Confidence-based Reasoning in Stochastic Constraint Programming

TL;DR

This paper presents a sampling-based method for efficiently solving stochastic constraint satisfaction and optimization problems by reducing problem size and providing solutions with probabilistic guarantees.

Contribution

It introduces a novel framework combining stochastic constraint programming and statistical sampling, applicable with existing solvers, and validated through computational experiments.

Findings

Effective reduction of problem complexity

High-confidence solutions within error thresholds

Versatile approach for stochastic combinatorial problems

Abstract

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the original problem being analysed; by solving this reduced problem, with a given confidence probability, we obtain assignments that satisfy the chance constraints in the original model within prescribed error tolerance thresholds. To achieve this, we blend concepts from stochastic constraint programming and statistics. We discuss both exact and approximate variants of our method. The framework we introduce can be immediately employed in concert with existing approaches for solving stochastic constraint programs. A thorough computational study on a number of stochastic combinatorial optimisation problems demonstrates the effectiveness of our approach.