Constraint-based reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expressions. These have been successfully applied to diverse tasks such as design, diagnosis, truth maintenance, scheduling, spatiotemporal reasoning, logic programming and user interface. Constraint networks are graphical representations used to guide strategies for solving constraint satisfaction problems (CSPs).

This paper describes a simple heuristic approach to solving large-scale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a value-ordering heuristic, the min-conflicts heuristic, that attempts to minimize the number of constraint violations after each step. The heuristic can be used with a variety of different search strategies. We demonstrate empirically that on the n-queens problem, a technique based on this approach performs orders of magnitude better than traditional backtracking techniques. We also describe a scheduling application where the approach has been used successfully. A theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective.

A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

We present a simple algorithm for determining the satis ability of propositional formulas in Conjunctive Normal Form. As the procedure searches for a satisfying truth assignment it dynamically rearranges the order in which variables are considered. The choice of which variable to assign a truth value next is guided by an upper bound on the size of the search remaining � the procedure makes the choice which yields the smallest upper bound on the size of the remaining search. We describe several upper bound functions and discuss the tradeo between accurate upper bound functions and the overhead required to compute the upper bounds. Experimental data shows that for one easily computed upper bound the reduction in the size of the search space more than compensates for the overhead involved in selecting the next variable. 1

This paper presents an evaluation of two orthogonal schemes for improving the efficiency of solving constraint satisfaction problems (CSPs). The first scheme involves a class of pre-processing techniques designed to make the representation of the CSP more explicit, including directional-arcconsistency, directional-path-consistency and adaptive-consistency. The second scheme aims at improving the order in which variables are chosen for evaluation during the search. In the first part of the experiment we tested the performance of backtracking (and its common enhancement-backjumping) with and without each of the preprocessings techniques above. The results show that directional arc-consistency, a scheme which embodies the simplest form of constraint recording, outperforms all other preprocessing techniques. The results of the second part of the experiment suggest that the best variable ordering is achieved by the fixed max-cardinality search order. 1.

It is known that isolated executions of parallel backtrack search exhibit speedup anomalies. In this paper we present analytical models and experimental results on the average case behavior of parallel backtracking. We consider two types of backtrack search algorithms: (i) simple backtracking (which does not use any heuristic information) ; (ii) heuristic backtracking (which uses heuristics to order and prune search). We present analytical models to compare the average number of nodes visited in sequential and parallel search for each case. For simple backtracking, we show that the average speedup obtained is (i) linear when distribution of solutions is uniform and (ii) superlinear when distribution of solutions is non-uniform. For heuristic backtracking, the average speedup obtained is at least linear (i.e., either linear or superlinear), and the speedup obtained on a subset of instances (called difficult instances) is superlinear. We also present experimental results over ...

The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependency-directed backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronologica...

Real-world scheduling is decision making under vague constraints of different importance, often using uncertain data, where compromises between antagonistic criteria are allowed. We explain in theory and by detailed examples a new combination of fuzzy set based constraints and repair based heuristics that help to model these scheduling problems. We simplify the mathematics needed for a method of eliciting the criteria's importances from human experts. We introduce a new consistency test for configuration changes. This test also helps to evaluate the sensitivity to configuration changes. We describe the implementation of these concepts in our fuzzy constraint library ConFLIP++ and in our heuristic repair library D'ej`aVu. Finally, we present results from scheduling a continuous caster unit in a steel plant.

The performance of backtracking algorithms for solving finite-domain constraint satisfaction problems can be improved substantially by look-back and look-ahead methods. Look-back techniques extract information by analyzing failing search paths that are terminated by dead-ends. Look-ahead techniques use constraint propagation algorithms to avoid such dead-ends altogether. This survey describes a number of look-back variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space. The last portion of the paper gives an overview of look-ahead methods such as forward checking and dynamic variable ordering, and discusses their combination with backjumping.