Applying a Hybrid Gray Wolf-Enhanced Whale Optimization Algorithm to the Capacitated Vehicle Routing Problem

The study presents a novel hybrid gray wolf and whale optimization algorithm (hGWOAM) for the capacitated vehicle routing problem (CVRP). By integrating the enhanced whale optimization algorithm (EWOA) and gray wolf optimizer (GWO) with tournament selection, opposition-based learning, and mutation techniques, hGWOAM enhances routing efficiency under capacity constraints. Computational evaluations demonstrate its superior performance, achieving lower percentage deviations (%dev) compared to existing algorithms across multiple case studies and real-world applications. In Case Study 1, hGWOAM achieved a mean percentage deviation (%dev) lower than EWOA (0.89%), GWO (0.74%), SCA (0.59%), DA (1.63%), ALO (2.26%), MHPSO (1.85%), PSO (1.96%), DPGA (2.85%), and SGA (4.14%). In Case Study 2, hGWOAM outperformed EWOA (12.05%), GWO (2.53%), ALO (21.07%), and DA (17.58%). In a real-world application, it achieved the best %dev, surpassing EWOA (6.64%), GWO (6.34%), ALO (9.01%), and DA (12.24%). These findings highlight hGWOAM’s potential for optimizing logistics, reducing operational costs, and minimizing environmental impact while also paving the way for future advancements in metaheuristic optimization.