Techniques for Bundling the Solution Space of Finite Constraint Satisfaction Problems

We study the backtrack-search procedure with forward checking (FCBT) for finding all solutions to a finite Constraint Satisfaction Problem (CSP). We describe how to use dynamic interchangeability to enhance the performance of search and represent the solution space in a compact manner. We evaluate this strategy (FC-DNPI) in terms of the numbers of nodes visited, constraints checked, and solution bundles generated by comparing it, theoretically and empirically, to other search strategies. We show that FC-DNPI is equivalent to search with the Cross Product Representation (FC-CPR) of [Hubbe and Freuder 1992] in terms of the numbers of solution bundles and constraint checks, while it reduces the number of nodes visited. We establish that both strategies are always superior to FC-BT in terms of all three criteria and dynamic bundling is always beneficial. Further, we compare FC-DNPI to the search procedure of [Haselböck 1993], which exploits static, pre-computed interchangeability relations. We show that the former never generates more solution bundles nor expands more nodes than the latter, and often reduces the number of constraint checks. We also propose, without evaluating them, amendments to the strategy of [Haselböck 1993] to improve its performance and reduce the number of constraint checks

Towards 40 years of constraint reasoning

Research on constraints started in the early 1970s. We are approaching 40 years since the beginning of this successful field, and it is an opportunity to revise what has been reached. This paper is a personal view of the accomplishments in this field. We summarize the main achievements along three dimensions: constraint solving, modelling and programming. We devote special attention to constraint solving, covering popular topics such as search, inference (especially arc consistency), combination of search and inference, symmetry exploitation, global constraints and extensions to the classical model. For space reasons, several topics have been deliberately omitted.Partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya grant 2009-SGR-1434.Peer Reviewe

Finding regions of local repair in hierarchical constraint satisfaction

Algorithms for solving constraint satisfaction problems (CSP) have been successfully applied to several fields including scheduling, design, and planning. Latest extensions of the standard CSP to constraint optimization problems (COP) additionally provided new opportunities for solving several problems of combinatorial optimization more efficiently. Basically, two classes of algorithms have been used for searching constraint satisfaction problems (CSP): local search methods and systematic tree search extended by the classical constraint-processing techniques like e.g. forward checking and backmarking. Both classes exhibit characteristic advantages and drawbacks. This report presents a novel approach for solving constraint optimization problems that combines the advantages of local search and tree search algorithms which have been extended by constraint-processing techniques. This method proved applicability in a commercial nurse scheduling system as well as on randomly generated problems

Planning Graph as a (Dynamic) CSP: Exploiting EBL, DDB and other CSP Search Techniques in Graphplan

This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation based learning, dependency directed backtracking, dynamic variable ordering, forward checking, sticky values and random-restart search strategies can be adapted to Graphplan. Empirical results are provided to demonstrate that these augmentations improve Graphplan's performance significantly (up to 1000x speedups) on several benchmark problems. Special attention is paid to the explanation-based learning and dependency directed backtracking techniques as they are empirically found to be most useful in improving the performance of Graphplan