Authors: Brimberg, Jack
Mladenović, Nenad 
Todosijević, Raca 
Urošević, Dragan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Local and variable neighborhood searches for solving the capacitated clustering problem
Journal: Springer Optimization and Its Applications
Volume: 130
First page: 33
Last page: 55
Issue Date: 1-Jan-2017
ISBN: 978-3-319-68639-4
ISSN: 1931-6828
DOI: 10.1007/978-3-319-68640-0_3
Abstract: 
The capacitated clustering problem requires finding a partition of a given set of elements with associated positive weights into a specified number of groups (or clusters) so that the sum of diversities of the individual clusters is maximized and the sum of weights of the elements in each cluster is within some capacity limits. We examine here various neighborhood structures for conducting local search for this type of problem and then describe a powerful variable neighborhood descent (VND) that employs three of these neighborhoods in a deterministic fashion and has appeared recently in the literature as a stand-alone heuristic. We then examine some recently developed heuristics for solving the problem that are based on variable neighborhood search (VNS), including a new one that applies a recently proposed variant of VNS known as nested VNS. These heuristics all use the prescribed VND in their local improvement step. A summary is given of extensive computational tests that demonstrate the effectiveness of these VNS-based heuristics over the state of the art.
Publisher: Springer Link
Project: Mathematical Modelas and Optimization Methods on Large-Scale Systems 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Ministry of Education and Sciences, Republic of Kazakhstan, project number 01115PK00546
Natural Sciences and Engineering Research Council of Canada Discovery Grant (NSERC #205041-2014)

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