Chaotic Sech–Tanh dynamic opposition-based learning for metaheuristic optimization. Part I: strategy development and validation on benchmark and engineering design problems

Abstract

Metaheuristic optimization algorithms frequently struggle to maintain an effective balance between exploration and exploitation, particularly on high-dimensional problems where premature convergence and reduced population diversity degrade performance. Opposition-based Learning (OBL) is a widely used remedy, yet its established variants, including the Dynamic Opposition-based Learning (DOBL) method, construct opposite solutions that can still trap the search in local optima. This study proposes the Chaotic Sech-Tanh Dynamic Opposition-based Learning (CHSTDOBL) strategy, which integrates two complementary mechanisms into the dynamic opposition framework: pseudo-random sequences generated by the Ikeda chaotic map, which inject aperiodic variability to resist premature convergence, and hyperbolic secant and tangent functions, which compress these sequences into a bounded range that enables controlled local refinement. The strategy was integrated into the Whale Optimization Algorithm and compared against five established OBL variants on 500-dimensional benchmark functions, the CEC 2013 test suite, and 12 constrained engineering design problems. CHSTDOBL outperformed or matched its competitors on 20 of 24 multimodal and 21 of 24 unimodal benchmark functions and was ranked first by the Friedman test. In the CEC 2013 suite, it attained the best mean and objective values on 12 and 13 functions, respectively. For constrained design problems, it achieved the best feasible objective value in eight of 12 cases, failing to retain the best-known optimum in only four, while producing consistently tighter solution distributions than seven competing optimizers. Its generality was confirmed by embedding it into eight recently proposed metaheuristic algorithms, establishing CHSTDOBL as a competitive, algorithm-agnostic enhancement.