El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization

Carmen Gervet, Sylvie Galichet

2015

Abstract

In this project we address the problem of modelling and solving constraint based problems permeated with data uncertainty, due to imprecise measurements or incomplete knowledge. It is commonly specified as bounded interval parameters in a constraint problem. For tractability reasons, existing approaches assume independence of the data, also called parameters. This assumption is safe as no solutions are lost, but can lead to large solution spaces, and a loss of the problem structure. In this paper we present two approaches we have investigated in the El MUNDO project, to handle data parameter dependencies effectively. The first one is generic whereas the second one focuses on a specific problem structure. The first approach combines two complementary paradigms, namely constraint programming and regression analysis, and identifies the relationships between potential solutions and parameter variations. The second approach identifies the context of matrix models and shows how dependency constraints over the data columns of such matrices can be modeled and handled very efficiently. Illustrations of both approaches and their benefits are shown.

References

  1. Benhamou, F. Inteval constraint logic programming. In Constraint Programming: Basics and Trends. LNCS, Vol. 910, 1-21, Springer, 1995.
  2. Benhamou F. and Goualard F. Universally quantified interval constraints. In Proc. of CP2000, LNCS 1894, Singapore, 2000.
  3. Ben-Tal, A; and Nemirovski, A. Robust solutions of uncertain liner programs. Operations Research Letters, 25, 1-13, 1999.
  4. Bertsimas, D. and Brown, D. Constructing uncertainty sets for robust linear optimization. Operations Research, 2009.
  5. Bordeaux L., and Monfroy, E. Beyond NP: Arc-consistency for quantified constraints. In Proc. of CP 2002.
  6. Boukezzoula R., Galichet S. and Bisserier A. A MidpointRadius approach to regression with interval data International Journal of Approximate Reasoning,Volume 52, Issue 9, 2011.
  7. Brown K. and Miguel I. Chapter 21: Uncertainty and Change Handbook of Constraint Programming Elsevier, 2006.
  8. Cheadle A.M., Harvey W., Sadler A.J., Schimpf J., Shen K. and Wallace M.G. ECLiPSe: An Introduction. Tech. Rep. IC-Parc-03-1, Imperial College London, London, UK.
  9. Chinneck J.W. and Ramadan K. Linear programming with interval coefficients. J. Operational Research Society, 51(2):209-220, 2000.
  10. De Raedt L., Mannila H., O'Sullivan and Van Hentenryck P. organizers. Constraint Programming meets Machine Learning and Data Mining Dagstuhl seminar 2011.
  11. Fargier H., Lang J. and Schiex T. Mixed constraint satisfaction: A framework for decision problems under incomplete knowledge. In Proc. of AAAI-96, 1996.
  12. Gent, I., and Nightingale, P., and Stergiou, K. QCSP-Solve: A Solver for Quantified Constraint Satisfaction Problems. In Proc. of IJCAI 2005.
  13. Gervet C. and Galichet S. On combining regression analysis and constraint programming. Proceedings of IPMU, 2014.
  14. Gervet C. and Galichet S. Uncertain Data Dependency Constraints in Matrix Models. Proceedings of CPAIOR, 2015.
  15. Inuiguchi, M. and Kume, Y. Goal programming problems with interval coefficients and target intervals. European Journl of Oper. Res. 52, 1991.
  16. Medina A., Taft N., Salamatian K., Bhattacharyya S. and Diot C. Traffic Matrix Estimation: Existing Techniques and New Directions. Proceedings of ACM SIGCOMM02, 2002.
  17. Oettli W. On the solution set of a linear system with inaccurate coefficients. J. SIAM: Series B, Numerical Analysis, 2, 1, 115-118, 1965.
  18. Ratschan, S. Efficient solving of quantified inequality constraints over the real numbers. ACM Trans. Computat. Logic, 7, 4, 723-748, 2006.
  19. Rossi F., van Beek P., and Walsh T. Handbook of Constraint Programming. Elsevier, 2006.
  20. Saad A., Gervet C. and Abdennadher S. Constraint Reasoning with Uncertain Data usingCDF-Intervals Proceedings of CP'AI-OR, Springer,2010.
  21. Van Hentenryck P., Michel L. and Deville Y. Numerica: a Modeling Language for Global Optimization The MIT Press, Cambridge Mass, 1997.
  22. Tarim, S. and Kingsman, B. The stochastic dynamic production/inventory lot-sizing problem with service-level constraints. International Journal of Production Economics 88, 105119,2004.
  23. Yorke-Smith N. and Gervet C. Certainty Closure: Reliable Constraint Reasoning with Uncertain Data ACM Transactions on Computational Logic 10(1), 2009.
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Paper Citation


in Harvard Style

Gervet C. and Galichet S. (2015). El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization . In European Project Space on Intelligent Systems, Pattern Recognition and Biomedical Systems - EPS Lisbon, ISBN 978-989-758-095-6, pages 70-89. DOI: 10.5220/0006162500700089


in Bibtex Style

@conference{eps lisbon15,
author={Carmen Gervet and Sylvie Galichet},
title={El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization},
booktitle={European Project Space on Intelligent Systems, Pattern Recognition and Biomedical Systems - EPS Lisbon,},
year={2015},
pages={70-89},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006162500700089},
isbn={978-989-758-095-6},
}


in EndNote Style

TY - CONF
JO - European Project Space on Intelligent Systems, Pattern Recognition and Biomedical Systems - EPS Lisbon,
TI - El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization
SN - 978-989-758-095-6
AU - Gervet C.
AU - Galichet S.
PY - 2015
SP - 70
EP - 89
DO - 10.5220/0006162500700089