An iterated greedy algorithm for the obnoxious p-median problem

The obnoxious p-median problem (OpM) is one of the NP-hard combinatorial optimization problems, in which the goal is to find optimal places to facilities that are undesirable (e.g. noisy, dangerous, or pollutant) such that the sum of the minimum distances between each non-facility location and its nearest facility is maximized. In this paper, for the first time in the literature, Iterated Greedy (IG) metaheuristic has been applied at a higher level to solve this problem. A powerful composite local search method has also been developed by combining two fast and effective local search algorithms, namely RLS1 and RLS2, which were previously used to solve the OpM. Comprehensive experiments have been conducted to test the performance of the proposed algorithm using a common benchmark for the problem. The computational results show the effectiveness of the IG algorithm that it can find high-quality solutions in a short time. Based on the set of selected instances, the results also reveal that the developed IG algorithm outperforms most of the state-of-the-art algorithms and contributes to the literature with 5 new best-known solutions.