A Scatter Search Algorithm for the Split Delivery Vehicle Routing Problem

Abstract

Abstract. In this paper we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which the demands of the clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based on the scatter search methodology, produces a feasible solution using the minimum number of vehicles. The results obtained compare with the best results known up to date on a set of instances previously published in the literature.

An iterated local search heuristic for the split delivery vehicle routing problem

“…The characteristics of the instances of this set are similar to those generated by Campos et al [14], but the demand values are different.…”

“…Unfortunately, this set is no longer available. Therefore, the second set of instances that we actually considered was generated by Campos et al [14] following the same procedure employed by Archetti et al [9]. The set is composed of 49 test-problems with up to 199 customers and it is divided into seven groups.…”

“…Chen et al [15] developed a hybrid algorithm for the SDVRP-UF by combining a savings based heuristic with a mixed integer programming formulation and a record-to-record procedure. Campos et al [14] proposed a Scatter Search based algorithm for the SDVRP-LF with two different procedures for generating initial populations. Boudia et al [13] developed a Memetic Algorithm with population management for the SDVRP-UF and three new neighborhood structures especially devoted to the SDVRP.…”

“…If the sum of the residual capacities is not enough to meet the demand of i the procedure is aborted. Otherwise, for each route r A L, the least additional cost u r of inserting customer i in route r is computed (lines [12][13][14]. The problem of deciding the combination that minimizes the sum of the insertion costs in such a way that the demand of i is fully met can be seen as a knapsack problem.…”

“…The algorithm executes I Max iterations (lines [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and at each of them an initial solution is generated using an insertion-based constructive procedure (line 4). The initial solution is improved by applying a RVND procedure in the local search phase (lines 7-15).…”