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Column Generation Algorithms for the Capacitated m-Ring-Star Problem

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Computing and Combinatorics (COCOON 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5092))

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Abstract

In this paper we propose an integer programming formulation for the capacitated m-ring-star problem () based on a set covering model and develop an exact branch-and-price () algorithm to solve it exactly. The is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some connection point present in a route. The set of potential connection points and the number m of vehicles are given a priori. Routing and connection costs are also known and the goal is to minimize the sum of routing and connection costs. To our knowledge, the only exact approach for the is a branch-and-cut () proposed in [2]. Extensive experimentation reported here shows that our algorithm is competitive with the algorithm. This performance was achieved after a profound investigation of the alternatives for column generation relaxation and a careful implementation of the pricing algorithm.

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References

  1. Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs (1993)

    Google Scholar 

  2. Baldacci, R., Dell’Amico, M., Salazar, J.: The Capacitated m-Ring Star Problem. Operations Research 55, 1147–1162 (2007)

    Article  MathSciNet  Google Scholar 

  3. Beasley, J., Nascimento, E.: The Vehicle Routing-Allocation Problem: A Unifying Framework. Trabajos de OPerativa 4, 65–86 (1996)

    MathSciNet  MATH  Google Scholar 

  4. Christofides, N., Mingozzi, A., Toth, P.: Exact Algorithms for the Vehicle Routing Problem, Based on Spanning Tree and Shortest Path Relaxations. Mathematical Programming 20, 255–282 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dell’Amico, M., Maffioli, F., Varbrand, P.: On Prize-Collecting Tours and the Asymmetric Travelling Salesman Problem. International Transactions in Operational Research 2(3), 297–308 (1995)

    Article  MATH  Google Scholar 

  6. Feillet, D., Dejax, P., Gendreau, M.: Traveling Salesman Problems with Profits. Transportation Science 39(2), 188–205 (2005)

    Article  Google Scholar 

  7. Fukasawa, R., Longo, H., Lysgaard, J., de Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.: Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing problem. Mathematical Programming 106(3), 491–511 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Houck, D., Picard, J., Queyranne, M., Vemuganti, R.: The Travelling Salesman Problem as a Constrained Shortest Path Problem: Theory and Computational Experience. Opsearch 17, 93–109 (1980)

    MathSciNet  MATH  Google Scholar 

  9. Irnich, S., Desaulniers, G.: Shortest Path Problems with Resource Constraints. In: Column Generation, pp. 33–65. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Irnich, S., Villeneuve, D.: The Dhortest Path Problem with Tesource Vonstraints and k-Cycle Elimination for k ≥ 3. INFORMS J. on Computing 18(3), 391–406 (2006)

    Article  MathSciNet  Google Scholar 

  11. Labbé, M., Laporte, G., Martín, I.R., González, J.S.: The Ring-Star Problem: Polyhedral Analysis and Exact Algorithm. Networks 43, 117–189 (2004)

    Article  Google Scholar 

  12. Lasdon, L.: Optimization Theory for Large Systems. Macmillan, Basingstoke (1970)

    MATH  Google Scholar 

  13. Lysgaard, J., Letchford, A., Eglese, R.: A New Branch-and-Cut Algorithm for the Capacitated Vehicle Routing problem. Mathematical Programming 100(2), 423–445 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mauttone, A., Nesmachnow, S., Olivera, A., Robledo, F.: A Hybrid Metaheuristic Algorithm to Solve the Capacitated m-Ring Star Problem. In: International Network Optimization Conference (2007)

    Google Scholar 

  15. TSPLIB, http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/tsp/

  16. Wolsey, L.A.: Integer Programming. Wiley-Interscience, Chichester (1998)

    MATH  Google Scholar 

  17. Xpress-Optimizer. Dash Optimization (2007)

    Google Scholar 

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Xiaodong Hu Jie Wang

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Hoshino, E.A., de Souza, C.C. (2008). Column Generation Algorithms for the Capacitated m-Ring-Star Problem. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_62

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  • DOI: https://doi.org/10.1007/978-3-540-69733-6_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69732-9

  • Online ISBN: 978-3-540-69733-6

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