Enhanced Whale Optimization Algorithm with Novel Strategies for 3D TSP Problem

To address the insufficient global search efficiency of the original Whale Optimization Algorithm (WOA), this paper proposes an enhanced variant (ImWOA) integrating three strategies. First, a dynamic cluster center-guided search mechanism based on K-means clustering divides the population into subgroups that conduct targeted searches around dynamically updated centroids, with real-time centroid recalculation enabling evolutionary adaptation. This strategy innovatively combines global optima with local centroids, significantly improving global exploration while reducing redundant searches. Second, a dual-modal diversity-driven adaptive mutation mechanism simultaneously evaluates spatial distribution and fitness-value diversity to comprehensively characterize population heterogeneity. It dynamically adjusts mutation probability based on diversity states, enhancing robustness. Finally, a pattern search strategy (GPSPositiveBasis2N algorithm) is embedded as a periodic optimization module, synergizing WOA’s global exploration with GPSPositiveBasis2N’s local precision to boost solution quality and convergence. Evaluated on the CEC2017 benchmark against the original WOA, eight state-of-the-art metaheuristics, and five advanced WOA variants, ImWOA achieves: (1) optimal mean values for 20/29 functions in 30D tests; (2) optimal mean values for 26/29 functions in 100D tests; and (3) first rank in 3D-TSP validation, demonstrating superior capability for complex optimization.