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...

. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.

Satisfiability is a class of NP-complete problems that model a wide range of real-world applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Instead of restarting from a new starting point when a search reaches a local trap, the Lagrange multipliers in our method provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. One of the major advantages of our method is that it has very few algorithmic parameters to be tuned by users, and the se...

The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. Traditional methods treat the SAT problem as a constrained decision problem. During past research, the number of unsatisfiable clauses as the value of an objective function was formulated. This transforms the SAT problem into a search problem --- an unconstrained optimization problem to the objective function. A variety of iterative optimization techniques can be used to solve this optimization problem. In this paper, we show how to use local search techniques to solve the SAT problem. The average time complexity analysis and numerous real algorithm executions were performed. They indicate that the local search algorithms are much more efficient than the existing SAT algorithms for certain classes of conjunctive normal form (...

Weighted maximum satisfiability problems (MAX-SAT) are difficult to solve due to the large number of local minima in their search space. In this paper we propose a new discrete Lagrangian based search method (DLM) for solving these problems. Instead of restarting from a new point when the search reaches a local minimum, the Lagrange multipliers in DLM provide a force to lead the search out of the local minimum and move it in a direction provided by the multipliers. Since DLM has very few parameters to be tuned, it can be made deterministic and the results, reproducible. We compare DLM with GRASP in solving a large set of test problems, and show that it finds better solutions and is substantially faster. DLM has a solid theoretical foundation that can be used as a systematic approach for solving general discrete optimization problems. 1 Introduction The satisfiability (SAT) problem is defined as follows. Given a set of n clauses fC 1 , C 2 , \Delta \Delta \Delta, Cn g on m variables x...

Backtracking search is frequently applied to solve a constraint-based search problem but it often suffers from exponential growth of computing time. We present an alternative to backtracking search: local search based on conflict minimization. We have applied this general search framework to study a benchmark constraint-based search problem, the n-queens problem. An efficient local search algorithm for the n-queens problem was implemented. This algorithm, running in linear time, does not backtrack at all. It is capable of finding a solution for extremely large size n-queens problems. For example, on a workstation computer, it can find a solution for 3,000,000 queens in less than 55 seconds. Keywords: conflict minimization, local search, n-queens problem, nonbacktracking search. 1 This research has been supported in part by the University of Utah research fellowships, in part by the Research Council of Slovenia, and in part by ACM/IEEE academic scholarship awards. 1 Introduction A ...

The Reactive Search (RS) method proposes the integration of a simple history-based feedback scheme into local search for the on-line determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component based on local search with temporary prohibitions is complemented with a reactive scheme that determines ("learns") the appropriate value of the prohibition parameter by monitoring the Hamming distance along the search trajectory (algorithm H-RTS). In addition, the non-oblivious functions recently introduced in the framework of approximation algorithms are used to discover a better local optimum in the initial part of the search.

The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT problem on Boolean space f0; 1g m into an unconstrained global optimization problem on real space E m . A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtracking /resolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF ) formulas. It offers a complementary approach to the existing SAT algorithms.

. In this paper we present a method called NOVEL (Nonlinear Optimization via External Lead) for solving continuous and discrete global optimization problems. NOVEL addresses the balance between global search and local search, using a trace to aid in identifying promising regions before committing to local searches. We discuss NOVEL for solving continuous constrained optimization problems and show how it can be extended to solve constrained satisfaction and discrete satisfiability problems. We first transform the problem using Lagrange multipliers into an unconstrained version. Since a stable solution in a Lagrangian formulation only guarantees a local optimum satisfying the constraints, we propose a global search phase in which an aperiodic and bounded trace function is added to the search to first identify promising regions for local search. The trace generates an information-bearing trajectory from which good starting points are identified for further local searches. Taking only a sm...