In this paper, we study the approach of dynamic local search for the SAT problem. We focus on the recent and promising Exponentiated Sub-Gradient (ESG) algorithm, and examine the factors determining the time complexity of its search steps. Based on the insights gained from our analysis, we developed Scaling and Probabilistic Smoothing (SAPS), an efficient SAT algorithm that is conceptually closely related to ESG. We also introduce a reactive version of SAPS (RSAPS) that adaptively tunes one of the algorithm's important parameters. We show that for a broad range of standard benchmark problems for SAT, SAPS and RSAPS achieve significantly better performance than both ESG and the state-of-the-art WalkSAT variant, Novelty.

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.

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.

Recent dynamic local search (DLS) algorithms such as SAPS are amongst the state-of-the-art methods for solving the propositional satisfiability problem (SAT). DLS algorithms modify the search landscape during the search process by means of dynamically changing clause penalties. In this work, we study whether the resulting, ‘warped ’ landscapes are easier to search than the landscapes that correspond to the original problem instances. We present empirical evidence indicating that (somewhat contrary to common belief) this is not the case, and that the main benefit of the dynamic penalty update mechanism in SAPS is an effective diversification of the search process. In most other high-performance stochastic local search algorithms, the same effect is achieved by the strong use of randomised decisions throughout the search. We demonstrate that in SAPS, random decisions are only required in the (standard) search initialisation procedure, and can be completely eliminated from the remainder of the subsequent search process without any significant change in the behaviour or performance of the resulting algorithms compared to the original, fully randomised SAPS algorithm. We conjecture that the reason for this unexpected result lies in the ability of the deterministic variants of the scaling and smoothing mechanism and the subsidiary iterative best improvement mechanism underlying SAPS to effectively propagate the effects of initial randomisation throughout a search process that shows the sensitive dependence on inditial conditions that is characteristic for chaotic processes. 1

In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAX-SAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances.

Abstract. In recent years, dynamic local search (DLS) clause weighting algorithms have emerged as the local search state-of-the-art for solving propositional satisfiability problems. However, most DLS algorithms require the tuning of domain dependent parameters before their performance becomes competitive. If manual parameter tuning is impractical then various mechanisms have been developed that can automatically adjust a parameter value during the search. To date, the most effective adaptive clause weighting algorithm is RSAPS. However, RSAPS is unable to convincingly outperform the best non-weighting adaptive algorithm AdaptNovelty +, even though manually tuned clause weighting algorithms can routinely outperform the Novelty + heuristic on which AdaptNovelty + is based. In this study we introduce R+DDFW +, an enhanced version of the DDFW clause weighting algorithm developed in 2005, that not only adapts the total amount of weight according to the degree of stagnation in the search, but also incorporates the latest resolution-based preprocessing approach used by the winner of the 2005 SAT competition (R+AdaptNovelty +). In an empirical study we show R+DDFW + improves on DDFW and outperforms the other leading adaptive (R+Adapt-Novelty +, R+RSAPS) and non-adaptive (R+G 2 WSAT) local search solvers over a range of random and structured benchmark problems. 1

Abstract. In recent years, dynamic local search (DLS) clause weighting algorithms have emerged as the local search state-of-the-art for solving propositional satisfiability problems. This paper introduces a new approach to clause weighting, known as Divide and Distribute Fixed Weights (DDFW), that transfers weights from neighbouring satisfied clauses to unsatisfied clauses in order to break out from local minima. Unlike earlier approaches, DDFW continuously redistributes a fixed quantity of weight between clauses, and so does not require a weight smoothing heuristic to control weight growth. It also exploits inherent problem structure by redistributing weights between neighbouring clauses. To evaluate our ideas, we compared DDFW with two of the best reactive local search algorithms, AdaptNovelty+ and RSAPS. In both these algorithms, a problem sensitive parameter is automatically adjusted during the search, whereas DDFW uses a fixed default parameter. Our empirical results show that DDFW has consistently better performance over a range of SAT benchmark problems. This gives a strong indication that neighbourhood weight redistribution strategies could be the key to a next generation of structure exploiting, parameter-free local search SAT solvers. 1

A large number of problems that occur in knowledge-representation, learning, VLSI-design, and other areas of artificial intelligence, are essentially satisfiability problems. The satisfiability problem refers to the task of finding a truth assignment that makes a Boolean expression true. The growing need for more efficient and scalable algorithms has led to the development of several SAT solvers. This paper reports the first approach based on combining finite learning automata with metaheuristics. In brief, we introduce a new algorithm that combines finite learning automata with traditional random walk. Furthermore, we present a detailed comparative analysis of the new algorithm's performance, using a benchmark set containing instances from randomized distributions, as well as SAT-encoded problems from various domains.

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