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The Reformulation-Optimization Software Engine

  • Conference paper
Mathematical Software – ICMS 2010 (ICMS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6327))

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Abstract

Most optimization software performs numerical computation, in the sense that the main interest is to find numerical values to assign to the decision variables, e.g. a solution to an optimization problem. In mathematical programming, however, a considerable amount of symbolic transformation is essential to solving difficult optimization problems, e.g. relaxation or decomposition techniques. This step is usually carried out by hand, involves human ingenuity, and often constitutes the “theoretical contribution” of some research papers. We describe a Reformulation- Optimization Software Engine (ROSE) for performing (automatic) symbolic computation on mathematical programming formulations.

Supported by grants: ANR 07-JCJC-0151 “ARS”, Digiteo 2009-14D “RMNCCO”, Digiteo 2009-55D “ARM”. We acknowledge the contributions of Dr. C. D’Ambrosio (University of Bologna) and of Mr. P. Janes (Australian National University).

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References

  1. Fourer, R., Gay, D.: The AMPL Book. Duxbury Press, Pacific Grove (2002)

    Google Scholar 

  2. Lougee-Heimer, R.: The common optimization interface for operations research: Promoting open-source software in the operations research community. IBM Journal of Research and Development 47(1), 57–66 (2003)

    Article  Google Scholar 

  3. Liberti, L.: Writing global optimization software. In: Liberti, L., Maculan, N. (eds.) Global Optimization: from Theory to Implementation, pp. 211–262. Springer, Berlin (2006)

    Google Scholar 

  4. Belotti, P., Lee, J., Liberti, L., Margot, F., Wächter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optimization Methods and Software 24(4), 597–634 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Schichl, H., Neumaier, A.: Interval analysis on directed acyclic graphs for global optimization. Journal of Global Optimization 33(4), 541–562 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fukuda, K., Prodon, A.: Double description method revisited. In: Deza, M., Manoussakis, I., Euler, R. (eds.) CCS 1995. LNCS, vol. 1120, pp. 91–111. Springer, Heidelberg (1996)

    Google Scholar 

  7. Christof, T., Löbel, A.: The porta manual page. Technical Report v. 1.4.0, ZIB, Berlin (1997)

    Google Scholar 

  8. Sahinidis, N., Tawarmalani, M.: BARON 7.2.5: Global Optimization of Mixed-Integer Nonlinear Programs, User’s Manual (2005)

    Google Scholar 

  9. Brook, A., Kendrick, D., Meeraus, A.: GAMS, a user’s guide. ACM SIGNUM Newsletter 23(3-4), 10–11 (1988)

    Article  Google Scholar 

  10. Orban, D., Fourer, R.: Dr. AMPL: a meta solver for optimization (2004) (Presentation slides)

    Google Scholar 

  11. Colombo, M., Grothey, A., Hogg, J., Woodsend, K., Gondzio, J.: A structure-conveying modelling language for mathematical and stochastic programming. Mathematical Programming Computation 1(4), 223–247 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kucherenko, S., Belotti, P., Liberti, L., Maculan, N.: New formulations for the kissing number problem. Discrete Applied Mathematics 155(14), 1837–1841 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Maculan, N., Michelon, P., MacGregor Smith, J.: Bounds on the kissing numbers in ℝn: Mathematical programming formulations. Technical report, University of Massachusetts, Amherst, USA (1996)

    Google Scholar 

  14. Gill, P.: User’s guide for SNOPT version 7. Systems Optimization Laboratory, Stanford University, California (2006)

    Google Scholar 

  15. Liberti, L.: Symmetry in mathematical programming. In: Lee, J., Leyffer, S. (eds.) Mixed Integer Nonlinear Programming, vol. IMA, Springer, New York (accepted)

    Google Scholar 

  16. Bachoc, C., Vallentin, F.: New upper bounds for kissing numbers from semidefinite programming. Journal of the American Mathematical Society 21, 909–924 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  17. Liberti, L.: Reformulations in mathematical programming: Definitions and systematics. RAIRO-RO 43(1), 55–86 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Liberti, L., Cafieri, S., Tarissan, F.: Reformulations in mathematical programming: A computational approach. In: Abraham, A., Hassanien, A.E., Siarry, P., Engelbrecht, A. (eds.) Foundations of Computational Intelligence. SCI, vol. 3, 203, pp. 153–234. Springer, Berlin (2009)

