Optimization Letters

, Volume 2, Issue 3, pp 351–361 | Cite as

Expanding neighborhood search–GRASP for the probabilistic traveling salesman problem

  • Yannis Marinakis
  • Athanasios Migdalas
  • Panos M. Pardalos
Original Paper

Abstract

The Probabilistic Traveling Salesman Problem is a variation of the classic traveling salesman problem and one of the most significant stochastic routing problems. In probabilistic traveling salesman problem only a subset of potential customers need to be visited on any given instance of the problem. The number of customers to be visited each time is a random variable. In this paper, a variant of the well-known Greedy Randomized Adaptive Search Procedure (GRASP), the Expanding Neighborhood Search–GRASP, is proposed for the solution of the probabilistic traveling salesman problem. expanding neighborhood search–GRASP has been proved to be a very efficient algorithm for the solution of the traveling salesman problem. The proposed algorithm is tested on a numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the classic GRASP algorithm and with a Tabu Search algorithm are also presented. Also, a comparison is performed with the results of a number of implementations of the Ant Colony Optimization algorithm from the literature and in six out of ten cases the proposed algorithm gives a new best solution.

Keywords

Expanding neighborhood search–GRASP Metaheuristics Probabilistic traveling salesman problem 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Yannis Marinakis
    • 1
  • Athanasios Migdalas
    • 1
  • Panos M. Pardalos
    • 2
  1. 1.Decision Support Systems Laboratory, Department of Production Engineering and ManagementTechnical University of CreteChaniaGreece
  2. 2.Department of Industrial and Systems Engineering, Center of Applied OptimizationUniversity of FloridaGainesvilleUSA

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