Matrix Factorization Based Heuristics Learning for Solving Constraint Satisfaction Problems

Abstract

In configuration systems, and especially in Constraint Satisfaction Problems (CSP), heuristics are widely used and commonly referred to as variable and value ordering heuristics. The main challenges of those systems are: producing high quality configuration results and performing real-time recommendations. This paper addresses both challenges in the context of CSP based configuration tasks. We propose a novel learning approach to determine transaction-specific variable and value ordering heuristics to solve configuration tasks with high quality configuration results in real-time. Our approach employs matrix factorization techniques and historical transactions (past purchases) to learn accurate variable and value ordering heuristics. Using all historical transactions, we build a sparse matrix and then apply matrix factorization to find transaction-specific variable and value ordering heuristics. Thereafter, these heuristics are used to solve the configuration task with a high prediction quality in a short runtime. A series of experiments on real-world datasets has shown that our approach outperforms existing heuristics in terms of runtime efficiency and prediction quality.