## Stochastic Constraint Programming (2000)

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Citations: | 58 - 8 self |

### BibTeX

@INPROCEEDINGS{Walsh00stochasticconstraint,

author = {Toby Walsh},

title = {Stochastic Constraint Programming},

booktitle = {},

year = {2000},

pages = {111--115},

publisher = {Press}

}

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### 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

1259 |
Markov Decision Processes: Discrete Stochastic Dynamic Programming
- Puterman
- 1994
(Show Context)
Citation Context ... MDP is a policy, which specifies the best action to take in each possible state. MDPs These have been very influential in AI of late for dealing with situations involving reasoning under uncertainty =-=[Put94]-=-. Stochastic constraint programs can model problems which lack the Markov property that the next state and reward depend only on the previous state and action taken. To represent a stochastic constrai... |

693 | A New Method for Solving Hard Satisfiability Problems - Selman, Levesque, et al. - 1992 |

430 | Partial constraint satisfaction
- Freuder, Wallace
- 1992
(Show Context)
Citation Context ... satisfaction problem model constraints that are uncertain, probabilistic or not necessarily satisfied. For example, in partial constraint satisfaction we maximize the number of constraints satisfied =-=[FW92]-=-. As a second example, in probabilistic constraint satisfaction each constraint has a certain probability independent of all other probabilities of being part of the problem [FL93]. As a third example... |

371 | Noise Strategies for Improving Local Search - Selman, Kauts, et al. - 1994 |

133 | On the complexity of solving Markov decision problems - Littman, Dean, et al. - 1995 |

83 |
Uncertainty in constraint satisfaction problems: a probabilistic approach
- Fargier, Lang
- 1993
(Show Context)
Citation Context ...nstraints satisfied [FW92]. As a second example, in probabilistic constraint satisfaction each constraint has a certain probability independent of all other probabilities of being part of the problem =-=[FL93]-=-. As a third example, both valued and semi-ring based constraint satisfaction [BFM + 96] generalizes probabilistic constraint satisfaction as well as a number of other frameworks. In semi-ring based c... |

52 |
Influence Diagrams, Belief Nets and Decision Analysis
- Oliver, Smith
- 1990
(Show Context)
Citation Context ...ewards. Stochastic constraint programs are also closely related to influence diagrams. Influence diagrams are Bayesian networks in which the chance nodes are augmented with decision and utility nodes =-=[OS90]-=-. The usual aim is to maximize the sum of the expected utilities. Chance nodes in an influence diagram correspond to stochastic variables in a stochastic constraint program, whilst decision nodes corr... |

51 | Stochastic Boolean satisfiability
- Littman, Majercik, et al.
- 2001
(Show Context)
Citation Context ... hope to be able to reason about it more efficiently. 11 Related work in constraints Stochastic constraint programming is inspired by both stochastic integer programming and stochastic satisfiability =-=[LMP00]-=-. It shares the advantages that constraint programming has over integer programming (e.g. non-linear constraints, and constraint propagation). It also shares the advantages that constraint programming... |

43 | Mixed constraint satisfaction: A framework for decision problems under incomplete knowledge
- Fargier, Lang, et al.
- 1996
(Show Context)
Citation Context ...traint propagation). It also shares the advantages that constraint programming has over satisfiability (e.g. global and arithmetic constraints, and more compact models). Mixed constraint satisfaction =-=[FLS96]-=- is closely related to one stage stochastic constraint satisfaction. In a mixed CSP, the decision variables are set after the stochastic variables are given random values. In addition, the random valu... |

30 | Branching constraint satisfaction problems for solutions robust under likely changes
- Fowler, Brown
- 2000
(Show Context)
Citation Context ... using the probability distribution. The maximum expected overlap solution could be found by solving a suitable one stage stochastic constraint optimization problem. Branching constraint satisfaction =-=[FB00]-=- models problems in which there is uncertainty in the number of variables. For example, we can model a nurse rostering problem by assigning shifts to nurses. Branching constraint satisfaction then all... |

27 | A constraint satisfaction framework for decision under uncertainty
- Fargier, Lang, et al.
- 1995
(Show Context)
Citation Context ...ability, the aim is to find values for the decision variables in a mixed CSP so that we satisfy as many possible worlds. An earlier constraint satisfaction model for decision making under uncertainty =-=[FLMCS95]-=- also included a probability distribution over the space of possible worlds. Constraint satisfaction has been extended to include probabilistic preferences on the values assigned to variables [SLK99].... |

15 |
The computational complexity of probabilistic plan existence and evaluation
- Littman, Goldsmith, et al.
- 1998
(Show Context)
Citation Context ...exists an assignment for a set of Boolean variables so that, given randomized choices of values for the other variables, the formula is satisfiable with probability at least equal to some threshold θ =-=[LGM98]-=-. This can be reduced very immediately to an one stage stochastic CSP. A number of other reasoning problems like finding optimal sizebounded plans in uncertain domains are NP PP -complete. PSPACE is t... |

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.
(Show Context)
Citation Context ...FLMCS95] also included a probability distribution over the space of possible worlds. Constraint satisfaction has been extended to include probabilistic preferences on the values assigned to variables =-=[SLK99]-=-. Associated with the values for each variable is a probability distribution. A “best” solution to the constraint satisfaction problem is then found. This may be the maximum probability solution (whic... |