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Cost Relaxation Using an Arc Set Likely to Construct an Optimal Solution for the Asymmetric Traveling Salesman Problem  

Kwon, Sang-Ho (삼성전자)
SaGong, Seon-Hwa (삼성전자)
Kang, Maing-Kyu (한양대학교 정보경영공학과)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.33, no.2, 2008 , pp. 17-26 More about this Journal
Abstract
The traveling salesman problem is to find tours through all cities at minimum cost ; simply visiting the cities only once that a salesman wants to visit. As such, the traveling salesman problem is a NP-complete problem ; an heuristic algorithm is preferred to an exact algorithm. In this paper, we suggest an effective cost relaxation using a candidate arc set which is obtained from a regression function for the traveling salesman problem. The proposed method sufficiently consider the characteristics of cost of arcs compared to existing methods that randomly choose the arcs for relaxation. For test beds, we used 31 instances over 100 cities existing from TSPLIB and randomly generated 100 instances from well-known instance generators. For almost every instances, the proposed method has found efficiently better solutions than the existing method.
Keywords
TSP; Cost Relaxation; Perturbation; Candidate Arc Set;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 Reinelt, G., The Traveling Salesman：Computational Solutions for TSP Applications, Springer-Verlag, Berlin, 1991
2 Applegate, D., W. Cook, and A. Rohe, "Chained Lin-Kernighan for Large Traveling Salesman Problems," Technical Report No.99887, Forschungsinstitut fur Diskrete Mathematik, University of Bonn, Germany, 1999
3 Codenotti, B., G. Manzini, L. Margara, and G. Resta, "Perturbation：An Efficient Technique for the Solution of Very Large Instances of the Euclidean TSP," INFORMS Journal on Computing, Vol.8(1996), pp.125-133   DOI   ScienceOn
4 Kwon, S.H., Y.G.G., and M.K. Kang, "Application of the Out-of-Kilter Algorithm to the Asymmetric Traveling Salesman Problem," Journal of the Operational Research Society, Vol.54, No.10(2003), pp. 1085-1092   DOI   ScienceOn
5 Cirasella, J., D. Johnson, L. McGeoch, and W. Zhang, "The Asymmetric Traveling Salesman Problem：Algorithms, Instance Generators, and Tests," Lecture Notes in Computer Science, Vol.2153(2001), pp.32-59, Springer, Berlin   DOI   ScienceOn
6 권상호, 김성민, 강맹규, "외판원문제의 국지해를 탈출하기 위한 비용완화법", 대한산업공학회지, 제30권, 제2호(2004), pp.84-92
7 김여근, 윤복식, 이상복, 메타 휴리스틱, 영지문화사, 1999
8 Zhang, W., "Depth-First Branch and Bound Versus Local Search：A Case Study," 17th national Conf. on Artificial Intelligence(AAAI-2000), pp.930-935, Austin, TX, 2000
9 Gutin, G. and A. Punnen, The Traveilng Saleman Problem and Its Variations, Springer, 2002
10 Helsgaun, K., "An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic," European Journal of Operational Research, Vol.126(2000), pp.106-130   DOI   ScienceOn
11 Reinelt, G., "TSPLIB：A Traveling Salesman Problem Library," ORSA Journal on Computing, Vol.3(1991), pp.376-384   DOI
12 Lin, S. and B.W. Kernighan, "An Effective Heuristic Algorithm for the Traveling Salesman Problem," Operations Research, Vol.21(1973), pp.498-516   DOI   ScienceOn
13 강맹규, 네트워크와 알고리듬, 박영사, 1991
14 Martin, O., S.W. Otto, and E.W. Felten, "Large-step Markov Chains for the TSP Incorporating Local Search Heuristics," Operations Research Letters, Vol.11(1992), pp.219-224   DOI   ScienceOn
15 김헌태, 권상호, 지영근, 강맹규, "비대칭 외판원 문제에서 호의 후보집합 결정", 경영과학회지, 제28권, 제2호(2003), pp.129-138
16 Blum, C. and A. Roli, "Metaheuristics in Combinatorial Optimization：Overview and Conceptual Comparison," ACM Computing Surveys, Vol.35, No.3(2003), pp.268-308   DOI   ScienceOn
17 Lin, S., "Computer Solution of Traveling Salesman Problem," Bell System Tech. Journal, Vol.44(1965), pp.2245-2269   DOI