A hybrid ant colony optimization algorithm for a multi-objective vehicle routing problem with flexible time windows

In this paper, we present a multi-objective vehicle routing problem with flexible time windows (MOVRPFIexTW). In this problem, a fleet of vehicles can service a set of customers earlier and later than the required time with a given tolerance. This flexibility enables a logistics company to save distribution costs at the expense of customer satisfaction. This paper uses a direct interpretation of the vehicle routing problem with flexible time windows (VRPFIexTW) as a multi-objective problem, where the total distribution costs (including travel costs and fixed vehicle costs) are minimized and the overall customer satisfaction is maximized. We propose a solution strategy based on ant colony optimization and three mutation operators, which incorporates the concept of Pareto optimality for multi-objective optimization. The performance of the proposed approach was evaluated using the well-known benchmark Solomon's problems. Our experimental results show that the suggested approach is effective, because it provides solutions that are comparative to the best known results in the literatures. Finally, we not only highlight the advantages of MOVRPFIexTW when compared with the single objective VRPFIexTW, but also illustrate its applicability and validation by analyzing a real case. (C) 2019 Elsevier Inc. All rights reserved.