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International Symposium on Experimental Algorithms

SEA 2015: Experimental Algorithms pp 181–192Cite as

Reoptimization Techniques for MIP Solvers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9125))

Abstract

Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to “warmstart” using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.

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References

  1. Achterberg, T.: Constraint Integer Programming. Ph.D. thesis, TU Berlin (2007)

    Google Scholar 

  2. Achterberg, T.: SCIP: solving constraint integer programs. Mathematical Programming Computation 1(1), 1–41 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: On the solution of traveling salesman problems. Documenta Mathematica Journal der Deutschen Mathematiker-Vereinigung Extra Volume ICM III, 645–656 (1998)

    Google Scholar 

  4. COLOR02/03/04. http://mat.gsia.cmu.edu/COLOR03/

  5. Dakin, R.J.: A tree-search algorithm for mixed integer programming problems. The Computer Journal 8(3), 250–255 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  6. Danna, E., Fenelon, M., Gu, Z., Wunderling, R.: Generating multiple solutions for mixed integer programming problems. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 280–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Operations Research 8(1), 101–111 (1960)

    Article  MATH  Google Scholar 

  8. Desrochers, M., Soumis, F.: A reoptimization algorithm for the shortest path problem with time windows. European J. Oper. Res. 35(2), 242–254 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. DIP - Decomposition for Int. Programming. https://projects.coin-or.org/Dip

  10. Fischetti, M., Lodi, A.: Mipping closures: An instant survey. Graphs and Combinatorics 23, 233–243 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fischetti, M., Lodi, A.: Optimizing over the first Chvátal closure. Math. Program., Ser. B 110, 3–20 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Frangioni, A., Manca, A.: A computational study of cost reoptimization for min cost flow problems. INFORMS Journal on Computing 18(1) (2006)

    Google Scholar 

  13. Gamrath, G.: Generic branch-cut-and-price. Master’s thesis, TU Berlin (2010)

    Google Scholar 

  14. Gamrath, G., Lübbecke, M.E.: Experiments with a generic dantzig-wolfe decomposition for integer programs. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 239–252. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. GCG - Generic Column Generation. http://www.or.rwth-aachen.de/gcg/

  16. Güzelsoy, M.: Dual methods in mixed integer linear programming. Ph.D. thesis, Lehigh University, Bethlehem, Pennsylvania, USA (2009)

    Google Scholar 

  17. Hiller, B., Klug, T., Witzig, J.: Reoptimization in branch-and-bound algorithms with an application to elevator control. In: Demetrescu, C., Marchetti-Spaccamela, A., Bonifaci, V. (eds.) SEA 2013. LNCS, vol. 7933, pp. 378–389. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Karzan, F.K., Nemhauser, G.L., Savelsbergh, M.W.P.: Information-based branching schemes for binary linear mixed integer problems. Mathematical Programming Computation 1(4), 249–293 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  19. Land, A.H., Doig, A.G.: An automatic method of solving discrete programming problems. Econometrica 28(3), 497–520 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  20. Létocart, L., Nagih, A., Plateau, G.: Reoptimization in Lagrangian methods for the 0–1 quadratic knapsack problem. Comput. Oper. Res. 39(1), 12–18 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  21. Miller-Hooks, E., Yang, B.: Updating paths in time-varying networks given arc weight changes. Transportation Science 39(4), 451–464 (2005)

    Article  Google Scholar 

  22. Ralphs, T.K., Galati, M.V.: Decomposition in integer linear programming. In: Karlof, J.K. (ed.) Integer Programming: Theory and Practice. CRC Press (2006)

    Google Scholar 

  23. Ralphs, T.K., Güzelsoy, M.: Duality and warm starting in integer programming. In: The Proceedings of the 2006 NSF Design, Service, and Manufacturing Grantees and Research Conference (2006)

    Google Scholar 

  24. Savelsbergh, M.W.P.: Preprocessing and probing techniques for mixed integer programming problems. ORSA Journal on Computing 6, 445–454 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  25. SCIP - Solving Constraint Integer Programs. http://scip.zib.de/

  26. Tanaka, M., Kobayashi, K.: MISOCP formulation and route generation algorithm for ship navigation problem. Tech. Rep. 2013–8, Tokyo Inst. of Technology (2013)

    Google Scholar 

  27. Witzig, J.: Reoptimization Techniques for MIP Solvers. Master’s thesis, TU Berlin (2014)

    Google Scholar 

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustraße 7, 14195, Berlin, Germany

    Gerald Gamrath, Benjamin Hiller & Jakob Witzig

Authors
  1. Gerald Gamrath
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  2. Benjamin Hiller
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  3. Jakob Witzig
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Corresponding author

Correspondence to Jakob Witzig .

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Editors and Affiliations

  1. Université Pierre et Marie Curie LIP6, Paris, France

    Evripidis Bampis

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Gamrath, G., Hiller, B., Witzig, J. (2015). Reoptimization Techniques for MIP Solvers. In: Bampis, E. (eds) Experimental Algorithms. SEA 2015. Lecture Notes in Computer Science(), vol 9125. Springer, Cham. https://doi.org/10.1007/978-3-319-20086-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-20086-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20085-9

  • Online ISBN: 978-3-319-20086-6

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