Constraint Weighting Local Search for Constraint Satisfaction

Abstract

One of the challenges for the constraint satisfaction community has been to develop an automated approach to solving Constraint Satisfaction Problems (CSPs) rather than creating specific algorithms for specific problems. Much of this work has concentrated on the development and improvement of general purpose backtracking techniques. However, the success of relatively simple local search techniques on larger satisfiability problems [Selman et a!. 1992] and CSPs such as the n-queens [Minton et al. 1992] has caused interest in applying local search to constraint satisfaction. In this thesis we look at the usefulness of constraint weighting as a local search technique for constraint satisfaction. The work is based on the clause weighting ideas of Selman and Kautz [1993] and Moths [1993] and applies, evaluates and extends these ideas from the satisfiability domain to the more general domain of CSPs. Specifically, the contributions of the thesis are: 1. The introduction of a local search taxonomy. We examine the various better known local search techniques and recognise four basic strategies: restart, randomness, memory and weighting. 2. The extension of the CSP modelling framework. In order to represent and efficiently solve more realistic problems we extend the C SP modelling framework to include array-based domains and array-based domain use constraints. 3. The empirical evaluation of constraint weighting. We compare the performance of three constraint weighting strategies on a range of CSP and satisflability problems and with several other local search techniques. We find that no one technique dominates in all problem domains. 4. The characterisation of constraint weighting performance. Based on our empirical study we identiIS' the weighting behaviours and problem features that favour constrtt weighting. We conclude weighting does better on structured problems where the algorithm can recognise a harder sub-group of constraints. 5. The extension of constraint weighting. We introduce an efficient arc weighting algorithm that additionally weights connections between constraints that are simultaneously violated at a local minimum. This algorithm is empirically shown to outperform standard constraint weighting on a range of CSPs and within a general constraint solving system. Also we look at combining constraint weighting with other local search heuristics and find that these hybrid techniques can do well on problems where the parent algorithms are evenly matched. 6. The application of constraint weighting to over constrained domains. Our empirical work suggests constraint weighting does well for problems with distinctions between constraint groups. This led us to investigate solving real-world over constrained problems with hard and soft constraint groups and to introduce two dynamic constraint weighting heuristics that maintain a distinction between hard and soft constraint groups while still adding weights to violated constraints in a local minimum. In an empirical study, the dynamic schemes are shown to outperform other fixed weighting and non-weighting systems on a range of real world problems. In addition, the performance of weighting is shown to degrade less severely when soft constraints are added to the system, suggesting constraint weighting is especially applicable to realistic, hard and soft constraint problems