An ant colony optimization technique for solving min–max Multi-Depot Vehicle Routing Problem

The Multi-Depot Vehicle Routing Problem (MDVRP) involves minimizing the total distance traveled by vehicles originating from multiple depots so that the vehicles together visit the specified customer locations (or cities) exactly once. This problem belongs to a class of Nondeterministic Polynomial Hard (NP Hard) problems and has been used in literature as a benchmark for development of optimization schemes. This article deals with a variant of MDVRP, called min–max MDVRP, where the objective is to minimize the tour-length of the vehicle traveling the longest distance in MDVRP. Markedly different from the traditional MDVRP, min–max MDVRP is of specific significance for time-critical applications such as emergency response, where one wants to minimize the time taken to attend any customer. This article presents an extension of an existing ant-colony technique for solving the Single Depot Vehicle Routing Problem (SDVRP) to solve the multiple depots and min–max variants of the problem. First, the article presents the algorithm that solves the min–max version of SDVRP. Then, the article extends the algorithm for min–max MDVRP using an equitable region partitioning approach aimed at assigning customer locations to depots so that MDVRP is reduced to multiple SDVRPs. The proposed method has been implemented in MATLAB for obtaining the solution for the min–max MDVRP with any number of vehicles and customer locations. A comparative study is carried out to evaluate the proposed algorithm's performance with respect to a currently available Linear Programming (LP) based algorithm in literature in terms of the optimality of solution. Based on simulation studies and statistical evaluations, it has been demonstrated that the ant colony optimization technique proposed in this article leads to more optimal results as compared to the existing LP based method.