Less is more approach: basic variable neighborhood search for the obnoxious p-median problem

Abstract

The goal of the less is more approach (LIMA) for solving optimization problems that has recently been proposed in Mladenović et al. (2016) is to find the minimum number of search ingredients that make a heuristic more efficient than the currently best. In this paper, LIMA is successfully applied to solve the obnoxious p-median problem (OpMP). More precisely, we developed a basic variable neighborhood search for solving the OpMP, where the single search ingredient, the interchange neighborhood structure, is used. We also propose a new simple local search strategy for solving facility location problems, within the interchange neighborhood structure, which is in between the usual ones: first improvement and best improvement strategies. We call it facility best improvement local search. On the basis of experiments, it appeared to be more efficient and effective than both first and best improvement. According to the results obtained on the benchmark instances, our heuristic turns out to be highly competitive with the existing ones, establishing new state-of-the-art results. For example, four new best-known solutions and 133 ties are claimed in testing the set with 144 instances. © 2019 The Authors. International Transactions in Operational Research © 2019 International Federation of Operational Research Societies15YJC630097Higher Education Discipline Innovation ProjectMinistarstvo Prosvete, Nauke i TehnoloÅ¡kog Razvoja, MPNTR: BR05236839, 044006, 174010National Natural Science Foundation of China, NSFC: 71601065, 71690235, 71521001, 71871080, 71501058This research is partially supported by Serbian Ministry of Education, Science and Technological Development under the grants nos. 174010 and 044006. In addition, this research is partially supported by the framework of the grant number BR05236839 ?Development of information technologies and systems for stimulation of personality's sustainable development as one of the bases of development of digital Kazakhstan? and by the National Natural Science Foundation of China (Nos. 71871080, 71601065, 71690235, 71501058), Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), and the Base of Introducing Talents of Discipline to Universities for Optimization and Decision-Making in the Manufacturing Process of Complex Product (111 project)