Solving a New Mathematical Model for a Multi-Objective and Multi-Depot Vehicle Routing Problem by a Non-dominated Sorting Genetic Algorithm

The vehicle routing problem (VRP) can be studied in variant cases, in which two related important problems are the VRP with hard time windows and the multi-depot VRP with heterogeneous vehicles. Most problems presented in this field are single-objective problems with the aim of the minimum 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 the NP-hard one, the non-dominated sorted genetic algorithm - II is used. To show its efficiency for solving small-sized problems, the obtained results are evaluated with the results obtained by the ε-constraint method. The results show that the obtained gap of the objective function values is less than 4% in all the solved problems indicating the efficiency of the proposed algorithm.