GRASP with path relinking for the symmetric Euclidean clustered traveling salesman problem

Authors:
Mário Mestria;Luiz Satoru Ochi;Simone De Lima Martins
Affiliations:
Instituto de Computação, Rua Passo da Pátria 156 - Bloco E - 3oandar - São Domingos UFF, Niterói, RJ, CEP: 24210-240, Brazil;Instituto de Computação, Rua Passo da Pátria 156 - Bloco E - 3oandar - São Domingos UFF, Niterói, RJ, CEP: 24210-240, Brazil;Instituto de Computação, Rua Passo da Pátria 156 - Bloco E - 3oandar - São Domingos UFF, Niterói, RJ, CEP: 24210-240, Brazil
Venue:
Computers and Operations Research
Year:
2013

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Abstract

In this paper, we propose new heuristics using several path-relinking strategies to solve the Clustered Traveling Salesman Problem (CTSP). The CTSP is a generalization of the Traveling Salesman Problem (TSP) in which the set of vertices is partitioned into clusters and the objective is to find a minimum cost Hamiltonian cycle such that the vertices of each cluster are visited continuously. A comparison among the performance of the several different adopted path-relinking strategies is presented using instances with up to 2000 vertices and clusters varying between 4 and 150 vertices. Also computational experiments were performed to compare the performance of the proposed heuristics with an exact algorithm and a Genetic Algorithm. The obtained computational results showed that the proposed heuristics were able to obtain competitive results related to the quality of the solutions and computational execution time.