A Heuristic Procedure with Local Branching for the Fixed Charge Network Design Problem with User-optimal Flow

Pedro Henrique González, Luidi Gelabert Simonetti, Carlos Alberto de Jesus Martinhon, Philippe Yves Paul Michelon, Edcarllos Santos

2014

Abstract

Due to the constant development of society, increasing quantities of commodities have to be transported in large urban centers. Therefore, network design problems arise as tools to support decision-making, aiming to meet the need of finding efficient ways to perform the transportation of each commodity from its origin to its destination. This paper reviews a bi-level formulation, an one level formulation obtained by applying the complementary slackness theorem, Bellman’s optimality conditions and Big-M linearizing technique. A heuristic procedure is proposed, through combining a randomized constructive algorithm with a Relax-and-Fix heuristic to generate an initial solution. After that a Local Branching technique is applied to improve the constructed solution, so high quality solutions can be found. Besides that, our computational results are compared with the results found in the literature, showing the efficiency of the proposed method.

References

  1. Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. (1993). Network flows: theory, algorithms, and applications. Prentice-Hall, Inc., Upper Saddle River, NJ, USA.
  2. Aiex, R. M., R. M. G. C. and Ribeiro, C. C. (2006). Ttt plots: A perl program to create time-to-target plots. Optimization Letters.
  3. Amaldi, E., Bruglieri, M., and Fortz, B. (2011). On the hazmat transport network design problem. In Proceedings of the 5th international conference on Network optimization, INOC'11, pages 327-338, Berlin, Heidelberg. Springer-Verlag.
  4. Bazaraa, M. S., Jarvis, J. J., and Sherali, H. D. (2004). Linear Programming and Network Flows. WileyInterscience.
  5. Billheimer, J. W. and Gray, P. (1973). Network Design with Fixed and Variable Cost Elements. Transportation Science, 7(1):49-74.
  6. Boesch, F. T. (1976). Large-scale Networks: Theory and Design. IEEE Press selected reprint series, 1 edition.
  7. Boyce, D. and Janson, B. (1980). A discrete transportation network design problem with combined trip distribution and assignment. Transportation Research Part B: Methodological, 14(1-2):147-154.
  8. Colson, B., Marcotte, P., and Savard, G. (2005). Bilevel programming: A survey. 4OR, 3(2):87-107.
  9. Erkut, E. and Gzara, F. (2008). Solving the hazmat transport network design problem. Computers & Operations Research, 35(7):2234-2247.
  10. Erkut, E., Tjandra, S. A., and Verter, V. (2007). Hazardous Materials Transportation. In Handbooks in Operations Research and Management Science, volume 14, chapter 9, pages 539-621.
  11. Fischetti, M. and Lodi, A. (2003). Local branching. Mathematical Programming, 98(1-3):23-47.
  12. González, P. H., Martinhon, C. A. d. J., Simonetti, L. G., Santos, E., and Michelon, P. Y. P. (2013). Uma Metaheurística GRASP para o Problema de Planejamento de Redes com Rotas O timas para o Usuário. In XLV Simpósio Brasileiro de Pesquisa Operacional, Natal.
  13. Graves, S. C. and Lamar, B. W. (1983). An Integer Programming Procedure for Assembly System Design Problems. Operations Research, 31(3):522-545.
  14. Hettmansperger, T. P. and McKean, J. W. (1998). Robust nonparametric statistical methods. CRC Press.
  15. Holmberg, K. and Yuan, D. (2004). Optimization of Internet Protocol network design and routing. Networks, 43(1):39-53.
  16. Johnson, D. S., Lenstra, J. K., and Kan, A. H. G. R. (1978). The complexity of the network design problem. Networks, 8(4):279-285.
  17. Kara, B. Y. and Verter, V. (2004). Designing a Road Network for Hazardous Materials Transportation. Transportation Science, 38(2):188-196.
  18. Kimemia, J. and Gershwin, S. (1978). Network flow optimization in flexible manufacturing systems. In 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, pages 633-639. IEEE.
  19. Loureno, H., O. M. and S., T. (2010). Handbook of Metaheuristics, volume 146 of International Series in Operations Research & Management Science. Springer US, Boston, MA.
  20. Luigi De Giovanni (2004). The Internet Protocol Network Design Problem with Reliability and Routing Constraints. PhD thesis, Politecnico di Torino.
  21. Magnanti, T. L. (1981). Combinatorial optimization and vehicle fleet planning: Perspectives and prospects. Networks, 11(2):179-213.
  22. Magnanti, T. L. and Wong, R. T. (1984). Network Design and Transportation Planning: Models and Algorithms. Transportation Science, 18(1):1-55.
  23. Mandl, C. E. (1981). A survey of mathematical optimization models and algorithms for designing and extending irrigation and wastewater networks. Water Resources Research, 17(4):769-775.
  24. Mauttone, A., Labbé, M., and Figueiredo, R. M. V. (2008). A Tabu Search approach to solve a network design problem with user-optimal flows. In V ALIO/EURO Conference on Combinatorial Optimization, pages 1- 6, Buenos Aires.
  25. Simpson, R. W. (1969). Scheduling and routing models for airline systems. Massachusetts Institute of Technology, Flight Transportation Laboratory.
  26. Wong, R. T. (1978). Accelerating Benders decomposition for network design. PhD thesis, Massachusetts Institute of Technology.
  27. Wong, R. T. (1980). Worst-Case Analysis of Network Design Problem Heuristics. SIAM Journal on Algebraic Discrete Methods, 1(1):51-63.
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Paper Citation


in Harvard Style

Henrique González P., Gelabert Simonetti L., Alberto de Jesus Martinhon C., Yves Paul Michelon P. and Santos E. (2014). A Heuristic Procedure with Local Branching for the Fixed Charge Network Design Problem with User-optimal Flow . In Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 1: ICEIS, ISBN 978-989-758-027-7, pages 384-394. DOI: 10.5220/0004885903840394


in Bibtex Style

@conference{iceis14,
author={Pedro Henrique González and Luidi Gelabert Simonetti and Carlos Alberto de Jesus Martinhon and Philippe Yves Paul Michelon and Edcarllos Santos},
title={A Heuristic Procedure with Local Branching for the Fixed Charge Network Design Problem with User-optimal Flow},
booktitle={Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 1: ICEIS,},
year={2014},
pages={384-394},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004885903840394},
isbn={978-989-758-027-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 1: ICEIS,
TI - A Heuristic Procedure with Local Branching for the Fixed Charge Network Design Problem with User-optimal Flow
SN - 978-989-758-027-7
AU - Henrique González P.
AU - Gelabert Simonetti L.
AU - Alberto de Jesus Martinhon C.
AU - Yves Paul Michelon P.
AU - Santos E.
PY - 2014
SP - 384
EP - 394
DO - 10.5220/0004885903840394