives = list(objective1, objective2), lower = c(-5, -5, -5), upper = c(5, 5, 5), popSize = 50, maxiter = 100, n_var = 3 ) summary(multi_result)