Spread-Repair-Shrink: A Hybrid Algorithm for Solving Fuzzy Constraint Satisfaction Problems

A fuzzy constraint satisfaction problem (FCSP) is an extension of the classical CSP, a powerful tool for modeling various problems based on constraints among variables. Basically, the algorithms for solving CSPs are classified into two categories: the systematic search (complete methods based on search trees) and the local search (approximate methods based on iterative improvement). Both have merits and demerits. Recently, much attention has been paid to hybrid methods for integrating both merits to solve CSPs efficiently, but almost no attempt has been made so far for solving FCSPs. In this paper, we present a hybrid, approximate method for solving FCSPs. The method, called the spread-repair shrink (SRS) algorithm, combines a systematic .search with the spread-repair (SR) algorithm, a local search method recently developed by the authors. SRS repeats spreading and shrinking a set of search trees in order to repair local constraints until the satisfaction degree of the worst constraints (which arc the roots of the trees) is improved. We empirically show that SRS outperforms SR and other well-known methods such as Forward Checking and Fuzzy GENET, when we want to quickly get a good-quality approximate solution of sufficiently large size of problems.