Identifying preferred solutions for multi-objective optimization: application to capacitated vehicle routing problem

Abstract

In this paper, the preference-based methods are proposed to solve the multi-objective optimization of the capacitated vehicle routing problem (CVRP) considering transportation time on different types of road. The objective functions are to minimize the transportation distance and time subject to capacity constraint when the transportation time depends on types of road. We perform the multi-objective optimization for CVRP in three steps. In the first step, the customer nodes are clustered according to the geographical coordinates of the nodes. Therefore, each cluster can be handled separately and in parallel by using cloud computing which is effectively applied in various applications for a large data analysis. In the second step, non-dominated sorting genetic algorithm-II which is a well-known searching algorithm is applied to find the optimal routing paths from the depot to customers in each cluster. Finally, the preference-based method is considered to identify the appropriate solutions among the trade-off solutions (the non-dominated solutions) according to the decision maker's preferences. This method expresses the decision maker's preference as the reference values or ranking of the objective functions. The algorithm is demonstrated with a well-known instance of the CVRP.