A combinatorial social group whale optimization algorithm for numerical and engineering optimization problems

This article presents two new hybrid swarm-human based meta-heuristic optimization algorithms benefitting from the synergy of whale optimization algorithm (WOA) and social group optimization (SGO) known as Hybrid Social Whale Optimization Algorithm (HS-WOA and HS-WOA+). HS-WOA and HS-WOA+ are hybridized combining the exploratory capabilities of WOA and convergence capabilities of SGO with a perfect balance between exploration and exploitation. A comparative analysis of the new proposed hybrid algorithm is performed through various benchmark functions. Various test cases to analyze the algorithm's performance like influence of population size, effect of dimensionality, effect of iterative count is performed and compared. The proposed algorithms are compared with modern-meta-heuristics and variants of WOA and SGO to justify its performance. The performance is evaluated statistically through the Wilcoxon's rank-sum test and Friedman's non-parametric test while the convergence curves and acceleration rates are provided to demonstrate the convergence capabilities of the proposed hybrid algorithms and the computational times are recorded to showcase the computational speeds of all the algorithms used in comparison. Composite benchmarking functions are considered to analyze the exploratory prowess and the algorithms' capability to avoid local entrapment. To assess and evaluate the performance of the proposed algorithms with real world optimization tasks, four standard engineering problems with penalty constraints are added to the test bench. Further, a multi-unit production planning problem with correction constraints is deployed through the proposed algorithms. The benchmarking results prove that HS-WOA and HS-WOA+ s' performance is competitive and better than the various algorithms tested against and had a statistically significant performance with lower computational times. The algorithms performed well for both standard engineering problems and the multi-unit production planning problem outperforming the various algorithms in the literature.