Abstract
Problem solving under uncertainty has a high impact on the real-world applications, since most real-world optimization problems are inherently dynamic and stochastic. Today, uncertainty and dynamism have become more relevant in many practical applications. This chapter describes how to use the ABSS to solve the probabilistic TSP, based on simulation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Applegate, D. L., Bixby, R. E., Chvátal, V., & Cook, W. J. (2006). The traveling salesman problem: A computational study. Princeton University Press.
Balaprakash, P., Piratari, M., Stützle, T., & Dorigo, M. (2009). Adaptive sample size and importance sampling in estimation-based local search for the probabilistic traveling salesman problem. European Journal of Operational Research, 199(1), 98–110. https://doi.org/10.1016/j.ejor.2008.11.027
Balaprakash, P., Piratari, M., Stützle, T., & Dorigo, M. (2010). Estimation-based metaheuristics for the probabilistic traveling salesman problem. Computer & Operations Research, 37(1), 1939–1951. https://doi.org/10.1016/j.cor.2009.12.005
Bertsimas, D. (1988). Probabilistic combinatorial optimization problems. PhD Dissertation. Boston: Department of Mathematics, Massachusetts Institute of Technology
Bertsimas, D., Jaillet, P., & Odoni, A. R. (1990). A priori optimization. Operations Research, 38(6), 1019–1033. https://doi.org/10.1287/opre.38.6.1019
Bertsimas, D., & Howell, L. H. (1993). Further results on the probabilistic traveling salesman problem. European Journal of Operational Research, 65(1), 68–95. https://doi.org/10.1016/0377-2217(93)90145-D
Besu, M. M., & Raghavarao, D. (1990). Sample size methodology. Academic Press.
Binachi, L. (2006). Ant colony optimization and local search for the probabilistic traveling salesman problem: A case study in stochastic combinatorial optimization. Ph.D Dissertation. Brussels, Belgium: Universite Libre de Bruxelles
Binachi, L., & Campbell, A. M. (2007). Extension of the 2-p-opt and 1-shift algorithm to the heterogeneous probabilistic traveling salesman problem. European Journal of Operational Research, 176(1), 131–144. https://doi.org/10.1016/j.ejor.2005.05.027
Binachi, L., Dorigo, M., Gambardella, L. M., & Gutjahr, W. J. (2009). A survey on metaheuristics for stochastic combinatorial optimization. Natural Computing, 8, 239–287. https://doi.org/10.1007/s11047-008-9098-4
Binachi, L., Gambardella, L. M., & Dorigo, M. (2002). An ant colony optimization approach to the probabilistic traveling salesman problem. In: Proceedings of the 7th International Conference on Parallel Problem Solving from Nature, LNCS (vol. 2439, pp. 883–892). Berlin: Springer. https://doi.org/10.1007/3-540-45712-7_85
Binachi, L., Gambardella, L. M., & Dorigo, M. (2002). Solving the homogeneous probabilistic traveling salesman problem by the ACO metaheuristic. In: M. Marco Dorigo, G. Di Caro, & M. Sampels (Eds.), Proceedings of the 3rd International Workshop on Ant Algorithms, LNCS (vol. 2463, pp. 176–187). London: Springer
Binachi, L., Knowles, J., & Bowler, N. E. (2005). Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms. European Journal of Operational Research, 162(1), 206–219. https://doi.org/10.1016/j.ejor.2003.10.016
Birattari, M., Balaprakash, P., & Dorigo, M. (2005). ACO/F-Race: ant colony optimization and racing techniques for combinatorial optimization under uncertainly. In: K. F. Doerner, M. Gendreau, P. Greistorfer, W. J. Gutjahr, R. F. Hartl, & M. Reimann (Eds.), Proceedings of the 6th Metaheuristics International Conference (pp. 107–112)
Birattari, M., Balaprakash, P., & Dorigo, M. (2006). The ACO-F-race algorithm for combinatorial optimization under uncertainty. In: K. F. Doerner, M. Gendreau, P. Greistorfer, W. J. Gutjahr, R. F. Hartl, & M. Reimann (Eds.), Metaheuristics–progress in complex systems optimization. operations research/computer science interfaces series (pp. 189–203). Berlin: Springer
Birattari, M., Balaprakash, P., Stützle, T., & Dorigo, M. (2008). Estimation-based local search for stochastic combinatorial optimization using delta evaluations: A case study on the probabilistic traveling salesman problem. INFORMS Journal on Computing, 20(4), 644–658. https://doi.org/10.1287/ijoc.1080.0276
Bowler, N. E., Fink, T. M., & Ball, R. C. (2003). Characterization of the probabilistic traveling salesman problem. Physical Review E, 68(3), 1–7. https://doi.org/10.1103/PhysRevE.68.036703
Branke, J., & Guntsch, M. (2005). Solving the probabilistic TSP with ant colony optimization. Journal Mathematical Modeling and Algorithms, 3, 403–425. https://doi.org/10.1007/s10852-005-2585-z
Campbell, A. M. (2006). Aggregation for the probabilistic traveling salesman problem. Computers & Operations Research, 33(9), 2703–2724. https://doi.org/10.1016/j.cor.2005.02.024
Choi, J., Lee, J. H., & Realff, M. J. (2004). An algorithmic framework for improving heuristic solutions: Part II, a new version of the stochastic traveling salesman problem. Computers & Chemical Engineering, 28(8), 1297–1307. https://doi.org/10.1016/j.compchemeng.2003.09.002
Gutjahr, W. J. (2003). A converging ACO algorithm for stochastic combinatorial optimization. In: A. Albrecht, K. Steinhöfel (Eds.), Proceedings of the 2nd Symposium on Stochastic Algorithms, Foundations and Applications, LNCS (vol. 2827, pp. 10–25). Berlin: Springer
Gutjahr, W. J. (2004). S-ACO: an ant-based approach to combinatorial optimization under uncertainty. In: M. Dorigo, M. Biraattari, C. Blum, L. M. Gambardella, F. Mondada, & T. Stützle (Eds.), Proceedings of the 4th International Workshop on Ant Colony Optimization and Swarm Intelligence, LNCS (vol. 3172, pp. 238–249). Berlin: Springer
Homem-de-Mello, T. (2003). Variable-sample methods for stochastic optimization. ACM Transactions on Modeling and Computer Simulation 13(2), 108–133.https://doi.org/10.1145/858481.858483
Jaillet, P. (1985). Probabilistic traveling salesman problems. PhD Thesis. Massachusetts Institute of Technology
Jaillet, P. (1988). A priori solution of a traveling salesman problem in which a random subset of the customers are visited. Operations Research 36(6), 929–936.https://doi.org/10.1287/opre.36.6.929
Jaillet, P. (1993). Analysis of probabilistic combinatorial optimization problems in Euclidean spaces. Mathematics of Operations Research, 18(1), 51–70
Jaillet, P., & Odoni, A. R. (1988). The probabilistic vehicle routing problem. Vehicle Routing: Methods and Studies (pp. 293–318). North-Holland.
