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Less is more approach: basic variable neighborhood search for the obnoxious p ‐median problem
Author(s) -
Mladenović Nenad,
Alkandari Abdulaziz,
Pei Jun,
Todosijević Raca,
Pardalos Panos M.
Publication year - 2020
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12646
Subject(s) - benchmark (surveying) , variable neighborhood search , heuristic , mathematical optimization , local search (optimization) , set (abstract data type) , computer science , simple (philosophy) , facility location problem , mathematics , variable (mathematics) , metaheuristic , algorithm , mathematical analysis , philosophy , geodesy , epistemology , programming language , geography
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.