4 research outputs found
Stochastic Constraint Programming
To model combinatorial decision problems involving uncertainty and
probability, we introduce stochastic constraint programming. Stochastic
constraint programs contain both decision variables (which we can set) and
stochastic variables (which follow a probability distribution). They combine
together the best features of traditional constraint satisfaction, stochastic
integer programming, and stochastic satisfiability. We give a semantics for
stochastic constraint programs, and propose a number of complete algorithms and
approximation procedures. Finally, we discuss a number of extensions of
stochastic constraint programming to relax various assumptions like the
independence between stochastic variables, and compare with other approaches
for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial
Intelligenc
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
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 SanchÃs, 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, MartÃnez 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):