An Ant Colony-Based Matheuristic Approach for Solving a Class of Vehicle Routing Problems

Abstract

Abstract. We propose a matheuristic approach to solve several types of vehicle routing problems (VRP). In the VRP, a fleet of capacitated vehicles visits a set of customers exactly once to satisfy their demands while obeying problem specific characteristics and constraints such as homogeneous or heterogeneous fleet, customer service time windows, single or multiple depots. The proposed matheuristic is based on an ant colony optimization (ACO) algorithm which constructs good feasible solutions. The routes obtained in the ACO procedure are accumulated in a pool as columns which are then fed to an integer programming (IP) optimizer that solves the set-partitioning (-covering) formulation of the particular VRP. The (near-)optimal solution found by the solver is used to reinforce the pheromone trails in ACO. This feedback mechanism between the ACO and IP procedures helps the matheuristic better converge to high quality solutions. We test the performance of the proposed matheuristic on different VRP variants using well-known benchmark instances from the literature. Our computational experiments reveal competitive results: we report six new best solutions and meet the best-known solution in 120 instances out of 193. Keywords: Vehicle routing problem · Matheuristic · Ant colony optimization IntroductionThere is an increasing trend towards matheuristics in the recent literature as they incorporate relatively fast and effective solutions while preserving the solution quality. Matheuristics can do so by combining heuristics/metaheuristics with exact solution approaches. According to Boschetti et al. (2009), the interoperation of metaheuristics and mathematical programming techniques yields the matheuristics. The metaheuristic further exploits the features derived by the mathematical model of the problem. Bertazzi and Speranza (2011) simply define a matheuristic as any heuristic that uses mathematical programming in one of its solution steps such as solving sub-problems, solving parts of an instance, restricting the search space and exploring neighborhoods.

The Vehicle Routing Problem with Ftl and Ltl Carriers

“…The use of SPP as a postoptimization technique is reported in (Mancini, 2017;Gschwind and Drexl, 2019). The hybridization with heuristics is reported in many papers including (Prescott-Gagnon et al, 2009;Groër et al, 2011;Mendoza and Villegas, 2013;Subramanian et al, 2013;Parragh and Schmid, 2013;Yıldırım and Çatay, 2015;Grangier et al, 2017;Tellez et al, 2018;Dumez et al, 2021).…”

“…The solution obtained is repaired if a customer is served more than once. Yıldırım and Çatay (2015) showed that solving an SCP instead of an SPP slightly shortens solving time. Additionally, an exact reparation is rarely needed and a greedy procedure generally finds the optimal reparation.…”