求解可满足问题的改进的蚁群算法

可满足问题（SAT）是一个NP-hard问题,将SAT问题转换为无约束的离散优化（最小值）问题。并根据M Dorigo提出的蚁群算法,给出了一种求解SAT问题的新方法：改进的最大最小蚁群系统（MMAS-SAT）。在改进的算法中,给出了SAT问题的构造图,指出了启发式信息值的求法,对衰变系数进行了动态调整。测试问题的数值实验表明,采用MMAS-SAT的结果优于Gwsat、Walksat、Novelty等局部搜索算法,因此该算法是求解SAT问题的一种可行高效的算法。     

Evolutionary algorithms for the satisfiability problem

Several evolutionary algorithms have been proposed for the satisfiability problem. We review the solution representations suggested in literature and choose the most promising one - the bit string representation - for further evaluation. An empirical comparison on commonly used benchmarks is presented for the most successful evolutionary algorithms and for WSAT, a prominent local search algorithm for the satisfiability problem. The key features of successful evolutionary algorithms are identified, thereby providing useful methodological guidelines for designing new heuristics. Our results indicate that evolutionary algorithms are competitive to WSAT.     

Heuristic-Based Backtracking Relaxation for Propositional Satisfiability

In recent years backtrack search algorithms for propositional satisfiability (SAT) have been the subject of dramatic improvements. These improvements allowed SAT solvers to successfully solve instances with thousands or tens of thousands of variables. However, many new challenging problem instances are still too hard for current SAT solvers. As a result, further improvements to SAT technology are expected to have key consequences in solving hard real-world instances. This paper introduces a new idea: choosing the backtrack variable using a heuristic approach with the goal of diversifying the regions of the space that are explored during the search. The proposed heuristics are inspired by the heuristics proposed in recent years for the decision branching step of SAT solvers, namely, VSIDS and its improvements. Completeness conditions are established, which guarantee completeness for the new algorithm, as well as for any other incomplete backtracking algorithm. Experimental results on hundreds of instances derived from real-world problems show that the new technique is able to speed SAT solvers, while aborting fewer instances. These results clearly motivate the integration of heuristic backtracking in SAT solvers.     

Randomized local search,evolutionary algorithms,and the minimum spanning tree problem

Randomized search heuristics, among them randomized local search and evolutionary algorithms, are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimization. The analysis of these randomized search heuristics has been started for some well-known problems, and this approach is followed here for the minimum spanning tree problem. After motivating this line of research, it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms.     

Exploiting multivalued knowledge in variable selection heuristics for SAT solvers

We show that we can design and implement extremely efficient variable selection heuristics for SAT solvers by identifying, in Boolean clause databases, sets of Boolean variables that model the same multivalued variable and then exploiting that structural information. In particular, we define novel variable selection heuristics for two of the most competitive existing SAT solvers: Chaff, a solver based on look-back techniques, and Satz, a solver based on look-ahead techniques. Our heuristics give priority to Boolean variables that belong to sets of variables that model multivalued variables with minimum domain size in a given state of the search process. The empirical investigation conducted to evaluate the new heuristics provides experimental evidence that identifying multivalued knowledge in Boolean clause databases and using variable selection heuristics that exploit that knowledge leads to large performance improvements.      

SAT问题中局部搜索法的改进

局部搜索方法在求解SAT问题的高效率使其成为一研究热点．提出用初始概率的方法对局部搜索算法中变量的初始随机指派进行适当的约束．使在局部搜索的开始阶段,可满足的子句数大大增加,减少了翻转的次数,加快了求解的速度．用该方法对目前的一些重要的SAT问题的局部搜索算法(如WSAT,TSAT,NSAT,SDF等)进行改进,通过对不同规模的随机3-SAT问题的实例和一些不同规模的结构性SAT问题的实例,以及利用相变现象构造的难解SAT实例测试表明,改进后的这些局部搜索算法的求解效率有了很大的提高．该方法对其他局部搜索法的改进具有参考价值。     

MAX-SAT问题一种改进的局部搜索算法

局部搜索算法是求解大规模SAT问题的高效算法。经典的局部搜索算法有GSAT、WSAT、TSAT、NSAT等,但这些算法的初始解都是随机产生的。本文提出了用单纯形法产生“初始概率”（每个变量取1的概率）,用“初始概率”对局部搜索算法中变量的初始随机指派进行适当的约束,使在局部搜索的开始阶段,满足的子句数大大增加,加快了收敛的速度。通过对不同规模的随机STA问题实例的实验表明,这些改进有效地提高了局部搜索算法求解SAT问题的效率。     

