Identifying Inconsistent CSPs by Relaxation

Nordlander, Tomas Eric and Brown, Ken and Sleeman, Derek (2003) Identifying Inconsistent CSPs by Relaxation. Ninth International Conference on Principles and Practice of Constraint Programming, Cork Irland.

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MUSKRAT (Multistrategy Knowledge Refinement and Acquisition Toolbox) [1] aims to unify problem solving, knowledge acquisition and knowledge-base refinement in a single computational framework. Given a set of Knowledge Bases (KBs) and Problem Solvers (PSs), the MUSKRAT-Advisor investigates whether the available KBs will fulfil the requirements of the selected PS for a given problem. We would like to reject impossible combinations of KBs and PSs quickly. We propose to represent combinations of KBs and PSs as CSPs. If a CSP is not consistent, then the combination does not fulfil the requirements. The problem then becomes one of quickly identifying inconsistent CSPs. To do this, we propose to relax the CSPs: if we can prove that the relaxed version is inconsistent then we know that the original CSP is also inconsistent. It is not obvious that solving relaxed CSPs is any easier. In fact, phase transition research (e.g. [2]) seems to indicate the opposite when the original CSP is inconsistent. We have experimented with randomly generated CSPs [3], where the tightness of the constraints in a problem varies uniformly. We have shown that careful selection of the constraints to relax can save up to 70% of the search time. We have also investigated practical heuristics for relaxing CSPs. Experiments show that the simple strategy of removing constraints of low tightness is effective, allowing us to save up to 30% of the time on inconsistent problems without introducing new solutions. In the constraints area, future work will look at extending this approach to more realistic CSPs. The focus will be on scheduling problems, which are likely to involve non-binary and global constraints, and constraint graphs with particular properties (e.g. [4]). We will also investigate more theoretical CSP concepts, including higher consistency levels and problem hardness. Success in this research will allow us to apply constraint satisfaction and relaxation techniques to the problem of knowledge base reuse.

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