Improved whale optimization algorithm with a stable solution preservation mechanism for multimodal multi-objective optimization - Sun, Yu; Chang, Yuqing; Hou, Shengle (Cluster computing, 2026)
Multimodal multi-objective optimization problems (MMOPs) pose a challenge due to the need to identify multiple Pareto-optimal solution sets (PSs) distributed across both global and local regions. Although the whale optimization algorithm (WOA) has shown effectiveness in various optimization tasks, recent multi-objective WOA variants still suffer from premature convergence and inadequate preservation of solution diversity, limiting their ability to handle MMOPs. To address these issues, this paper proposes an improved whale optimization algorithm with a stable solution preservation mechanism (IWOA-SSPM). The proposed algorithm integrates a self-organizing map-based dual guidance mechanism to balance exploration and exploitation, and a stable solution preservation mechanism (SSPM) that combines a radius-based localized clearing method to identify and preserve multiple PSs with an intersection-based strategy to retain high-quality solutions across generations. Extensive experiments on benchmark MMOPs demonstrate that IWOA-SSPM achieves superior convergence and diversity compared to several competitive algorithms. Furthermore, a map-based optimization case study validates its practical effectiveness in solving complex real-world problems.