Bilevel competitive facility location and pricing problems

We propose new models for competitive facility location and pricing as bilevel Boolean linear programming problems. We obtain results that characterize the complexity of the problem where a monopolist’s profit on each of the markets is defined with a monotone nonincreasing function of the servicing cost. For this problem, we also propose two approximate algorithms based on the ideas of alternating heuristics and local search. We give results of a computational experiment that show a possibility for fast computation of approximate solutions.     

Machine Discovery of Effective Admissible Heuristics

Admissible heuristics are an important class of heuristics worth discovering: they guarantee shortest path solutions in search algorithms such as A ^* and they guarantee less expensively produced, but boundedly longer solutions in search algorithms such as dynamic weighting. Unfortunately, effective (accurate and cheap to compute) admissible heuristics can take years for people to discover. Several researchers have suggested that certain transformations of a problem can be used to generate admissible heuristics. This article defines a more general class of transformations, called abstractions, that are guaranteed to generate only admissible heuristics. It also describes and evaluates an implemented program (Absolver II) that uses a means-ends analysis search control strategy to discover abstracted problems that result in effective admissible heuristics. Absolver II discovered several well-known and a few novel admissible heuristics, including the first known effective one for Rubik's Cube, thus concretely demonstrating that effective admissible heuristics can be tractably discovered by a machine.     

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function—i.e. a ratio of two polynomials—of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGS’s performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.     

Local Search Algorithms for SAT: An Empirical Evaluation

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 that contains instances from randomized 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.     

Accelerating Differential Evolution Using an Adaptive Local Search

We propose a crossover-based adaptive local search (LS) operation for enhancing the performance of standard differential evolution (DE) algorithm. Incorporating LS heuristics is often very useful in designing an effective evolutionary algorithm for global optimization. However, determining a single LS length that can serve for a wide range of problems is a critical issue. We present a LS technique to solve this problem by adaptively adjusting the length of the search, using a hill-climbing heuristic. The emphasis of this paper is to demonstrate how this LS scheme can improve the performance of DE. Experimenting with a wide range of benchmark functions, we show that the proposed new version of DE, with the adaptive LS, performs better, or at least comparably, to classic DE algorithm. Performance comparisons with other LS heuristics and with some other well-known evolutionary algorithms from literature are also presented.     

Guided Local Search for Solving SAT and Weighted MAX-SAT Problems

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 meta-heuristic, 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 traveling 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 with the results of other local search algorithms for the SAT problem.     

Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: Overview and progress report

Nowadays, a promising way to obtain hybrid metaheuristics concerns the combination of several search algorithms with strong specialization in intensification and/or diversification. The flexible architecture of evolutionary algorithms allows specialized models to be obtained with the aim of providing intensification and/or diversification. The outstanding role that is played by evolutionary algorithms at present justifies the choice of their specialist approaches as suitable ingredients to build hybrid metaheuristics.This paper focuses on hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification. We first give an overview of the existing research on this topic, describing several instances grouped into three categories that were identified after reviewing specialized literature. Then, with the aim of complementing the overview and providing additional results and insights on this line of research, we present an instance that consists of an iterated local search algorithm with an evolutionary perturbation technique. The benefits of the proposal in comparison to other iterated local search algorithms proposed in the literature to deal with binary optimization problems are experimentally shown. The good performance of the reviewed approaches and the suitable results shown by our instance allow an important conclusion to be achieved: the use of evolutionary algorithms specializing in intensification and diversification for building hybrid metaheuristics becomes a prospective line of research for obtaining effective search algorithms.     

Efficient data structures for backtrack search SAT solvers

The implementation of efficient Propositional Satisfiability (SAT) solvers entails the utilization of highly efficient data structures, as illustrated by most of the recent state-of-the-art SAT solvers. However, it is in general hard to compare existing data structures, since different solvers are often characterized by fairly different algorithmic organizations and techniques, and by different search strategies and heuristics. This paper aims the evaluation of data structures for backtrack search SAT solvers, under a common unbiased SAT framework. In addition, advantages and drawbacks of each existing data structure are identified. Finally, new data structures are proposed, that are competitive with the most efficient data structures currently available, and that may be preferable for the next generation SAT solvers.     

Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

Randomized search heuristics like local search, tabu search, simulated annealing, or all kinds of evolutionary algorithms have many applications. However, for most problems the best worst-case expected run times are achieved by more problem-specific algorithms. This raises the question about the limits of general randomized search heuristics. Here a framework called black-box optimization is developed. The essential issue is that the problem but not the problem instance is knownto the algorithm which can collect information about the instance only by asking for the value of points in the search space. All known randomized search heuristics fit into this scenario. Lower bounds on the black-box complexity of problems are derived without complexity theoretical assumptions and are compared with upper bounds in this scenario.     

Efficient data structures for backtrack search SAT solvers

The implementation of efficient Propositional Satisfiability (SAT) solvers entails the utilization of highly efficient data structures, as illustrated by most of the recent state-of-the-art SAT solvers. However, it is in general hard to compare existing data structures, since different solvers are often characterized by fairly different algorithmic organizations and techniques, and by different search strategies and heuristics. This paper aims the evaluation of data structures for backtrack search SAT solvers, under a common unbiased SAT framework. In addition, advantages and drawbacks of each existing data structure are identified. Finally, new data structures are proposed, that are competitive with the most efficient data structures currently available, and that may be preferable for the next generation SAT solvers.     

Configuration landscape analysis and backbone guided local search.: Part I: Satisfiability and maximum satisfiability

Boolean satisfiability (SAT) and maximum satisfiability (Max-SAT) are difficult combinatorial problems that have many important real-world applications. In this paper, we first investigate the configuration landscapes of local minima reached by the WalkSAT local search algorithm, one of the most effective algorithms for SAT. A configuration landscape of a set of local minima is their distribution in terms of quality and structural differences relative to an optimal or a reference solution. Our experimental results show that local minima from WalkSAT form large clusters, and their configuration landscapes constitute big valleys, in that high quality local minima typically share large partial structures with optimal solutions. Inspired by this insight into WalkSAT and the previous research on phase transitions and backbones of combinatorial problems, we propose and develop a novel method that exploits the configuration landscapes of such local minima. The new method, termed as backbone-guided search, can be embedded in a local search algorithm, such as WalkSAT, to improve its performance. Our experimental results show that backbone-guided local search is effective on overconstrained random Max-SAT instances. Moreover, on large problem instances from a SAT library (SATLIB), the backbone guided WalkSAT algorithm finds satisfiable solutions more often than WalkSAT on SAT problem instances, and obtains better solutions than WalkSAT on Max-SAT problem instances, improving solution quality by 20% on average.     

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significant number of applications in Artificial Intelligence as well as in other fields of Computer Science and Engineering. Algorithmic solutions for SAT include, among others, local search, backtrack search and algebraic manipulation. In recent years, several different organizations of local search and backtrack search algorithms for SAT have been proposed, in many cases allowing larger problem instances to be solved in different application domains. While local search algorithms have been shown to be particularly useful for random instances of SAT, recent backtrack search algorithms have been used for solving large instances of SAT from real-world applications. In this paper we provide an overview of backtrack search SAT algorithms. We describe and illustrate a number of techniques that have been empirically shown to be highly effective in pruning the amount of search on significant and representative classes of problem instances. In particular, we review strategies for non-chronological backtracking, procedures for clause recording and for the identification of necessary variable assignments, and mechanisms for the structural simplification of instances of SAT.     

基于加强概率控制策略的SAT局部搜索算法

局部搜索算法是目前求解SAT问题比较有效的方法,而Sattime算法是在SAT国际大赛中获得大奖的一种典型局部搜索算法。在Sattime算法的求解过程中,记录变元翻转事件流数据库,通过数据分析与模式挖掘,发现Sattime算法的局部搜索行为中会出现相邻搜索步选择同一个变元的现象,即所谓的回环现象,从而降低了求解效率。为解决此问题,提出两种概率控制策略：加强子句选择策略和加强变元选择策略,并将这两种策略应用到Sattime算法中,形成新的局部搜索算法Sattime-P。实验结果表明,与Sattime算法相比,改进后的Sattime-P算法求解效率有显著的提升。该方法也对其他局部搜索算法的改进具有参考价值。