Abstract

To model decision problems involving uncertainty and probability, we propose stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow some probability distribution), and 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. Using these algorithms, we observe phase transition behavior in stochastic constraint programs. Interestingly, the cost of both optimization and satisfaction peaks in the satisfaction phase boundary. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables. Introduction Many real world decision problems contain uncertainty. Data about event...

Citations

878	Markov Decision Processes: Discrete Stochastic Dynamic Programming - Puterman - 1994
620	A New Method for Solving Hard Satisfiability Problems - Selman, Levesque, et al. - 1992
390	Partial constraint satisfaction - Freuder, Wallace - 1992
318	Noise strategies for improving local search - Selman, Kautz, et al. - 1994
114	On the complexity of solving Markov decision problems - Littman, Dean, et al. - 1995
76	Uncertainty in constraint satisfaction problems: a probabilistic approac h - Fargier, Lang - 1993
44	Influence Diagrams, Belief Nets and Decision Analysis - Oliver, Smith - 1990
40	Stochastic Boolean satisfiability - Littman, Majercik, et al. - 2000
31	Mixed constraint satisfaction: A framework for decision problems under incomplete knowledge - Fargier, Lang, et al. - 1996
21	Branching constraint satisfaction problems for solutions robust under likely changes - Fowler, Brown - 2000
21	A constraint satisfaction framework for decision under uncertainty - Fargier, Lang, et al. - 1995
14	The computational complexity of probabilistic plan existence and evaluation - Littman, Goldsmith, et al. - 1998
10	Semi-ring based CSPs and valued CSPs: Basic properties and comparison - Bistarelli, Fargier, et al. - 1996
6	Constraint satisfaction with probabilistic preferences on variable values - Shazeer, Littman, et al.