Parseh Designers Transportation Research Institute Quarterly Journal of Transportation Engineering 2008-6598 6 2 2014 12 22 Solving a Multi-Depot Routing Problem with Time Windows and Heterogeneous Vehicles by Multi-objective Differential Evolution Algorithm: A Case Study Solving a Multi-Depot Routing Problem with Time Windows and Heterogeneous Vehicles by Multi-objective Differential Evolution Algorithm: A Case Study 325 340 9841 FA Shaghayegh Masoudi Hasan Javanshir Reza Tavakkoli-Moghaddam 0000-0002-6757-926X Journal Article 2013 12 05 A Multi-depot Heterogeneous Vehicle Routing Problem with Time Windows (MDHVRPTW) is a variant of the Vehicle Routing Problem (VRP), in which the vehicles do not necessarily have the same capacity and they belong to different depots. Therefore, the MDHVRPTW involves designing a set of vehicle routes, each starting and ending at the depot, for a heterogeneous fleet of vehicles which services a set of customers with known demands. Most problems presented in this field are single-objective problems with the aim of minimizing the cost; however, the complexity of real problems usually doubts the use of single-objective problems. This paper considers not only the minimum travel cost, but also the distance travelled by the used vehicles and their loads. Since this problem is NP-hardness, the use of a meta-heuristic algorithm is obligatory. Therefore a meta-heuristic algorithm based on Multi-Objective Differential Evolution (MODE) is proposed. In addition, to show the efficiency of the proposed MODE, a number of test problems in small and large sizes are considered and then solved. The associated results are evaluated with the results obtained by the ε-constraint method and results showed that the gained function gap was less than 3.5% in all the solved problems. Furthermore, to run the proposed MODE, a real-case study in an oil distribution company is carried out. Finally, the obtained results are reported and discussed. A Multi-depot Heterogeneous Vehicle Routing Problem with Time Windows (MDHVRPTW) is a variant of the Vehicle Routing Problem (VRP), in which the vehicles do not necessarily have the same capacity and they belong to different depots. Therefore, the MDHVRPTW involves designing a set of vehicle routes, each starting and ending at the depot, for a heterogeneous fleet of vehicles which services a set of customers with known demands. Most problems presented in this field are single-objective problems with the aim of minimizing the cost; however, the complexity of real problems usually doubts the use of single-objective problems. This paper considers not only the minimum travel cost, but also the distance travelled by the used vehicles and their loads. Since this problem is NP-hardness, the use of a meta-heuristic algorithm is obligatory. Therefore a meta-heuristic algorithm based on Multi-Objective Differential Evolution (MODE) is proposed. In addition, to show the efficiency of the proposed MODE, a number of test problems in small and large sizes are considered and then solved. The associated results are evaluated with the results obtained by the ε-constraint method and results showed that the gained function gap was less than 3.5% in all the solved problems. Furthermore, to run the proposed MODE, a real-case study in an oil distribution company is carried out. Finally, the obtained results are reported and discussed. https://jte.sinaweb.net/article_9841_300bedd5a8a0b2f1c4bf26d3cd69cc9b.pdf