规划问题编码成SAT问题研究

智能规划问题是一个NP-hard的问题。近年来,由于在可满足问题(SAT)研究领域取得了较大进展,出现了一大批快速的能达到工业级应用的SATsolver求解器的出现,这使得运用可满足技术来求解规划问题的方法越来越得到智能规划研究者们的重视。用可满足技术求解规划问题的首要任务是必须将规划问题"翻译"成可满足问题。讨论了如何将规划问题编码成命题可满足问题的一般技术,并对"直接编码"和"基于规划图的编码"两种编码技术进行了比较,指出了两种编码技术各自的优缺点。在此基础上,深入地分析了各种不同的编码方案之间的异同点以及它们各自的优缺点。最后,指出了用SAT技术求解规划问题中存在的一些问题以及相关改进方法。     

方位关系约束满足问题的推理求解

约束满足问题（Constraint Satisfaction Problems CSP）是人工智能的一个研究领域，诸如空间查找、规划等问题都可转化为约束满足问题。方位关系是空间关系的重要组成部分，用以确定空间对象间的一种顺序。本文研究了空间方位关系模型，给出了方位关系约束的一般表示形式。在此基础上，利用组合表推理给出了方位关系约束满足问题的一个推理求解算法，该算法的时间复杂度为O（n^2）。     

基于约束规划的一类排序问题通用求解方法

多约束排序问题是生产调度中常遇到的问题,传统的优化模型及方法在适应约束改变等方面存在诸多不足。鉴于此,将多约束排序问题定义为约束满足问题,系统设计时将模型定义与求解算法分离,利用约束规划平台的基本约束构建特定领域的抽象约束库,形成可重构的多约束排序问题通用求解框架。应用时,根据问题需求不同可利用抽象约束库快速重构优化模型,针对重构的优化模型配置相应的求解算法即可实现问题求解。应用结果表明,提出的方法通用性强,可满足实际应用的要求。     

约束满足问题求解的符号OBDD桶消元算法

桶消元算法是求解约束满足问题的一种典型推理方法.针对桶消元算法面临的状态空间爆炸问题,将有序二叉决策图( OBDD)技术与该算法结合起来,给出了约束满足问题的一种求解算法.通过对约束满足问题中变量和域值的编码,将CSP问题转化为命题可满足性问题,给出了约束满足问题的OBDD表示方法;基于桶消元的算法思想,在约束满足问题...     

多UCAV 任务分配的混合遗传算法与约束处理

针对多UCAV协同作战任务分配问题，建立了多目标整数规划模型，提出了基于整数编码的混合遗传算法．将约束分为全局约束和局部约束，根据局部约束将决策变量分为自由变量和非自由变量，仅对非自由变量进行编码，减少了染色体变化要素．设计了交叉算子和变异算子，以提高个体的约束满足率．以UCAV的SEAD任务为想定进行仿真，实验结果表明，该混合遗传算法可有效解决大规模整数规划问题，在求解效率和约束满足率上比标准遗传算法有显著提高．     

一类非凸优化问题的遗传算法

线性二层规划是一类特殊的非凸优化问题,为了有效求解该问题,提出了一种基于单纯形方法的遗传算法。首先基于下层约束给出了一种新的编码方法;其次利用单纯形表的信息得到了下层问题的解函数,并结合最优性条件给出了适应度函数;最后基于个体编码的特点,设计了新的遗传算子。数值结果表明,所提出的算法是可行有效的。     

多资源约束的项目调度问题离散粒子群算法

提出了一种求解多资源约束项目调度问题的离散粒子群算法。调度方案采用了优先权整数编码方法,使用稀疏存储邻接矩阵判定先后约束,使用活动单位时间推迟策略来满足资源约束。算法的创新点在于直接使用了整数编码的调度方案参与迭代计算,并依据计算结果提供的信息做出位置交换。不但解决了处理离散整数编码粒子的难题,而且容易实现,亦可推广至类似整数编码优化问题。测试用例计算结果表明了算法的可行性和有效性。     

求解0-1规划问题的DNA计算模型(英文)

DNA计算是以DNA分子作为数据的一种新型计算模式．在DNA计算中首要面对的问题是编码问题．文中提出了一种双编码方法,利用这种编码方法可以使得在DNA计算的读解过程类似于DNA测序过程,容易实现自动化操作．基于该编码方法所建立的DNA计算模型可用于求解0-1规划问题,只需4次PCR反应即可读取问题的可行解．与其他DNA计算模型相比,该模型具有操作简单、易于实现的优点．     

基于遗传算法的多模式资源约束项目调度问题研究*

为解决多模式资源约束项目调度问题,提出了一种混合遗传算法的求解方法。该算法采用二维编码方法来表示问题的解,基因的值表示任务的优先权和执行模式,每条染色体对应一个满足逻辑关系约束的可行任务排序,根据染色体所对应的任务调度顺序和执行模式序列可以获得一个满足资源约束的项目调度方案。应用该编码方法进行选择、交叉和变异等遗传操作,能够使搜索范围遍及整个问题解空间。实际应用表明,该算法能快速求得问题的最优解或近似最优解。     

