Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. Many real life problems come from uncertain and dynamic environments, where the initial constraints and domains may change during its execution. Thus, the solution found for the problem may become invalid. The search forrobustsolutions for constraint satisfaction problems (CSPs) has become an important issue in the ¿eld of constraint programming. In some cases, there exists knowledge about the uncertain and dynamic environment. In other cases, this information is unknown or hard to obtain. In this paper, we consider CSPs with discrete and ordered domains where changes only involve restrictions or expansions of domains or constraints. To this end, we model CSPs as weighted CSPs (WCSPs) by assigning weights to each valid tuple of the problem constraints and domains. The weight of each valid tuple is based on its distance from the borders of the space of valid tuples in the corresponding constraint/domain. This distance is estimated by a new concept introduced in this paper: coverings. Thus, the best solution for the modeled WCSP can be considered as a most robust solution for the original CSP according to these assumptionsThis work has been partially supported by the research projects TIN2010-20976-C02-01 (Min. de Ciencia e Innovacion, Spain) and P19/08 (Min. de Fomento, Spain-FEDER), and the fellowship program FPU.Climent Aunés, LI.; Wallace, RJ.; Salido Gregorio, MA.; Barber Sanchís, F. (2013). Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings. Artificial Intelligence Review. 1-26. https://doi.org/10.1007/s10462-013-9420-0S126Climent L, Salido M, Barber F (2011) Reformulating dynamic linear constraint satisfaction problems as weighted csps for searching robust solutions. In: Ninth symposium of abstraction, reformulation, and approximation (SARA-11), pp 34–41Dechter R, Dechter A (1988) Belief maintenance in dynamic constraint networks. In: Proceedings of the 7th national conference on, artificial intelligence (AAAI-88), pp 37–42Dechter R, Meiri I, Pearl J (1991) Temporal constraint networks. Artif Intell 49(1):61–95Fargier H, Lang J (1993) Uncertainty in constraint satisfaction problems: a probabilistic approach. In: Proceedings of the symbolic and quantitative approaches to reasoning and uncertainty (EC-SQARU-93), pp 97–104Fargier H, Lang J, Schiex T (1996) Mixed constraint satisfaction: a framework for decision problems under incomplete knowledge. In: Proceedings of the 13th national conference on, artificial intelligence, pp 175–180Fowler D, Brown K (2000) Branching constraint satisfaction problems for solutions robust under likely changes. In: Proceedings of the international conference on principles and practice of constraint programming (CP-2000), pp 500–504Goles E, Martínez S (1990) Neural and automata networks: dynamical behavior and applications. Kluwer Academic Publishers, DordrechtHays W (1973) Statistics for the social sciences, vol 410, 2nd edn. Holt, Rinehart and Winston, New YorkHebrard E (2006) Robust solutions for constraint satisfaction and optimisation under uncertainty. PhD thesis, University of New South WalesHerrmann H, Schneider C, Moreira A, Andrade Jr J, Havlin S (2011) Onion-like network topology enhances robustness against malicious attacks. J Stat Mech Theory Exp 2011(1):P01,027Larrosa J, Schiex T (2004) Solving weighted CSP by maintaining arc consistency. Artif Intell 159:1–26Larrosa J, Meseguer P, Schiex T (1999) Maintaining reversible DAC for Max-CSP. J Artif Intell 107(1):149–163Mackworth A (1977) On reading sketch maps. In: Proceedings of IJCAI’77, pp 598–606Sam J (1995) Constraint consistency techniques for continuous domains. These de doctorat, École polytechnique fédérale de LausanneSchiex T, Fargier H, Verfaillie G (1995) Valued constraint satisfaction problems: hard and easy problems. In: Proceedings of the 14th international joint conference on, artificial intelligence (IJCAI-95), pp 631–637Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64(2):278–285Verfaillie G, Jussien N (2005) Constraint solving in uncertain and dynamic environments: a survey. Constraints 10(3):253–281Wallace R, Freuder E (1998) Stable solutions for dynamic constraint satisfaction problems. In: Proceedings of the 4th international conference on principles and practice of constraint programming (CP-98), pp 447–461Wallace RJ, Grimes D (2010) Problem-structure versus solution-based methods for solving dynamic constraint satisfaction problems. In: Proceedings of the 22nd international conference on tools with artificial intelligence (ICTAI-10), IEEEWalsh T (2002) Stochastic constraint programming. In: Proceedings of the 15th European conference on, artificial intelligence (ECAI-02), pp 111–115William F (2006) Topology and its applications. Wiley, New YorkWiner B (1971) Statistical principles in experimental design, 2nd edn. McGraw-Hill, New YorkYorke-Smith N, Gervet C (2009) Certainty closure: reliable constraint reasoning with incomplete or erroneous data. J ACM Trans Comput Log (TOCL) 10(1):

Robustness, stability, recoverability, and reliability in constraint satisfaction problems

