We describe a two phase algorithm for MAX--SAT and weighted MAX-- SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the Davis--Putnam--Loveland algorithm, to find a provably optimal solution. The first heuristic stage improves the performance of the algorithm by obtaining an upper bound on the minimum number of unsatisfied clauses that can be used in pruning branches of the search tree. We compare our algorithm with an integer programming branch and cut algorithm. Our implementation of the two phase algorithm is faster Research partially supported by ONR Grant number N00014--94--1--0391. y Mathematics Department, New Mexico Tech, Socorro, NM 87801. z Department of Mathematical Sciences, Clemson University, Clemson, SC 29634 than the integer programming approach on many problems. However, the integer programming approach is more effective than the two phase algorithm o...

Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the run-time behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the run-time distribution provides important information about the behaviour of SLS algorithms. In this paper we investigate the empirical run-time distributions for Walksat, one of the most powerful SLS algorithms for the Propositional Satisfiability Problem (SAT). Using statistical analysis techniques, we show that on hard Random-3-SAT problems, Walksat's run-time behaviour can be characterised by exponential distributions. This characterisation can be generalised to various SLS algorithms for SAT and to encoded problems from other domains. This result also has a number of consequences which are of theoretical as well as practical interest. One of these is the fact that these algorithms can be easily parallelised such that optimal speed-up is achieved for hard problem instances.

Abstract. In this paper, we show how Guided Local Search (GLS) can be applied to the SAT problem and show how the resulting algorithm can be naturally extended to solve the weighted MAX-SAT problem. GLS is a general, penalty-based metaheuristic, which sits on top of local search algorithms to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real life problems, such as the travelling salesman problem, BT's workforce scheduling problem, the radio link frequency assignment problem and the vehicle routing problem. We present empirical results of applying GLS to instances of the SAT problem from the DIMACS archive and also a small set of weighted MAX-SAT problem instances and compare them against the results of other local search algorithms for the SAT problem. Keywords: SAT problem, Local Search, Meta-heuristics, Optimisation 1.

Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. One important feature of SLS algorithms is the fact that their run-time behavior is characterized by a random variable. Consequently, the detailed knowledge of the run-time distribution provides important information for the analysis of SLS algorithms. In this paper we investigate the empirical run-time distributions for several state-of-the-art stochastic local search algorithms for SAT and CSP. Using statistical analysis techniques, we show that on a variety of problems from both randomized distributions and encodings of the blocks world planning and graph coloring domains, the observed run-time behavior can be characterized by exponential distributions. As a first direct consequence of this result, we establish that these algorithms can be easily parallelized with optimal speedup.

MAX-SAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAXSAT that combines Iterated Local Search and Tabu Search, two well-known SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current state-of-the-art MAX-SAT algorithms on various widely studied classes of unweighted and weighted MAX-SAT instances, particularly for Random-3-SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAX-SAT instances.

... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the learning of feedforward neural networks, (b) the design of quadrature-mirror-filter digital filter banks, (c) the satisfiability problem, (d) the maximum satisfiability problem, and (e) the design of multiplierless quadrature-mirror-filter digital filter banks. Our method achieves better solutions than existing methods, or achieves solutions of the same quality but at a lower cost.

In recent years, there has been an explosion of research in AI into propositional satis ability (or Sat). There are many factors behind the increased interest in this area. One factor is the improvement in search procedures for Sat. New local search procedures like Gsat are able to solve Sat problems with thousands of variables. At the same time, implementations of complete search algorithms like Davis-Putnam have been able to solve open mathematical problems. Another factor is the identi cation of hard Sat problems at a phase transition in solubility. A third factor is the demonstration that we can often solve real world problems by encoding them into Sat. There has also seen an improved theoretical understanding of Sat, particularly in the analysis of such phase transition behaviour. This paper reviews the state of the art for research into satis ability, and discuss applications in which algorithms for satis ability have proved successful.

Abstract. We describe a branch and cut algorithm for both MAX-SAT and weighted MAX-SAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. We compare our algorithm to an extension of the Davis Putnam Loveland (EDPL) algorithm. Our algorithm is more e ective than EDPL on some problems, notably MAX-2-SAT. EDPL is more e ective on some other classes of problems. 1.

Casting planning problems as propositional satisfiability problems has recently been shown to be an effective way of scaling up plan synthesis. Until now, the benefits of this approach have only been utilized in primitive action-based planning models. Motivated by the conventional wisdom in the planning community about the effectiveness of hierarchical task network (HTN) planning models, in this paper we adapt the "planning as satisfiability" approach to HTN planning models. HTN planning models can be thought of as an augmentation of primitive action based planning models with a grammar of legal solutions, provided in the form of non-primitive tasks and task reduction schemas. Accordingly, we argue that any action-based encoding scheme can be generalized to handle HTN planning models. Informally, this generalization involves adding constraints to the encoding to ensure that the solutions produced by solving the encoding will conform to the grammar provided by the HTN planning model. Th...

Meta-heuristics support managers in decision-making with robust tools that provide high-quality solutions to important applications in business, engineering, economics and science in reasonable time horizons. In this paper we give some insight into the state of the art of meta-heuristics. This primarily focuses on the significant progress which general frames within the meta-heuristics field have implied for solving combinatorial optimization problems, mainly those for planning and scheduling.