Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics

Abstract

Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map.

A Novel Approach to Combinatorial Problems: Binary Growth Optimizer Algorithm

“…Since we were solving a binary problem, each decision variable was randomly assigned a value of 1 or 0. • Termination conditions: In the literature, we found different term criteria, such as calls to the objective function [59] or the total number of iterations [60][61][62] that the metaheuristic will perform. We considered the total number of iterations as the completion criterion in our work.…”

A multi-strategy improved rime optimization algorithm for three-dimensional USV path planning and global optimization

“…The Tent map is a two-dimensional chaotic map known for its superior uniformity and ergodicity compared to pseudo-random number generation 31 , 38 . To address the issue of uneven distribution of rime particles initialized by the rime optimizer, the Tent map within the chaotic map is utilized to replace the pseudo-random method of rime particle initialization.…”