Expanding Neighborhood GRASP for the Traveling Salesman Problem

Authors: Marinakis, Yannis¹; Migdalas, Athanasios²; Pardalos, Panos³

Source: Computational Optimization and Applications, Volume 32, Number 3, December 2005 , pp. 231-257(27)

Publisher: Springer

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Abstract:

In this paper, we present the application of a modified version of the well known Greedy Randomized Adaptive Search Procedure (GRASP) to the TSP. The proposed GRASP algorithm has two phases: In the first phase the algorithm finds an initial solution of the problem and in the second phase a local search procedure is utilized for the improvement of the initial solution. The local search procedure employs two different local search strategies based on 2-opt and 3-opt methods. The algorithm was tested on numerous benchmark problems from TSPLIB. The results were very satisfactory and for the majority of the instances the results were equal to the best known solution. The algorithm is also compared to the algorithms presented and tested in the DIMACS Implementation Challenge that was organized by David Johnson.

Keywords: Traveling Salesman Problem; Greedy Randomized Adaptive Search Procedure; local search; Meta-Heuristics

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10589-005-4798-5

Affiliations: 1: Decision Support Systems Laboratory, Department of Production Engineering and Management, Technical University of Crete, 73100, Chania, Greece, Email: marinakis@ergasya.tuc.gr 2: Decision Support Systems Laboratory, Department of Production Engineering and Management, Technical University of Crete, 73100, Chania, Greece, Email: sakis@verenike.ergasya.tuc.gr 3: Department of Industrial and Systems Engineering, University of Florida, USA, Email: pardalos@cao.ise.ufl.edu

Publication date: 2005-12-01