A hybrid multi-objective evolutionary algorithm for open vehicle routing problem through cluster primary-route secondary approach

This study focuses on the cluster primary-route secondary approach to solve the multi-objective open green vehicle routing problem under a sustainable environment. An open green vehicle routing problem involves distributing products or services from a single depot to several customers placed at different geographical locations using third-party logistics to reduce pollution. The proposed model considers two conflicting realistic objectives: minimizing the operating costs and minimizing the carbon emission due to fuel consumption by the service vehicles. Unlike existing multi-objective problems, this multi-objective model chooses an optimal route based on the decision maker's choice from the set of alternative solutions. Initially, it clusters all the customers by applying a modified k-means algorithm. Each cluster is served by one vehicle only. Then a multi-objective evolutionary algorithm is employed to search for the best subroute to cover all the customers belonging to a cluster. We employ the extended Strength Pareto Evolutionary Algorithm (SPEA2) and Non-dominated Sorting-based Genetic Algorithm (NSGA-II) separately to obtain different approximate fronts. The VIKOR method is used to identify the decision maker's choice-based solution for each cluster. In the next step, all the compromise solutions are combined to produce the final result of the proposed problem. Some statistical analyses are performed to compare the performance of SPEA2 and NSGA-II. SPEA2 has shown better results compared to NSGA-II.