Authors: Elshaikh, Abdalla
Salhi, Said
Brimberg, Jack
Mladenović, Nenad 
Callaghan, Becky
Nagy, Gábor
Title: An adaptive perturbation-based heuristic: An application to the continuous p-centre problem
Journal: Computers and Operations Research
Volume: 75
First page: 1
Last page: 11
Issue Date: 1-Nov-2016
Rank: M21
ISSN: 0305-0548
DOI: 10.1016/j.cor.2016.04.018
A self-adaptive heuristic that incorporates a variable level of perturbation, a novel local search and a learning mechanism is proposed to solve the p-centre problem in the continuous space. Empirical results, using several large TSP-Lib data sets, some with over 1300 customers with various values of p, show that our proposed heuristic is both effective and efficient. This perturbation metaheuristic compares favourably against the optimal method on small size instances. For larger instances the algorithm outperforms both a multi-start heuristic and a discrete-based optimal approach while performing well against a recent powerful VNS approach. This is a self-adaptive method that can easily be adopted to tackle other combinatorial/global optimisation problems. For benchmarking purposes, the medium size instances with 575 nodes are solved optimally for the first time, though requiring a large amount of computational time. As a by-product of this research, we also report for the first time the optimal solution of the vertex p-centre problem for these TSP-Lib data sets.
Keywords: Adaptive search | Continuous space | Large instances | Optimal solutions | p-centre problem | Perturbation search
Publisher: Elsevier
Project: UK Research Council EPSRC (EP/I009299/1)
Natural Sciences & Engineering Research Council of Canada Discovery Grant (NSERC #20541 – 2008)
Russian Federation Grant RFS 14-41-00039
National Council for Scientific and Technological Development – CNPq/Brazil grant number 400350/2014-9
Spanish Ministry of Economy and Competitiveness, research project MTM2015-70260-P

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