The final publication is available at Springer via http://dx.doi.org/10.1007/s10115-014-0778-3Many real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise and dynamic such that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSP). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, which are addressed in engineering and other related areas.This work has been partially supported by the research project TIN2013-46511-C2-1 (MINECO, Spain). We would also thank the reviewers for their efforts and helpful comments.Barber Sanchís, F.; Salido Gregorio, MA. (2015). Robustness, stability, recoverability, and reliability in constraint satisfaction problems. Knowledge and Information Systems. 44(3):719-734. https://doi.org/10.1007/s10115-014-0778-3S719734443Abril M, Barber F, Ingolotti L, Salido MA, Tormos P, Lova A (2008) An assessment of railway capacity. Transp Res Part E 44(5):774–806Barber F (2000) Reasoning on intervals and point-based disjunctive metric constraints in temporal contexts. J Artif Intell Res 12:35–86Bartak R, Salido MA (2011) Constraint satisfaction for planning and scheduling problems. Constraints 16(3):223–227Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53Climent L, Wallace R, Salido M, Barber F (2013) Modeling robustness in CSPS as weighted CSPS. In: Integration of AI and OR techniques in constraint programming for combinatorial optimization problems CPAIOR 2013, pp 44–60Climent L, Wallace R, Salido M, Barber F (2014) Robustness and stability in constraint programming under dynamism and uncertainty. J Artif Intell Res 49(1):49–78Dechter R (1991) Temporal constraint network. Artif Intell 49:61–295Hazewinkel M (2002) Encyclopaedia of mathematics. Springer, New YorkHebrard E (2007) Robust solutions for constraint satisfaction and optimisation under uncertainty. PhD thesis, University of New South WalesHebrard E, Hnich B, Walsh T (2004) Super solutions in constraint programming. In: Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR-04), pp 157–172Jen E (2003) Stable or robust? What’s the difference? Complexity 8(3):12–18Kitano H (2007) Towards a theory of biological robustness. Mol Syst Biol 3(137)Liebchen C, Lbbecke M, Mhring R, Stiller S (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. In: LNCS, vol 5868Papapetrou P, Kollios G, Sclaroff S, Gunopulos D (2009) Mining frequent arrangements of temporal intervals. Knowl Inf Syst 21:133–171Rizk A, Batt G, Fages F, Solima S (2009) A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12):168–179Rossi F, van Beek P, Walsh T (2006) Handbook of constraint programming. Elsevier, New YorkRoy B (2010) Robustness in operational research and decision aiding: a multi-faceted issue. Eur J Oper Res 200:629–638Szathmary E (2006) A robust approach. Nature 439:19–20Verfaillie G, Schiex T (1994) Solution reuse in dynamic constraint satisfaction problems. In: Proceedings of the 12th national conference on artificial intelligence (AAAI-94), pp 307–312Wallace R, Grimes D, Freuder E (2009) Solving dynamic constraint satisfaction problems by identifying stable features. In: Proceedings of international joint conferences on artificial intelligence (IJCAI-09), pp 621–627Wang D, Tse Q, Zhou Y (2011) A decentralized search engine for dynamic web communities. Knowl Inf Syst 26(1):105–125Wiggins S (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, New YorkZhou Y, Croft W (2008) Measuring ranked list robustness for query performance prediction. Knowl Inf Syst 16:155–17

Robustness and Stability in Constraint Programming under Dynamism and Uncertainty

[EN] Many real life problems that can be solved by constraint programming, come from uncertain and dynamic environments. Because of the dynamism, the original problem may change over time, and thus the solution found for the original problem may become invalid. For this reason, dealing with such problems has become an important issue in the fields of constraint programming. In some cases, there is extant knowledge about the uncertain and dynamic environment. In other cases, this information is fragmentary or unknown. In this paper, we extend the concept of robustness and stability for Constraint Satisfaction Problems (CSPs) with ordered domains, where only limited assumptions need to be made as to possible changes. We present a search algorithm that searches for both robust and stable solutions for CSPs of this nature. It is well-known that meeting both criteria simultaneously is a desirable objective for constraint solving in uncertain and dynamic environments. We also present compelling evidence that our search algorithm outperforms other general-purpose algorithms for dynamic CSPs using random instances and benchmarks derived from real life problems.This work has been partially supported by the research project TIN2010-20976-C02-01 and FPU program fellowship (Min. de Ciencia e Innovacion, Spain). We wish to thank Dr. Christophe Lecoutre and Dr. Diarmuid Grimes for their assistance.Climent Aunés, LI.; Wallace, R.; Salido Gregorio, MA.; Barber Sanchís, F. (2014). Robustness and Stability in Constraint Programming under Dynamism and Uncertainty. Journal of Artificial Intelligence Research. 49(1):49-78. https://doi.org/10.1613/jair.4126S497849

Robustness, Stability, Recoverability and Reliability in CSP

Technical ReportMany real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise, and dynamic such that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency, and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSP). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, that are addressed in engineering and other related areas.Barber Sanchís, F.; Salido Gregorio, MA. (2013). Robustness, Stability, Recoverability and Reliability in CSP. http://hdl.handle.net/10251/2891