    Chapter  Google Scholar 

  19. Fortet, R.: Applications de l’algèbre de Boole en recherche opérationelle. Revue Française de Recherche Opérationelle 4, 17–26 (1960)

    Google Scholar 

  20. Smith, E., Pantelides, C.: A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Computers & Chemical Engineering 23, 457–478 (1999)

    Article  Google Scholar 

  21. D’Ambrosio, C., Frangioni, A., Liberti, L., Lodi, A.: Experiments with a feasibility pump approach for nonconvex MINLPs. In: Festa, P. (ed.) Experimental Algorithms. LNCS, vol. 6049, pp. 350–360. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Fischetti, M., Lodi, A.: Local branching. Mathematical Programming 98, 23–37 (2005)

    Article  MathSciNet  Google Scholar 

  23. McKay, B.: Nauty User’s Guide (Version 2.4). Computer Science Dept., Australian National University (2007)

    Google Scholar 

  24. The GAP Group: GAP – Groups, Algorithms, and Programming, Version 4.4.10 (2007)

    Google Scholar 

  25. Liberti, L.: Spherical cuts for integer programming problems. International Transactions in Operational Research 15, 283–294 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Cafieri, S., Lee, J., Liberti, L.: Comparison of convex relaxations of quadrilinear terms. In: Ma, C., Yu, L., Zhang, D., Zhou, Z. (eds.) Global Optimization: Theory, Methods and Applications I. Lecture Notes in Decision Sciences, vol. 12(B), pp. 999–1005. Global-Link Publishers, Hong Kong (2009)

    Google Scholar 

  27. Cafieri, S., Lee, J., Liberti, L.: On convex relaxations of quadrilinear terms. Journal of Global Optimization, doi: 10.1007/s10898-009-9484-1

    Google Scholar 

  28. Liberti, L.: Reformulations in mathematical programming: Automatic symmetry detection and exploitation. Mathematical Programming, doi: 10.1007/s10107-010-0351-0

    Google Scholar 

  29. Costa, A., Hansen, P., Liberti, L.: Formulation symmetries in circle packing. In: Mahjoub, R. (ed.) Proceedings of the International Symposium on Combinatorial Optimization. Electronic Notes in Discrete Mathematics. Elsevier, Amsterdam (accepted)

    Google Scholar 

  30. Costa, A., Hansen, P., Liberti, L.: Static symmetry breaking in circle packing. In: Faigle, U. (ed.) Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, University of Köln (2010)

    Google Scholar 

  31. Liberti, L., Mladenović, N., Nannicini, G.: A good recipe for solving MINLPs. In: Maniezzo, V., Stützle, T., Voß, S. (eds.) Hybridizing metaheuristics and mathematical programming. Annals of Information Systems, vol. 10, pp. 231–244. Springer, New York (2009)

    Google Scholar 

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Author information

Authors and Affiliations

  1. LIX, École Polytechnique, Palaiseau, France

    Leo Liberti & David Savourey

  2. Dept. Mathématiques et Informatique, ENAC, 7 av. E. Belin, 31055, Toulouse, France

    Sonia Cafieri

Authors
  1. Leo Liberti
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  2. Sonia Cafieri
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  3. David Savourey
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Editor information

Editors and Affiliations

  1. Institute for Operations Research and Institute of Theoretical Computer Science, ETH Zurich, 8092, Zurich, Switzerland

    Komei Fukuda

  2. LIX, CNRS, École polytechnique, 91128, Palaiseau cedex, France

    Joris van der Hoeven

  3. Fachbereich Mathematik, TU Darmstadt, 64289, Darmstadt, Germany

    Michael Joswig

  4. Department of Mathematics, Kobe University, 657-8501, Rokko, Kobe, Japan

    Nobuki Takayama

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Liberti, L., Cafieri, S., Savourey, D. (2010). The Reformulation-Optimization Software Engine. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_50

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  • DOI: https://doi.org/10.1007/978-3-642-15582-6_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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