Finding (α, ϑ)-solutions via sampled SCSPs

Authors:
Roberto Rossi;Brahim Hnich;S. Armagan Tarim;Steven Prestwich
Affiliations:
Logistics, Decision and Information Sciences, Wageningen University, The Netherlands;Department of Computer Engineering, Izmir University of Economics, Turkey;Department of Management, Hacettepe University, Ankara, Turkey;Cork Constraint Computation Centre,University College Cork, Ireland
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Year:
2011

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Abstract

We discuss a novel approach for dealing with single-stage stochastic constraint satisfaction problems (SCSPs) that include random variables over a continuous or large discrete support. Our approach is based on two novel tools: sampled SCSPs and (α, ϑ)-solutions. Instead of explicitly enumerating a very large or infinite set of future scenarios, we employ statistical estimation to determine if a given assignment is consistent for a SCSP. As in statistical estimation, the quality of our estimate is determined via confidence interval analysis. In contrast to existing approaches based on sampling, we provide likelihood guarantees for the quality of the solutions found. Our approach can be used in concert with existing strategies for solving SCSPs.