Smooth Exploration System: A novel ease-of-use and specialized module for improving exploration of whale optimization algorithm

Whale optimization algorithm (WOA) is a swarm-based optimization algorithm that has recently attracted extensive interest and attention because of its excellent exploitation ability. However, exploration process of WOA needs to be more valued and requires specialized mechanisms to maximize exploration ability. Therefore, based on the insight into the underlying logic of exploration process, a novel smooth exploration system (SES) is proposed to improve exploration process of WOA, and a variant of WOA is proposed called smooth WOA (SWOA). The SES comprises three mechanisms: unordered dimension sampling, random crossover, and sequential mutation. In detail, inspired by the sampling theory, unordered dimension sampling is used to adjust the sparsity of population and the proportion between exploration and exploitation. The random crossover and the sequential mutation complement each other to cover a vast search space. The performance of the SWOA is verified by comparing it with seven variants of WOA and six advanced algorithms based on 31 benchmark functions from CEC2015, CEC2021, and CEC2022. A total of six qualitative methods are introduced to analyze the performance of the SES comprehensively. Coupling coordination evaluation is introduced to present the synergy of mechanisms within the SES, which is an improvement of the ablation experiment and facilitates the consideration of rationality of each evolutionary strategy. Comprehensive qualitative analyses and fair comparisons demonstrate the remarkable performance of the SWOA.