Comparison Study of Neighborhood Structures in Local Search for Vehicle Routing Problem with Multiple Trips and Time Windows

Abstract

This paper deals with the vehicle routing problem with multiple trips and time windows (VRPMTTW). The problem combines two features to the basic vehicle routing problem (VRP): multiple trips and time windows. The basic VRP and its variants fall into hard combinatorial optimization problems. Therefore, many heuristics have been developed to solve large problems. Local search (LS) is one of the heuristics using a neighborhood structure in order to find a better solution. This paper focuses on the comparative study of neighborhood structures applied in LS for the VRPMTTW. Two classes of neighborhood structures are compared: Tour-based and permutation-based neighborhood structures. The tour-based neighborhood structures are the neighborhoods in which the moves are performed on the solution represented by a set of tours. The permutation-based neighborhood structures are the neighborhood structures in which the moves are carried out on the solution represented by a permutation of customers. Comparing the performance of the neighborhood structures uses two responses: (1) relative improvement in the objective function value and (2) computation time. The first response is used to measure effectiveness, while the second is used as efficiency. Based on the computational experiment results, it is generally revealed that the permutation-based neighborhood structures used in LS are more effective than the tour-based neighbourhood structures. However, the permutation-based neighborhood structures are less efficient because they give higher computation times.