NMUS: Structural Analysis for Improving the Derivation of All MUSes in Overconstrained Numeric CSPs

Abstract

Models are used in science and engineering for experimentation, analysis, model-based diagnosis, design and planning/sheduling applications. Many of these models are overconstrained Numeric Constraint Satisfaction Problems (NCSP), where the numeric constraints could have linear or polynomial relations. In practical scenarios, it is very useful to know which parts of the overconstrained NCSP instances cause the unsolvability. Although there are algorithms to find all optimal solutions for this problem, they are computationally expensive, and hence may not be applicable to large and real-world problems. Our objective is to improve the performance of these algorithms for numeric domains using structural analysis. We provide experimental results showing that the use of the different strategies proposed leads to a substantially improved performance and it facilitates the application of solving larger and more realistic problems.