Multi-level Stochastic Local Search for SAT

1999

Stochastic local search (SLS) algorithms for the propositional satisfiability problem (SAT) have been successfully applied to solve suitably encoded search problems from various domains. One drawback of these algorithms is that they are usually incomplete. We refine the notion of incompleteness for stochastic decision algorithms by introducing the notion of "probabilistic asymptotic completeness" (PAC) and prove for a number of well-known SLS algorithms whether or not they have this property. We also give evidence for the practical impact of the PAC property and show how to achieve the PAC property and significantly improved performance in practice for some of the most powerful SLS algorithms for SAT, using a simple and general technique called "random walk extension".

Artificial Intelligence, 1999

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. ¥ over ¦ truth variables § © § § (with domain ! t rue false" each), is a conjunction of Î values for a standard Ï Ð 7 T acceptance level are Ë © 4 E Ñ for 1000 tries and © ¥ Ñ T £

Current Journal of Applied Science and Technology

Stochastic Local Search (SLS) algorithms are of great importance to many fields of Computer Sciences and Artificial Intelligence. This is due to their efficient performance when applied for solving randomly generated satisfiability problems (SAT). Our focus in the current work is on one of the SLS dynamic weighting approaches known as multi-level weight distribution (mulLWD). We experimentally investigated the performance and the weight behaviors of mulLWD. Based on our experiments, we observed that the 2nd level weights movements could lead to poor performance of mulLWD, especially when applied for solving large and harder SAT problems. Therefore, we developed a new heuristic that could reduce the cost of the 2nd level neighborhood exploitation known as partial multi-level weight distribution mulLWD+. Experimental results indicate that mulLWD+ heuristic has significantly better performance than mulLWD in a wide range of SAT problems.

Lecture Notes in Computer Science, 2001

This paper proposes a stochastic, and complete, backtrack search algorithm for Propositional Satisfiability (SAT). In recent years, randomization has become pervasive in SAT algorithms. Incomplete algorithms for SAT, for example the ones based on local search, often resort to randomization. Complete algorithms also resort to randomization. These include, state-of-the-art backtrack search SAT algorithms that often randomize variable selection heuristics. Moreover, it is plain that the introduction of randomization in other components of backtrack search SAT algorithms can potentially yield new competitive search strategies. As a result, we propose a stochastic backtrack search algorithm for SAT, that randomizes both the variable selection and the backtrack steps of the algorithm. In addition, we describe and compare different organizations of stochastic backtrack search. Finally, experimental results provide empirical evidence that the new search algorithm for SAT results in a very competitive approach for solving hard real-world instances.

Journal of Automated Reasoning, 2000

Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and O perations 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

Lecture Notes in Computer Science, 2002

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 + .

Lecture Notes in Computer Science, 2007

In this paper we describe a stochastic local search (SLS) procedure for finding satisfying models of satisfiable propositional formulae. This new algorithm, gNovelty + , draws on the features of two other WalkSAT family algorithms: R+AdaptNovelty + and G 2 WSAT, while also successfully employing a dynamic local search (DLS) clause weighting heuristic to further improve performance. gNovelty + was a Gold Medal winner in the random category of the 2007 SAT competition. In this paper we present a detailed description of the algorithm and extend the SAT competition results via an empirical study of the effects of problem structure and parameter tuning on the performance of gNovelty + . The study also compares gNovelty + with two of the most representative WalkSAT-based solvers: G 2 WSAT, AdaptNovelty + , and two of the most representative DLS solvers: RSAPS and PAWS. Our new results augment the SAT competition results and show that gNovelty + is also highly competitive in the domain of solving structured satisfiability problems in comparison with other SLS techniques.

Journal on Satisfiability, Boolean Modeling and Computation, 2008

In this paper we describe a stochastic local search (SLS) procedure for finding models of satisfiable propositional formulae. This new algorithm, gNovelty + , draws on the features of two other WalkSAT family algorithms: AdaptNovelty + and G 2 WSAT, while also successfully employing a hybrid clause weighting heuristic based on the features of two dynamic local search (DLS) algorithms: PAWS and (R)SAPS.

Parallel Problem Solving from Nature, 2004

MAX-SAT is a well-known optimisation problem that can be seen as a generalisation of the propositional satisfiability problem. In this study, we in- vestigate how the performance of stochastic local search (SLS) algorithms — a large and prominent class of algorithms that includes, for example, Tabu Search, Evolutionary Algorithms and Simulated Annealing — depends on features of the underlying search

International Journal of Knowledge-based and …, 2005

The boolean satisfiability problem (SAT) is stated as follows: given a boolean formula in CNF, find a truth assignment that satisfies its clauses. In this paper, we present a general framework based on stochastic local search and the structure of the CNF formula for solving ...