求解多文字可满足SAT问题的置信传播算法

可满足(SAT)问题是指:是否存在一组布尔变元赋值,使得合取范式公式中每个子句至少有一个文字为真.多文字可满足SAT问题是指:是否存在一组布尔变元赋值,使得CNF公式中每个子句至少有两个文字为真.显然,此问题仍然是一个NP难问题.为了研究解决多文字可满足SAT问题的算法,引入随机实例产生模型,设计求解多文字可满足SAT问题的置信传播算法.最后,用实例模型产生了大量数据进行实验验证,结果表明:该算法求解多文字可满足SAT问题的性能优于其他启发式算法.     

可满足性问题中信念传播算法的收敛性分析

信念传播算法是基于因子图模型的消息传递算法,通过图中的边,将消息从一个结点传递给另一个结点,以高概率地确定部分变量的取值,这种方法被实验证明在求解可满足性问题时非常有效.然而,目前还未对其有效性从理论角度给予解释.通过对信念传播算法的收敛性分析,试图从理论上解释算法的有效性.在信息传播算法的信息迭代方程中,参数的取值范...     

一种改进的警示传播算法求解Max-SAT问题

Max-SAT问题是SAT问题的优化版本,目标是在给定的子句集中找到一组变元赋值,使得满足子句数最多,该问题是典型的NP-hard问题。随着大数据和人工智能的深度发展,过去原有的算法已不再适用,设计新的求解算法或对已有的求解算法进行优化是目前研究的热点。针对警示传播算法求解随机Max-3-SAT问题的局限性,提出了一种基于变元权值计算的警示传播算法,结合随机游走算法,给出一种新型算法WWP+WalkSAT,通过改进求解的局限性,更好地得到一组有效的初始解,从而提高算法的局部搜索能力。利用2016年Max-SAT国际竞赛部分基准实例,将WWP+WalkSAT算法与八种局部搜索算法进行精度方面的对比实验。实验结果表明,WWP+WalkSAT算法有较好的性能。     

求解可满足性问题的信息传播算法研究综述

信息传播算法来自统计物理,被广泛应用于人工智能各个领域,特别是求解组合优化问题时,具有良好的有效性。通过对信息传播算法的相关文献进行分析,综述了信息传播算法以及其相关应用的发展史,根据信息传播算法的发展,介绍了求解可满足性问题的信息传播算法相关概念,主要涉及到警示传播算法、置信传播算法和调查传播算法,描述了三种算法发展中出现的收敛性、有效性研究,分别综述了各个算法在相关领域的应用情况,并总结了信息传播算法的研究路径和应用方向。     

调查传播算法和蚁群算法相结合求解可满足性问题

布尔可满足性问题(Boolean Satisfiability Problem,SAT)是逻辑学的一个基本问题,也是NP-hard问题。调查传播算法(Survey Propagation,SP)是求解SAT的一种非常高效的算法,但SP在难解区域极易不收敛,或者出现错误赋值。将SP算法与蚁群算法结合,把SP算法得到的消息值应用到蚁群算法中来求解3-SAT问题,使用这些消息值引导蚁群算法求解,并在算法中加入高效的局部搜索。新算法对于SP算法不收敛的一些实例也能很快找到解。     

随机可满足实例集上警示传播算法的收敛性

信息传播算法在求解随机kSAT问题时有惊人的效果,难解区域变窄.对于这种现象,至今缺少系统的理论解释.警示传播(warning propagation,简称WP)算法是一种基础的信息传播算法,为有效分析WP算法在随机kCNF公式上的收敛性,给出了随机kCNF公式因子图上圈存在的相变点.在随机kCNF公式产生模型G(n,k,p)中,取k=3,p=d/n2,因子图中圈存在的相变点为p=1/8n2.当d＜1/8时,因子图中开始出现圈,且每个连通分支至多有一个圈,因子图中含圈的连通分支的数目以及圈的长度均与n无关.因此,因子图是由森林和一些含有唯一圈的连通分支构成.证明了WP算法在这些实例集上高概率收敛,并且给出了算法的迭代步数为O(logn+s),其中,s为连通分支的大小.     

基于多Agent的可满足性问题求解系统研究

为了得到高效可扩展的可满足性问题求解方法,融合目前解决可满足性问题(SAT)的诸多最新策略:快速DPLL、启发式极性决策算法等,提出了一种基于多Agent(Multi-Agent)的可满足性问题(SAT)验证方法.该方法给出了基于多Agent的可满足性问题求解系统的总体结构、工作流程和消息协议,详细分析了有关Agent的结构原理,在JADF(Java Agent development framework)基础上设计出智能仿真模型,通过实例研究表明该方法比传统的一般性求解方法精度高、速度快,且有较好的扩展性和可移植性.     

求解可满足性问题的改进的模拟退火算法

该文为可满足性问题的高效近似求解提出了改进的模拟退火算法。数值实验表明,对于该文随机产生的测试问题例,改进的模拟退火算法完全胜过局部搜索算法、模拟退火算法以及目前国际上流行的WSAT算法。     

求解QBF 问题的启发式调查传播算法

提出了一种启发式调查传播算法,并基于该算法设计了一种QBF(quantified Boolean formulae)求解器——HSPQBF(heuristic survey propagation algorithm for solving QBF)系统.它将Survey Propagation信息传递方法应用到QBF求解问题中.利用Survey Propagation作为启发式引导DPLL(Davis,Putnam,Logemann and Loveland)算法,选择合适的变量进行分支,从而可以减小搜索空间,并减少算法回退的次数.在分支处理过程中,HSPQBF系统结合了单元传播、冲突学习和满足蕴涵学习等一些优秀的QBF求解技术,从而能够提高QBF问题的求解效率.实验结果表明,HSPQBF无论在随机问题上还是在QBF标准测试问题上都有很好的表现,验证了调查传播技术在QBF问题求解中的实际价值.     

