Hybrid whale optimization algorithm for enhanced routing of limited capacity vehicles in supply chain management

The present study focuses on the problem of vehicle routing with limited capacity, with the objective of minimizing the transportation distance required to serve h clients with predetermined locations and needs. The aim is to create k trips that cover the shortest possible distance. To achieve this goal, a hybrid whale optimization algorithm (hGWOA) is proposed, which combines the whale optimization algorithm (WOA) with the grey wolf optimizer (GWO). The proposed hybrid model is comprised of two main steps. First step, the GWO's hunting mechanism is integrated transitioning to the utilization phase of WOA, and a newly devised state is introduced that is linked to GWO. In the second step, a novel technique is incorporated into the exploration mission phase to enhance the resolve after per iteration. The algorithm's performance is assessed and compared with other modern algorithms, including the GWO, WOA, ant lion optimizer (ALO), and dragonfly algorithm (DA) using 23 benchmark test functions and CEC2017 benchmark test function. The results indicate that the hybrid hGWOA method outperforms other algorithms in terms of delivery distance optimization for scenarios involving scale and complexity. These findings are corroborated through case studies related to cement delivery and a real-world scenario in Viet Nam.