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6. AcknowledgementThis work was supported primarily by the National Science Council of Taiwan under GrantNSC 96-2416-H-260-008. The author is indebted to Dr. Elise Miller-Hooks for providing mewith the test instances to be used in this paper.7. ReferencesBäck , T.; Fogel, D. B. & Michalewicz, Z. (1997).Handbook of Evolutionary Computation, OxfordUniversity Press, 0-75030392-1, Bristol, UK.Balakrishnan, P. V.; Gupta, R. & Jacob, V. S. (2006). An investigation of mating andpopulation maintenance strategies in hybrid genetic heuristics for product linedesigns.Computers & Operations Research,Vol. 33, No. 3, 639-659, ISSN: 0305-0548.Bartholdi, J. J. & Platzman, L. K. (1988). Heuristics based on spacefilling curves forcombinatorial problems in Euclidean space.Management Science, Vol. 34, No. 3, 291-305, ISSN: 0025-1909.Bartholdi, J. J.; Platzman, L. K.; Collins, R. L. & Warden, W. H. (1983). A minimal technologyrouting system for meals on wheels.Interfaces, Vol. 13, No. 3, 1-8, ISSN: 0092-2102.Basso, D.; Chiarandini, M. & Salmaso L. (2007). Synchronized permutation tests in replicatedI × J designs.Journal of Statistical Planning and Inference, Vol. 137, No. 8, 2564-2578,ISSN: 0378-3758.Bertsimas, D. (1988).Probabilistic combinatorial optimization problems, Ph.D. dissertation,Massachusetts Institute of Technology, MA, USA.Bertsimas, D.; Chervi, P. & Peterson, M. (1995). Computational approaches to stochasticvehicle routing problems.Transportation Science, Vol. 29, No. 4, 342-352, ISSN: 0041-1655.Bertsimas, D. & Howell, L. (1993). Further results on the probabilistic traveling salesmanproblem.European Journal of Operational Research,Vol. 65, No. 1, 68-95, ISSN: 0377-2217.Bertsimas, D.; Jaillet, P. & Odoni, A. R. (1990). A priori optimization.Operations Research,Vol. 38, No. 6, 1019-1033, ISSN: 0030-364X.Bianchi, L. (2006).Ant colony optimization and local search for the probabilistic traveling salesmanproblem: a case study in stochastic combinatorial optimization. Ph.D. dissertation,Université Libre de Bruxelles, Brussles, Belgium.
Solving the Probabilistic Travelling Salesman Problem Based on Genetic Algorithmwith Queen Selection Scheme171Bowler, N. E.; Fink, T. M. A. & Ball, R. C. (2003). Characterization of the probabilistictraveling salesman problem.Physical Review E, Vol. 68, 036703, ISSN: 1539-3755.Branke, J. & Guntsch, M. (2004). Solving the probabilistic TSP with ant colony optimization.Journal of Mathematical Modelling and Algorithms, Vol. 3, No. 4, 403-425, ISSN: 1570-1166.Campbell, A. M. (2006). Aggregation for the probabilistic traveling salesman problem.Computers & Operations Research,Vol. 33, No. 9, 2703-2724, ISSN: 0305-0548.Davis, L. (1991).Handbook of Genetic Algorithms. Van Nostrand Reinhold, ISBN: 0442001738,New York.Goldberg, D. E. (1989).Genetic Algorithms in Search, Optimization, and Machine Learning,Addison-Wesley, ISBN: 0201157675, Reading, PA.Holland, J. H. (1992).Adaptation in Natural and Artificial Systems: An Introductory Analysiswith Applications to Biology, Control, and Artificial Intelligence, MIT Press, ISBN:0262581116, Boston, MA.Jaillet, P. (1985).Probabilistic traveling salesman problems, Ph.D. dissertation, MassachusettsInstitute of Technology, MA, USA.

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Test, Ant colony optimization, Travelling salesman problem, NP complete, TSP, Combinatorial optimization

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