可满足性问题全部解的求解算法

SAT问题在人工智能、计算机基础理论研究和人工智能等领域有着广泛的应用,近年来,证明该问题的可满足性取得了巨大的成功,但在求出SAT问题的所有解方面还有待进一步研究。利用一个简单的变换,将可满足性（SAT）问题转化为多项式形式,然后根据命题逻辑的性质以及多项式的性质,得到一个求解出SAT问题所有解的算法。实验结果显示该算法是有效和可行的。     

A parsimony tree for the SAT2002 competition

Twenty of the programs (solvers) submitted to the SAT 2002 Contest had no disqualifying errors. These solvers were run on 2023 satisfiability problems of varying hardnesses. Each solver was judged by which problems it could solve within the allowed time limit. Twelve solvers were best on some problem – they could solve it and the others could not. Only two solvers could not beat each remaining solver on some problems (where the problems could vary depending on which solver it was trying to beat). Thus, there is evidence that 18 solvers were extremely good. It is interesting to analyze the contest results in a way that groups together solvers with similar strengths and weaknesses. This paper uses the parsimony algorithm to produce a classification of the twenty solvers. The paper also has a second classification, almost the same as the first, for the twenty solvers, updated versions of two solvers, and a fictitious state of the art solver. The contest problems came in three groups, Industrial, Hand Made, and Random. The Random group of problems was about three times as large as the other two together. The classification identifies four groups of solvers (plus a miscellaneous group): weak solvers, incomplete solvers which are very good at some satisfiable Random problems, complete solvers which are very good at most Random problems, and complete solvers which are very good at Industrial and Hand Made problems.     

A parsimony tree for the SAT2002 competition

Twenty of the programs (solvers) submitted to the SAT 2002 Contest had no disqualifying errors. These solvers were run on 2023 satisfiability problems of varying hardnesses. Each solver was judged by which problems it could solve within the allowed time limit. Twelve solvers were best on some problem — they could solve it and the others could not. Only two solvers could not beat each remaining solver on some problems (where the problems could vary depending on which solver it was trying to beat). Thus, there is evidence that 18 solvers were extremely good. It is interesting to analyze the contest results in a way that groups together solvers with similar strengths and weaknesses. This paper uses the parsimony algorithm to produce a classification of the twenty solvers. The paper also has a second classification, almost the same as the first, for the twenty solvers, updated versions of two solvers, and a fictitious state of the art solver. The contest problems came in three groups, Industrial, Hand Made, and Random. The Random group of problems was about three times as large as the other two together. The classification identifies four groups of solvers (plus a miscellaneous group): weak solvers, incomplete solvers which are very good at some satisfiable Random problems, complete solvers which are very good at most Random problems, and complete solvers which are very good at Industrial and Hand Made problems.     

利用近似解加速求解SAT问题的启发式完全算法

结合DPLL完全算法能够证明可满足性(SAT)问题的不可满足性和局部搜索算法快速的优点,提出利用近似解加速求解SAT问题的启发式完全算法.首先利用局部搜索算法快速地得到一个近似解,并将该近似解作为完全算法的初始输入,用于其中分支变量的相位决策.该算法引导完全算法优先搜索近似解所在的子空间,加速解决器找到可满足解的过程,为SAT问题的求解提供了一种新的有效途径.实验结果表明,该算法有效地提高了决策的精度和SAT解决器的效率,对很多实例非常有效.     

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.     

一种结合局部搜索策略的求解TSP的演化算法

介绍了一种结合局部搜索策略的求解流动旅行商问题（TSP）的演化算法。该算法的主要思想是将局部搜索策略在邻域内搜索的快速性与演化方法在全局搜索上的鲁棒性结合起来，从而跳离局部最优。将该算法用于TSPLIB中部分TSP实例上的试验结果表明：与传统的各种求解TSP的演化方法相比，该算法在获得全局最优解的精确度上有了一定的改善。     

改进万有引力搜索算法及在水位辨识中的应用

针对万有引力搜索算法(Gravitational Search Algorithm,GSA)的早熟收敛和寻优精度问题,提出了一种改进的GSA算法。算法采用混沌序列初始化种群位置,采用淘汰机制及变异操作增加种群的多样性,避免陷入局部最优。通过对6个非线性基准函数进行仿真测试,结果表明:所提出的算法对非线性函数具有良好的优化性能。将上述算法用于双容水箱水位的辨识,辨识结果验证了提出算法的有效性。     

蚁群优化算法及其应用

蚂蚁算法是由意大利学者M．Dorigo等人提出的一种新型的模拟进化算法。该算法首先应用于旅行商问题并获得了极大的成功,其后,又被用于求解指派问题、Job—shop调度问题、图着色问题和网络路由问题等。实践证明,蚂蚁算法是一种鲁棒性强、收敛性好、实用性广的优化算法,但同时也存在一些不足,如收敛速度慢和容易出现停滞现象等。     

基本蚂蚁算法中参数的讨论与改进

从基本蚂蚁算法出发,结合实验结果,讨论了ρ、Q及α、β的变化对实验结果的影响,提出了相应的参数改进方案。并将经此方案修正的蚂蚁算法与基本蚂蚁算法同时运用于经典TSP问题中,对仿真结果进行了比较。