Adaptive Shannon Entropy-Driven Chaotic Grey Wolf Optimization (ASE-CGWO) for Combinatorial Optimization Problems

Combinatorial optimization problems include many NP-hard problems such as assignment, scheduling, and routing, for which conventional approaches to solving become computationally infeasible for large instances, thereby necessitating the use of metaheuristics. This study introduces an algorithm, Adaptive Shannon Entropy-Driven Chaotic Grey Wolf Optimization (ASE-CGWO), for combinatorial optimization problems. The proposed approach adapts the level of chaos using an entropy-based diversity measure to ensure an efficient trade-off between exploration and exploitation. It also uses an entropy-adapted hunting parameter that couples exploration breadth directly to the pack's information content. An Elite Memory Archive and swap, along with insertion and flip operators to enhance neighborhood searches, are also incorporated to maintain high-quality solutions. ASE-CGWO is benchmarked against Standard GWO, Chaotic GWO (fixed r = 3.9 logistic map), Entropy-Adaptive GWO (entropy adapts "a" only), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO) on three NP-hard combinatorial optimization problems: the Quadratic Assignment Problem instance chr15a, the Fisher-Thompson 10 × 10 Job Shop Scheduling Problem (FT10) and the 20-city Traveling Salesman Problem (TSP20) over 20 independent runs each. ASE-CGWO achieves the best mean assignment cost on chr15a (9921.6 ± 147.3 in native QAPLIB units), with its best run reaching the known optimum of 9896, and obtains the second-best mean makespan on FT10 (1182.05 ± 3.32). The adaptive and self-regulating characteristics of ASE-CGWO also suggest potential for future applications in complex engineering optimization problems, including the design and operation of solar energy systems.