Jézéquel, A. (1985). Probabilistic Vehicle Routing Problems. Master thesis. Boston: Massachusetts Institute of Technology
Kleywegy, A. J., Shapiro, A., & Homem-de-Mello, T. (2001). The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization, 12(2), 479–502. https://doi.org/10.1137/S1052623499363220
Laporte, G., Louveaux, F. V., & Mercure, H. (1994). A priori optimization of the probabilistic traveling salesman problem. Operations Research, 42(3), 543–549. https://doi.org/10.1287/opre.42.3.543
Lindley, D. V. (1997). The choice of sample size. The Statistician, 46(2), 129–138. https://doi.org/10.1111/1467-9884.00068
Liu, Y.-H. (2007). A hybrid scatter search for the probabilistic traveling salesman problem. Computers & Operations Research, 34(10), 2949–2963. https://doi.org/10.1016/j.cor.2005.11.008
Liu, Y.-H. (2008). Diversified local search strategy under scatter search framework for the probabilistic traveling salesman problem. European Journal of Operational Research, 192(2), 332–346. https://doi.org/10.1016/j.ejor.2007.08.023
Liu, Y.-H. (2008). Solving the probabilistic traveling salesman problem based on genetic algorithm with queen selection scheme. In F. Greco (Ed.), Traveling Salesman Problem (pp. 157–172). Intech.
Liu, Y. -H. (2008). A memetic algorithm for the probabilistic traveling salesman problem. In: IEEE Congress on Evolutionary Computation (CEC2008), pp. 146–152, IEEE Press
Liu, Y.-H., Jou, R.-C., Wang, C.-C., & Chiu, C.-S. (2007). An evolutionary algorithm with diversified crossover operator for the heterogeneous probabilistic TSP. In J. G. Carbonell & J. Siekmann (Eds.), Modeling decisions for artificial intelligence MDAI 2007, LNCS (Vol. 4617, pp. 351–360). Springer.
Marinakis, Y., & Marinaki, M. Y. (2010). A hybrid multi-swarm particle swarm optimization algorithm for the probabilistic traveling salesman problem. Computer & Operations Research, 37(3), 432–442. https://doi.org/10.1016/j.cor.2009.03.004
Marinakis, Y., Migdalas, A., & Pardalos, P. M. (2008). Expanding neighborhood search GRASP for the probabilistic traveling salesman problem. Optimization Letters, 2, 351–361. https://doi.org/10.1007/s11590-007-0064-3
Rossi, F., & Gavioli, F. (1987). Aspects of heuristic methods in the probabilistic traveling salesman problem. Advanced school on stochastic in combinatorial optimization (pp. 214–227). World Scientific.
Shapiro, A., & Homem-de-Mello, T. (1998). A simulation-based approach to two-stage stochastic programming with recourse. Mathematical Programming 81, 301–325.https://doi.org/10.1007/BF01580086
Sudman, S. (1976). Applied sampling. Academic Press.
Verweij, B., Ahmed, S., Kleywegt, A. J., Nemhauser, G., & Shapiro, A. (2003). The sample average approximation method applied to stochastic routing problems: A computational study. Computational Optimization and Applications, 24, 289–333. https://doi.org/10.1023/A:1021814225969
Walson. (2001). How to determine a sample size. Tipsheet #60. Penn State Cooperative extension, University Park
Weiler, C., Biesinger, B., Hu, B., & Raidl, G. R. (2015). Heuristic approaches for the probabilistic traveling salesman problem. In: Computer Aided Systems Theory–EUROCAST 2015. LNCS (vol. 9520, pp. 342–349). Berlin: Springer. https://doi.org/10.1007/978-3-319-27340-2_43
Weyland, D., Bianchi, L., & Gambardella, L. M. (2009). New approximation-based local search algorithms for the probabilistic traveling salesman problem. In: Computer Aided Systems Theory–EUROCAST 2009, LNCS (vol. 5717, pp. 681–688). Heidelberg: Springer. https://doi.org/10.1007/978-3-642-04772-5_88
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Li, W. (2024). Solving Probabilistic Traveling Salesman Problem. In: The Traveling Salesman Problem. Synthesis Lectures on Operations Research and Applications. Springer, Cham. https://doi.org/10.1007/978-3-031-35719-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-35719-0_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-35718-3
Online ISBN: 978-3-031-35719-0
eBook Packages: Synthesis Collection of Technology (R0)