SAWHALE: A Surrogate-Assisted Self-Adaptive Whale Optimization Algorithm with Novel Asymmetric Opposition-Based Learning for Expensive Optimization Problems

Expensive optimization problems allow for only a small number of exact objective evaluations, and this is where most metaheuristics lose their value. This paper proposes SAWHALE, a surrogate-assisted and self-adaptive whale optimization framework built around two new asymmetric opposition-based learning operators. EDOFAS schedules entropy-driven oppositional probes at several scales, while OPADAMP perturbs the worst coordinates of promising solutions. Surrogate models price the candidates of a global phase and a local phase, and a logistic rule switches between the phases according to the state of the population. Four experiments examine the framework. A component study over nine whale variants at 500 and 1000 dimensions places EDOFAS first, with mean Friedman ranks of 1.650 and 1.575. On the CEC 2014 suite, the full framework attains the best mean rank against five surrogate-assisted optimizers, 2.233 at 30 dimensions and 2.267 at 50, with more Wilcoxon wins than losses against every one of them. An ablation over seven configurations keeps the complete design first at 1.333 and 2.033. On the CEC 2017 suite, the framework ranks first at 1.767 and 1.600 against six metaheuristics, including three newer whale variants, and the cost of the machinery on smooth unimodal ground is reported openly.