A Multiobjective Evolutionary Approach to Solving Single-Allocation Hub Median Problem

Abstract

This article presents a multiobjective formulation for the well-known Single-Allocation Hub Median Problem (MO-SA-H-MP). The objective of MO-SA-H-MP is to develop a three-level architecture consisting of demand nodes, hubs, and central hubs, for reducing transportation costs among nodes, while considering two objectives. The first objective is focused on reducing the overheads associated with hubs and central hubs, while the second objective is aimed at reducing transportation costs among nodes. The paper uses two approaches to solve MO-SA-H-MP. The first approach is based on the NSGA-II algorithm, while the second approach uses a Genetic Algorithm (GA) with a local refinement-based technique to solve each objective separately. The resultant network obtained from GA is applied to the other objective, and the solutions of both approaches are compared. The NSGA-II-based approach is found to perform equivalently to the exact method in 48.32% of cases, perform better than the indirect approach of solving each objective separately in more than 81.67% of cases, and have a deviation of less than 10% in 67.50% of cases from the direct approach for solving each objective separately using the Refined GA-based technique.