DOI QR코드

DOI QR Code

Dynamic Programming Approach for Prize Colleting Travelling Salesman Problem with Time Windows

시간제약이 있는 상금 획득 외판원 문제에 대한 동적 계획 접근 방법

  • Tae, Hyun-Chul (Department of Industrial and Management Engineering, Pohang University of Science and Technology) ;
  • Kim, Byung-In (Department of Industrial and Management Engineering, Pohang University of Science and Technology)
  • 태현철 (포항공과대학교 산업경영공학과) ;
  • 김병인 (포항공과대학교 산업경영공학과)
  • Received : 2010.12.04
  • Accepted : 2011.04.04
  • Published : 2011.06.01

Abstract

This paper introduces one type of prize collecting travelling salesman problem with time windows (PCTSPTW), proposes a mixed integer programming model for the problem, and shows that the problem can be reduced to the elementary shortest path problem with time windows and capacity constraints (ESPPTC). Then, a new dynamic programming algorithm is proposed to solve ESPPTC quickly. Computational results show the effectiveness of the proposed algorithm.

Keywords

References

  1. Desrochers, M., Desrosiers, J., and Solomon, M. (1992), A new optimization algorithm for the vehicle routing problem with time windows, Operations Research, 40, 342-354. https://doi.org/10.1287/opre.40.2.342
  2. Dror, M. (1994), Note on the complexity of the shortest path models for column generation in VRPTW, Operations Research, 42, 977-978. https://doi.org/10.1287/opre.42.5.977
  3. Feillet, D., Dejax, P., and Gendreau, M. (2005), Traveling salesman problems with profits, Transportation Science, 39, 188-205. https://doi.org/10.1287/trsc.1030.0079
  4. Garey, M. R. and Johnson, D. S. (1979), Computers and Intractability : A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco.
  5. Houck, D., Picard, J., Queyranne, M., and Vemuganti, R. (1980), The travelling salesman problem as a constrained shortest path problem : Theory and computational experience, Opsearch, 17, 93-109.
  6. Irnich, S. and Villeneuve, D. (2003), The shortest path problem with resource constraints and k-cycle elimination for k $\geq$ 3, Cahiers du GERAD G-2003-55, HEC Montreal.
  7. Righini, G. and Salani, M. (2006), Symmetry helps : Bounded bidirectional dynamic-programming for the elementary shortest path problem with resource constraints, Discrete Optimization, 3, 255-273. https://doi.org/10.1016/j.disopt.2006.05.007
  8. Righini, G. and Salani, M. (2008), New dynamic programming algorithms for the resource constrained elementary shortest path problem, Networks, 51, 155-170. https://doi.org/10.1002/net.20212
  9. Reuven, B.-Y., Guy, E., and Shimon, S. (2005), On approximating a geometric prize-collecting traveling salesman problem with time windows. Journal of Algorithms, 55, 76-92. https://doi.org/10.1016/j.jalgor.2003.11.002
  10. Solomon, M. M. (1987), Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints, Operations Research, 35, 254-265. https://doi.org/10.1287/opre.35.3.354
  11. Tae, H. C., Jun, Y., and Kim, B.-I. (2010), A vehicle routing cost allocation problem with time windows, Working Paper.
  12. Xiaohu, S., Liupu, W., You, Z., and Yanchun, L. (2008), An Ant Colony Optimization Method for Prize-collecting Traveling Salesman Problem with Time Windows Natural Computation, Fourth International Conference on Natural Computation, 480-484.
  13. Zhang, Y. and Tang, L. (2007), Solving Prize-Collecting Traveling Salesman Problem with Time Windows by Chaotic Neural Network, ISNN '07 Proceedings of the 4th international symposium on Neural Networks : Part II-Advances in Neural Networks, 63-71.