Innovative hybrid algorithm for efficient routing of limited capacity vehicles

This study addresses the critical challenges posed by the capacitated vehicle routing problem (CVRP), particularly in the logistics of cement transportation under capacity constraints. Existing algorithms, including grey wolf optimizer (GWO) and whale optimization algorithm (WOA), exhibit significant limitations such as imbalanced exploration and exploitation, inefficiency in refining solutions, and inadequate adaptability to dynamic routing conditions. These limitations hinder their ability to provide comprehensive solutions that optimize time, cost, and environmental sustainability. To address these critical challenges, this research proposes an enhanced hybrid metaheuristic algorithm, mGWOA, designed to overcome the limitations of existing approaches by combining the GWO's strong exploitation capabilities and the WOA's exploratory strengths. By integrating opposition-based learning (OBL) to expand the search space and mutation techniques to escape local optima, the mGWOA is tailored to provide more flexible, adaptive, and efficient solutions for the complex and dynamic requirements of the CVRP. The mGWOA framework leverages the exploratory advantages of WOA, the exploitative strengths of GWO, and the diversity-promoting features of OBL and mutation to address the complexities of CVRP. Through computational evaluations in various scenarios, including five case studies ranging from small to large, the algorithm demonstrates its superior ability to generate high-quality solutions, especially as the customer base expands. The results underscore the potential of mGWOA as a robust and adaptive approach to solving CVRP, minimizing time and cost, and contributing to sustainable logistics operations. By bridging existing knowledge gaps, this research provides an innovative global optimization framework, offering practical applications for CVRP and other engineering challenges.