Intelligent search strategies based on adaptive Constraint Handling Rules

The most advanced implementation of adaptive constraint processing with Constraint Handling Rules (CHR) allows the application of intelligent search strategies to solve Constraint Satisfaction Problems (CSP). This presentation compares an improved version of conflict-directed backjumping and two variants of dynamic backtracking with respect to chronological backtracking on some of the AIM instances which are a benchmark set of random 3-SAT problems. A CHR implementation of a Boolean constraint solver combined with these different search strategies in Java is thus being compared with a CHR implementation of the same Boolean constraint solver combined with chronological backtracking in SICStus Prolog. This comparison shows that the addition of ``intelligence'' to the search process may reduce the number of search steps dramatically. Furthermore, the runtime of their Java implementations is in most cases faster than the implementations of chronological backtracking. More specifically, conflict-directed backjumping is even faster than the SICStus Prolog implementation of chronological backtracking, although our Java implementation of CHR lacks the optimisations made in the SICStus Prolog system. To appear in Theory and Practice of Logic Programming (TPLP).Comment: Number of pages: 27 Number of figures: 14 Number of Tables:

Enhancing a Search Algorithm to Perform Intelligent Backtracking

This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that allows a program to store information when a dead end is reached. To illustrate the technique, a simple search program is enhanced. To appear in Theory and Practice of Logic Programming. Keywords: intelligent backtracking, dependency-directed backtracking, backjumping, conflict-directed backjumping, nogood sets, look-back.Comment: To appear in Theory and Practice of Logic Programmin

AN APPROACH TO DEPENDENCY DIRECTED BACKTRACKING USING DOMAIN SPECIFIC KNOWLEDGE

The idea of dependency directed backtracking proposed by Stallman and Sussman (1977) offers significant advantages over heuristic starch schemes with chronological backtracking which waste much effort by discarding many "good" choices when backtracking situations arise. However, we have found that existing non-chronological backtracking machinery is not suitable for certain types of problems, namely, those where choices do not follow logically from previous choices, but are based on a heuristic evaluation of a constrained set of alternatives. This is because a choice is not justified by a âset of supportâ (of previous choices), but because its advantages outweigh its drawbacks in comparison to its competitors. What is needed for these types of problems is a scheme where the advantages and disadvantages of choices are explicitly recorded during problem solving. Then, if an unacceptable situation arises, information about the nature of the unacceptability and the tradeoffs can be used to determine the most appropriate backtracking point. Further, this requires the problem solver to use its hindsight to preserve those "good" intervening choices that were made chronologically after the "bad" choice, and to resume its subsequent reasoning in fight of the modified set of constraints. In this paper, we describe a problem solver for non-chronological backtracking in situations involving tradeoffs. By endowing the backtracker with access to domain-specific knowledge, a highly contextual approach to reasoning in dependency directed backtracking situations can be achieved.Information Systems Working Papers Serie

Satisfiability-Based Algorithms for Boolean Optimization

This paper proposes new algorithms for the Binate Covering Problem (BCP), a well-known restriction of Boolean Optimization. Binate Covering finds application in many areas of Computer Science and Engineering. In Artificial Intelligence, BCP can be used for computing minimum-size prime implicants of Boolean functions, of interest in Automated Reasoning and Non-Monotonic Reasoning. Moreover, Binate Covering is an essential modeling tool in Electronic Design Automation. The objectives of the paper are to briefly review branch-and-bound algorithms for BCP, to describe how to apply backtrack search pruning techniques from the Boolean Satisfiability (SAT) domain to BCP, and to illustrate how to strengthen those pruning techniques by exploiting the actual formulation of BCP. Experimental results, obtained on representative instances indicate that the proposed techniques provide significant performance gains for a large number of problem instances

Conflict Analysis in Search Algorithms for Satisfiability

This paper introduces GRASP (Generic search Algorithm jr the Satisfiabili{y Problem), a new search algorithm jr Propositional Satisfiabili{y (SAT). GRASP incorporates several search-pruning techniques, some of which are specific to SAT, whereas others find equivalent in other fields of Artificial Intelligence. GRASP is premised on the inevitabili{y of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'gecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straigh&rward bookkeeping of the causali {y chains leading up to conflicts allows GRASP to identij) assignments that are necessary jr a solution to be jund. Experimental results obtained jom a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely efctive jr a large number of representative classes of SAT instances

GRASP: A New Search Algorithm for Satisfiability

This paper introduces GRASP (Generic search Algorithm J3r the Satisfiabilily Problem), an integrated algorithmic J3amework 30r SAT that unifies several previously proposed searchpruning techniques and jcilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'ecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Einally, straighrward bookkeeping of the causali y chains leading up to conflicts a/lows GRASP to identij) assignments that are necessary jr a solution to be found. Experimental results obtained jom a large number of benchmarks, including many J3om the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely ejctive jr a large number of representative classes of SAT instances

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significan