Chaotic Regulation of Exploration and Exploitation in Bio-Inspired Swarm Intelligence for Combinatorial Optimization

Abstract

The transition from continuous swarm intelligence algorithms to discrete combinatorial domains remains a critical challenge in bio-inspired computing. Traditional binarization techniques frequently induce premature convergence in highly constrained landscapes. This paper presents a chaotic discretization framework that replaces the classical behavior of the two-step binarization technique to regulate the balance between exploration and exploitation. The proposal systematically integrates three leading continuous metaheuristics in the literature, with twenty-four binarization configurations, across three distinct NP-hard problem archetypes: capacity-constrained (0–1 Knapsack), sparse (Set Covering), and mathematically degenerate flat landscapes (Unicost Set Covering). Nonparametric statistical tests confirm that chaotic discretization acts as a powerful regulator in the landscape (p < 0.05). Empirical evidence shows that the highest-performing chaotic mapping is heavily influenced by the specific landscape morphology evaluated: the 0–1 Knapsack Problem is statistically optimized by the Circle map under standard rules; the Set Covering Problem achieves optimal median performance with the Tent map under elitist formulations, although severe matrix constraints ultimately force statistical ties; and the Unicost Set Covering Problem utilizes the nonlinear sequences of the sinusoidal map under complementary operators to break convergence stagnation.