Abstract

This study investigates the binarization process of the Reptile Search Algorithm (RSA) using chaotic maps to solve the Knapsack Problem. We evaluate RSA, Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO) using the S4 transfer function with four binarization strategies: standard, standard with chaotic maps, elitist, and elitist with chaotic maps. Experimental results show that standard binarization strategies, particularly RSA with standard binarization rule (STD) and RSA with standard binarization rule with a chaotic map (STD_SINE), consistently outperform elitist strategies across various Knapsack problem instances. Including chaotic maps, especially the sine chaotic map, slightly improves performance. Convergence analysis reveals that standard binarization ensures steady and strong convergence, while elitist binarization accelerates convergence but may risk settling on local optima early. This research highlights the importance of selecting appropriate binarization strategies and suggests further exploration of chaotic maps to enhance the performance of metaheuristic algorithms in solving binary combinatorial optimization problems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.