Not All Chaos Is Equal: An In-Depth Evaluation of Ten Chaotic Maps in Dholes-Inspired Optimization for Constrained Engineering Problems

Dhara Buch; Hitarth Buch

doi:10.57159/jcmm.5.3.26667

Authors

Dhara Buch Department of Computer Engineering, Government Engineering College, Rajkot, Gujarat, India https://orcid.org/0000-0002-1036-5105
Hitarth Buch Department of Electrical Engineering, Government Engineering College, Rajkot, Gujarat, India https://orcid.org/0000-0001-9714-3750

DOI:

https://doi.org/10.57159/jcmm.5.3.26667

Keywords:

Chaotic maps, Dholes-Inspired Optimization, Constrained engineering optimization, Metaheuristic algorithms, Engineering design benchmarks, Chaos-enhanced optimization

Abstract

Chaos-enhanced search mechanisms are widely used to improve exploration and mitigate stagnation in metaheuristic optimization. However, their integration into the recently proposed Dholes-Inspired Optimization (DIO) algorithm has not yet been systematically investigated. This study presents a systematic evaluation of chaos-enhanced DIO variants by embedding ten structurally diverse chaotic maps into the original algorithm. The resulting eleven DIO variants are benchmarked on 17 classical constrained engineering design problems under identical experimental conditions. Prior to optimization, each chaotic map is analyzed using dynamical diagnostics, revealing substantial differences in behavior across maps that translate into distinct search characteristics when embedded in the optimizer. Experimental results demonstrate that Piecewise, Singer, Iterative, and Circle chaotic maps consistently improve DIO's robustness and convergence reliability, achieving the lowest mean ranks (4.71–5.00) and the smallest rank variability across the 17-problem benchmark suite. Non-parametric statistical tests confirm that these variants form the leading statistical cluster. Cliff's delta analysis further reveals that practical effect sizes among the ten non-Sinusoidal variants are negligible (|δ| < 0.147), while Sinusoidal is the only variant showing a meaningful performance deficit (|δ| ≈ 0.48–0.51). On three of four directly comparable classical benchmarks, the elite variants approach published best-known optima to within 2%, and on the Three-Bar Truss problem, DIO-Circle surpasses the widely cited reference value. Overall, the study identifies four chaotic maps (Piecewise, Singer, Iterative, and Circle) as the most effective mechanisms for enhancing DIO. These findings provide quantitative evidence and practical guidance for selecting chaotic dynamics in swarm-based optimization and contribute new insight into the relationship between chaotic system structure and metaheuristic search behavior.

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