In this paper, we are interested in studying the Maximum Dispersion Problem (MaxDP). In this problem, a set of objects are given such that each object has a non-negative weight. The objective of the MaxDP consists in partitioning the given set of objects into a predefined number of classes. The partitioning is subject to some conditions. First, the overall dispersion of objects, assigned to each class, must be maximized. Second, there is a predefined target weight assigned to each class and the total weight of each class must belong to an interval surrounding its target weight. It has been proven that the MaxDP is NP-hard and, consequently, difficult to solve by classical exact methods. In this paper, we provide a Variable Neighborhood Search (VNS) algorithm for solving the MaxDP. In order to evaluate the efficiency of the introduced VNS, we carried out numerical experiments on randomly generated instances. Then, we compared the results of our VNS algorithm with those provided by the standard solver Gurobi. According to our results, our VNS algorithm provides high-quality solutions within a short computation time and dominates the solver Gurobi.
Maximum Dispersion Problem Heuristic Variable Neighborhood Search Local Search
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The authors acknowledge the chair of Business Information Systems and Operations Research (BISOR) at the TU-Kaiserslautern (Germany) for the financial support, through the research program “CoVaCo”.
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