Adaptive Shannon Entropy-Driven Chaotic Grey Wolf Optimization (ASE-CGWO) for Combinatorial Optimization Problems.
4 affiliations
- 1Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru 560035, Karnataka, India.
- 2Department of Software Engineering, Firat University, 23119 Elazig, Türkiye.
- 3Department of Mechanical Engineering, Firat University, 23119 Elazig, Türkiye.
- 4Department of Computer Technologies, Antakya Vocational School, Hatay Mustafa Kemal University, 31060 Antakya, Türkiye.
Abstract
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.
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BibTeX
@article{kalathodi2026adaptive,
title = {{Adaptive Shannon Entropy-Driven Chaotic Grey Wolf Optimization (ASE-CGWO) for Combinatorial Optimization Problems.}},
author = {Simi Kalathodi and Sarada Jayan and Bilal Alatas and Mehmet Das and Merve Celebi and Ebru Akpinar},
journal = {Biomimetics (Basel, Switzerland)},
year = {2026},
month = sep,
doi = {10.3390/biomimetics11100689},
url = {https://europepmc.org/article/MED/42930241},
note = {CC BY},
}
RIS
TY - JOUR
TI - Adaptive Shannon Entropy-Driven Chaotic Grey Wolf Optimization (ASE-CGWO) for Combinatorial Optimization Problems.
AU - Simi Kalathodi
AU - Sarada Jayan
AU - Bilal Alatas
AU - Mehmet Das
AU - Merve Celebi
AU - Ebru Akpinar
PY - 2026
DA - 2026/09/23
JO - Biomimetics (Basel, Switzerland)
DO - 10.3390/biomimetics11100689
UR - https://europepmc.org/article/MED/42930241
AB - 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.
SN - 2313-7673
ER -