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.

Constraint satisfaction and optimisation is NP-complete by nature. The combinatorial explosion problem prevents complete constraint programming methods from solving many real-life constraint problems. In many situations, stochastic search methods, many of which sacrifice completeness for efficiency, are needed. This paper reports a family of stochastic algorithms for constraint satisfaction and optimisation. Developed with hardware implementation in mind, GENET is a class of computation models for constraint satisfaction. Genet is a connectionist approach. A problem is represented by a network with inhibitory connections. The network is designed to converge, in a fashion that resembles the min-conflict repair method. Reinforcement learning is used to bring GENET out of local optima. Building upon GENET as well as ideas from operations research, Guided Local Search (GLS) and Fast Local Search are novel meta-heuristic search methods for constraint optimisation. GLS sits on top of other l...

This paper reports promising algorithms that have been built on top of both operations research (OR) and constraint programming (CP) research. First we describe Guided Local Search (GLS), a penalty-based meta-heuristic algorithm that sits on top of local search algorithms and helps them to escape local optima. Then we describe Fast Local Search (FLS), a strategy that reduces the size of the neighbourhood. GLS and FLS have been demonstrated to be highly successful in a number of non-trivial problems, including commercial applications. We shall also, in this paper, report selected promising research by other groups in combining OR and CP ideas --- namely (a) Lagrangian Method and (b) fine-grain interaction between mixed integer programming (MIP) and finite domain constraint propagation. The main message that we want to convey in this paper is: there is no real boundary between OR and CP. In fact, OR has already become an important part of CP and a great deal can be gained by cross-fertil...

Local search is one of the fundamental paradigms for solving computationally hard combinatorial problems, including the constraint satisfaction problem (CSP). It provides the basis for some of the most successful and versatile methods for solving the large and difficult problem instances encountered in many real-life applications. Despite impressive advances in systematic, complete search algorithms, local search methods in many cases represent the only feasible way for solving these large and complex instances. Local search algorithms are also naturally suited for dealing with the optimisation criteria arising in many practical applications. The basic idea underlying local search is to start with a randomly or heuristically generated candidate solution of a given problem instance, which may be infeasible, sub-optimal or incomplete, and to iteratively improve this candidate solution by means of typically minor modifications. Different local search methods vary in the way in which improvements are achieved, and in particular, in the way in which situations are handled in which no direct improvement is possible. Most local search methods use randomisation to ensure that the search process does not

Guided Local Search is a general penalty-based optimisation method that sits on top of local search methods to help them escape local optimum. It has been applied to a variety of problems and demonstrated effective. The aim of this paper is not to produce further evidence that Guided Local Search is an effective algorithm, but to present an extension of Guided Local Search that potentially has no parameter to tune. Compared to other algorithms, Guided Local Search is relatively easy to apply, as there is only one major parameter (#) to set. In some applications, performance of Guided Local Search is insensitive to the value of this parameter. Nevertheless, the value of this parameter can affect the performance of Guided Local Search in some problems. In this paper, we show how (a) an aspiration criterion and (b) random moves may be added to Guided Local Search to reduce the sensitivity of its performance to the parameter value. The extended Guided Local Search is tested on the SAT, weighted MAX-SAT and Quadratic Assignment Problems with positive results.