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Decomposition-based exact algorithms for risk-constrained traveling salesman problems with discrete random arc costs

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Abstract

Recently increasing attentions have been given to uncertainty handling in network optimization research. Along this trend, this paper discusses traveling salesman problem with discrete random arc costs while incorporating risk constraints. Minimizing expected total cost might not be enough because total costs of some realizations of the random arc costs might exceed the resource limit. To this respect, this paper presents a model of the traveling salesman problem that incorporates risk constraints based on Conditional Value at Risk to evaluate those worst-cost scenarios. Exact solution methods are developed and applied on the risk-constrained traveling salesman problem. Numerical experiments are conducted, and the results show the ability of the proposed methods in reducing the computational complexity.

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References

  1. Alexander, G.J., Baptista, A.M.: A comparison of VAR and CVaR constraints on portfolio selection with the mean-variance model. Manag. Sci. 50(9), 1261–1273 (2004)

    Article  Google Scholar 

  2. Arulselvan, A., Commander, C.W., Pardalos, P.: A hybrid genetic algorithm for the target visitation problem (2007)

  3. Bertsimas, D.J.: A vehicle routing problem with stochastic demand. Oper. Res. 40, 574–585 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Boginski, V.L., Commander, C.W., Turko, T.: Polynomial-time identication of robust network flows under uncertain arc failures. Optim. Lett. 3, 461–473 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Boyles, S.D., Waller, S.T.: A mean-variance model for the minimum cost flow problem with stochastic arc costs. Networks 56(3), 215–227 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fan, N., Zheng, Q.P., Pardalos, P.M.: Robust optimization of graph partitioning involving interval uncertainty. Theor. Comput. Sci. 447, 53–61 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Glockner, G.D., Nemhauser, G.L., Tovey, C.A.: Dynamic network flow with uncertain arc capacities: decomposition algorithm and computational results. Comput. Optim. Appl. 18(3), 233–250 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Laporte, G.: A concise guide to the traveling salesman problem. J. Oper. Res. Soc. 61, 35–40 (2010)

    Article  MATH  Google Scholar 

  9. Leipälä, T.: On the solutions of stochastic traveling salesman problems. Eur. J. Oper. Res. 2(4), 291–297 (1978)

  10. Levy, D., Sundar, K., Rathinam, S.: Heuristics for routing heterogeneous unmanned vehicles with fuel constraints. Math. Probl. Eng. 2014, 1–12, Art ID 131450 (2014)

  11. Marlow, D.O., Kilby, P., Mercer, G.N.: The travelling salesman problem in maritime surveillance-techniques, algorithms and analysis. In: Proceedings of the International Congress on Modelling and Simulation, pp. 684–690 (2007)

  12. Mendoza, J.E., Villegas, J.G.: A multi-space sampling heuristic for the vehicle routing problem with stochastic demands. Optim. Lett. 7, 1503–1516 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. Oberlin, P., Rathinam, S., Darbha, S.: Today’s traveling salesman problem: heterogeneous, multiple depot, multiple uav routing problem. IEEE Robot. Autom. Mag. 17, 70–77 (2010)

    Article  Google Scholar 

  14. Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2(3), 21–42 (2000)

    Google Scholar 

  15. Ryan, J.L., Bailey, T.G., Moore, J.T., Carlton, W.B.: Reactive tabu search in unmanned aerial reconnaissance simulations. In: Proceedings of the I998 Winter Simulation Conference, vol. 1, pp. 873–879 (1998)

  16. Sarykalin, S., Serraino, G., Uryasev, S.: Value-at-risk vs. conditional value-at-risk in risk management and optimization. In: INFORMS Tutorial in Operations Research, pp. 270–294 (2008)

  17. Toriello, A., Haskell, W.B., Poremba, M.: A dynamic traveling salesman problem with stochastic arc costs. Oper. Res. (2014). http://dx.doi.org/10.1287/opre.2014.1301

  18. Verweij, B., Ahmed, S., Kleywegt, A.J., Nemhauser, G., Shapiro, A.: The sample average approximation method applied to stochastic routing problems: a computational study. Comput. Optim. Appl. 24(2), 289–333 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yadlapalli, S., Rathinam, S., Darbha, S.: 3-approximation algorithm for a two depot, heterogeneous traveling salesman problem. Optim. Lett. 6, 141–152 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zheng, Q.P., Pardalos, P.M.: Stochastic and risk management models and solution algorithm for natural gas transmission network expansion and lng terminal location planning. J. Optim. Theory Appl. 147, 337–357 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Zheng, Q.P., Shen, S., Shi, Y.: Loss-constrained minimum cost flow under arc failure uncertainty with applications in risk-aware kidney exchange (2014, submitted)

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Acknowledgments

This work is in part supported by the AFRL Mathematical Modeling and Optimization Institute, and National Science Foundation through Grant CMMI-1355939. The authors would also like to thank the reviewers and Editors for their helpful suggestions and comments.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, USA

    Zhouchun Huang & Qipeng P. Zheng

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  1. Zhouchun Huang
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  2. Qipeng P. Zheng
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Correspondence to Qipeng P. Zheng.

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Huang, Z., Zheng, Q.P. Decomposition-based exact algorithms for risk-constrained traveling salesman problems with discrete random arc costs. Optim Lett 9, 1553–1568 (2015). https://doi.org/10.1007/s11590-014-0798-7

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  • DOI: https://doi.org/10.1007/s11590-014-0798-7

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