Improved Harris Hawks Optimizer algorithm to solve the multi-depot open vehicle routing problem

The Multi-Depot Open Vehicle Routing Problem (MDOVRP) is only one example of several optimization problems that are classified as NP-hard. Therefore, heuristic and metaheuristic approaches are helpful in obtaining a near-optimal solution. A hybrid HHO algorithm called HHO-PSO is proposed in this work to address the MDOVRP. The goal is to minimize costs for the routes of a fleet of vehicles that start moving from depots and fulfill customers' demands. To improve the exploration of the Harris Hawks Optimization (HHO) algorithm, the exploration method of Particle Swarm Optimization (PSO) which is more robust, is used in this paper. Experimental results proved that the proposed hybrid algorithm works better than the original PSO and HHO in discrete space in terms of balance, exploitation, and exploration to solve the MDOVRP. Moreover, the suggested algorithm is compared to five cutting-edge approaches on 24 MDOVRP instances with a broad number of customers. The computational findings reveal that the suggested approach outperformed the other comparable metaheuristic techniques in solving the MDOVRP.