Resumen de Contributions to search and inference algorithms for csp and weighted csp

Marti Sanchez Fibla

• This thesis presents a collection of new algorithms for solving Constraint Satisfaction Problem (CSP) and Weighted Constraint Satisfaction Problem (WCSP), We pursue two main objectives: enhancing solving methods for WCSP, which are of recent development, and narrowing the gap between search and inference methods.

  The first part of the thesis is devoted to search methods for solving WCSP. In a branch-and-bound context, the lower bound computation in each node of the search is of great importance and has a serious impact in the practical efficiency of algorithms. We start from an algorithm called Russian Doll Search (RDS) that has a costly, yet very powerful lower bound and we develop three enhancements of it: Specialized RDS (SRDS), Full SRDS and Opportunistic SRDS. We then tackle the problem of exploiting the global structure of the problem inside search. An algorithm exists for CSP that is able to exploit what is called pseudo-tree structure extend it to WCSP, obtaining algorithm Pseudo Tree Partial Forward Checking (PT-PFC). This algorithm has a source of inefficiency mainly related to bad quality local lower and upper bounds. We suggest a solution to this problem by combining pseudo-tree search for WCSP with the RDS techniques that we previously developed obtaining algorithms PT-RDS and PT-SRDS. In all this first part the aim is enhancing the practical efficiency of existing search algorithms with respect to the time spent in solving several benchmarks.

  The second part of the thesis is devoted to complete inference methods for solving CSP and WCSP. Complete inference solves the problem by a sequence of transformations that obtain an equivalent problem. In these transformations variable elimination plays an important role. We present some new inference operations that permit us to factorize a constraint into a set of smaller size constraints. We then introduce factorization into variable elimination. The result is algorithm {\it Adaptive Consis