Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly well-known families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SAT-encoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithm-dependent and problem-dependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the best-performing algorithms and shows how this can be overcome.

Effective local search methods for finding satisfying assignments of CNF formulae exhibit several systematic characteristics in their search. We identify a series of measurable characteristics of local search behavior that are predictive of problem solving efficiency. These measures are shown to be useful for diagnosing inefficiencies in given search procedures, tuning parameters, and predicting the value of innovations to existing strategies. We then introduce a new local search method, SDF (“smoothed descent and flood”), that builds upon the intuitions gained by our study. SDF works by greedily descending in an informative objective (that considers how strongly clauses are satisfied, in addition to counting the number of unsatisfied clauses) and, once trapped in a local minima, “floods ” this minima by re-weighting unsatisfied clauses to create a new descent direction. The resulting procedure exhibits superior local search characteristics under our measures. We show that this method can compete with the state of the art techniques, and significantly reduces the number of search steps relative to many recent methods. © 2001 Elsevier Science B.V. All rights reserved.

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EA). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping GA on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping GA and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity. Keywords: evolutionary algorithms, genetic algorithms, constraint sati...

We investigate an improvement to GSAT which associates a weight with each clause. We change the objective function so that GSAT moves to assignments maximizing the weight of satis ed clauses, and each clause's weight is changed when GSAT moves to an assignment in which this clause is unsatis ed. We present results showing that this version of GSAT has good performance when clause weights are reduced geometrically throughout the course of a single try. We conclude that clause weights are best interpreted as short-term, context sensitive indicators of how hard di erent clauses are to satisfy. 1

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.

. We investigate three approaches to Boolean satisfiability problems. We study and compare the best heuristic algorithm WGSAT and two evolutionary algorithms, an evolution strategy and an evolutionary algorithm adapting its own fitness function while running. The results show that the adaptive EA outperforms the other two approaches. The power of this EA originates from the adaptive mechanism, which is completely problem independent and generally applicable to any constraint satisfaction problem. This suggests that the adaptive EA is not only a good solver for satisfiability problems, but for constraint satisfaction problems in general. 1 Introduction Handling NP-complete problems with evolutionary algorithms (EAs) is a great challenge. In particular, the presence of constraints makes finding solutions difficult for an EA. In this paper, we investigate solving constraint satisfaction problems (CSPs), in particular the 3-SAT problem, and try three different approaches for solving it: O...

In this chapter we describe a problem independent method for treating constraints in an evolutionary algorithm. Technically, this method amounts to changing the definition of the fitness function during a run of an EA, based on feedback from the search process. Obviously, redefining the fitness function means rede ning the problem to be solved. On the short term this deceives the algorithm making the fitness values deteriorate, but as experiments clearly indicate, on the long run it is beneficial. We illustrate the power of the method on different constraint satisfaction problems and point out other application areas of this technique.

Abstract. Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at escaping local minima but require expensive smoothing phases in which all weights are updated. We show that Walksat performance can be greatly enhanced by weighting variables instead of clauses, giving the best known results on some benchmarks. The new algorithm uses an efficient weight smoothing technique with no smoothing phase. 1

Currently there is a growing interest in the evolutionary algorithm paradigm, as it promises a robust and general search technique. Still, in spite of much research, for many people the question remains how good evolutionary algorithms really are. Therefore, in this research, a successful class of evolutionary algorithms, Steady State evolutionary algorithms, is thoroughly examined to find optimal settings on two NP-complete problems: Graph 3-Coloring and 3-Satisfiability. Several versions of the evolutionary algorithm are tested and evaluated and the best version for each NP-complete problem is compared to a good existing algorithm for each problem. Then extensions for the evolutionary algorithm are presented that make the evolutionary algorithms perform better than the more traditional algorithms on the hardest problem instances. i Preface This research was done as a Master's Thesis for graduating in Computer Science at Leiden University. It is about evolutionary algorithms, searc...

Evolutionary Algorithms, evolution based optimization algorithms, are often applied to combinatorial problems. An important issue in such problems is handling the constraints. This is also one of the most challenging areas within Evolutionary Computation. Several approaches for handling constraints exist, each with their own advantages and disadvantages. Which approach is suitable depends on the given problem. In this thesis, two constrained problems are investigated. For the bin packing problem, a number of constraint handling approaches is implemented, tested and compared. Furthermore, attention is payed to a hybrid approach, i.e., the combination of an evolutionary algorithm and a local optimizer, and asexual evolutionary algorithms. For the satisfiability problem a new idea is tested: a floating point representation together with a continuous graded penalty function. A comparison is made with an evolutionary algorithm with adaptive penalty function. Evolutionary algorithms for both...