基于模型检测的领域约束规划

基于模型检测的智能规划是当今通用的智能规划研究的热点,其求解效率比较高.但是,目前基于模型检测的智能规划系统没有考虑到利用领域知识来提高描述能力和求解效率.为此,研究了增加领域约束的基于模型检测的智能规划方法,并据此建立了基于模型检测的领域约束规划系统DCIPS(domain constraints integrated planning system).它主要考虑了领域知识在规划中的应用,将领域知识表示为领域约束添加到规划系统中.根据"规划=动作+状态",DCIPS将领域约束分为3种,即对象约束、过程约束和时序约束,采用对象约束来表达状态中对象之间的关系,采用过程约束来表达动作之间的关系,采用时序约束表达动作与状态中对象之间的关系.通过在2002年智能规划大赛AIPS 2002上关于交通运输领域的3个例子的测试,实验结果表明,利用领域约束的DCIPS可以方便地增加领域知识,更加实用化,其效率也有了相应的提高.     

meSAT: multiple encodings of CSP to SAT

One approach for solving Constraint Satisfaction Problems (CSP) (and related Constraint Optimization Problems (COP)) involving integer and Boolean variables is reduction to propositional satisfiability problem (SAT). A number of encodings (e.g., direct, log, support, order) for this purpose exist as well as specific encodings for some constraints that are often encountered (e.g., cardinality constraints, global constraints). However, there is no single encoding that performs well on all classes of problems and there is a need for a system that supports multiple encodings. We present a system that translates specifications of finite linear CSP problems into SAT instances using several well-known encodings, and their combinations. We also present a methodology for selecting a suitable encoding based on simple syntactic features of the input CSP instance. Thorough evaluation has been performed on large publicly available corpora and our encoding selection method improves upon the efficiency of existing encodings and state-of-the-art tools used in comparison.     

基于问题结构的启发式策略在析取时态问题求解中的应用

智能规划和调度中的许多时态(或时序)问题可以表达为析取时态问题(DTP).目前,多数析取时态问题求解器将析取时态问题看作约束可满足问题(CSP)或可满足问题(SAT),并使用标准的CSP(或SAT)技术来求解DTP.虽然这些技术在求解DTP时已经可以达到较好的效率,然而,文献中极少研究者关注利用DTP本身特殊的结构中隐含的信息来帮助DTP求解.尝试从DTP的拓扑结构中提取出一种启发式策略.这种启发式策略试图从DTP的结构中提取出定性和定量的标准(TVS)来选择优先赋给当前变量的值,同时基于这种定量值选择标准设计了一个动态变量选择策略(TVO).这种技术基于定义的一种DTP的图模型--析取时态网络(DTN).实验结果显示TVS和TVO策略均可以有效减小搜索中节点访问次数;同时它与已有的RSV值选择策略效果相当,而TVO优于最少剩余值(MRV)方法(节省一个数量级以上的访问节点数);此外,配合其他CSP启发技术,可以得到一个高效的DTP求解算法DTN-DTP.     

基于多起点和Mask策略的深度强化学习算法求解覆盖旅行商问题

覆盖旅行商问题(covering salesman problem,CSP) 是旅行商问题的变体,在防灾规划、急救管理中有着广泛应用.由于传统方法求解问题实例耗时严重,近年来深度神经网络被提出用于解决该类组合优化问题,在求解速度和泛化性上有明显的优势.现有基于深度神经网络求解CSP的方法求解质量较低,特别在大规模实例上与传统的启发式方法相比存在较大差距.针对上述问题,提出一种新的基于深度强化学习求解CSP的方法,由编码器对输入特征进行编码,提出新的Mask策略对解码器使用自注意力机制构造解的过程进行约束,并提出多起点策略改善训练过程、提高求解质量.实验结果表明,所提方法对比现有基于深度神经网络的求解方法进一步缩小了最优间隙,同时有着更高的样本效率,在不同规模和不同覆盖类型的CSP中展现出更强的泛化能力,与启发式算法相比在求解速度上有10sim40倍的提升.     

Solution Techniques for Constraint Satisfaction Problems: Foundations

The Constraint Satisfaction Problem (CSP) is ubiquitous in artificialintelligence. It has a wide applicability, ranging from machine visionand temporal reasoning to planning and logic programming. This paperattempts a systematic and coherent review of the foundations ofthe techniques for constraint satisfaction. It discusses in detail thefundamental principles and approaches. This includes an initialdefinition of the constraint satisfaction problem, a graphical meansof problem representation, conventional tree search solutiontechniques, and pre-processing algorithms which are designed to makesubsequent tree search significantly easier.     

一个基于最小冲突修补的动态约束满足求解算法

约束满足问题是人工智能中一个重要的研究方向,近年来,对动态变化的约束满足问题的研究逐渐成为该领域的热点.在目前该领域最流行的LC算法基础上,引入禁忌搜索策略,提出了一个基于最小冲突修补的算法Tabu_LC.算法在每次冲突调整时将所有冲突变量看成一个整体,并采用分支定界搜索策略求解冲突变量组成的子问题,极大地提高了求解效率.同时,在约束求解系统"明月1.0"架构下给出了算法的具体实现,并针对大量随机问题进行了对比实验.结果表明,Tabu_LC算法在求解效率和解的质量上都明显优于LC算法.     

Many hard examples in exact phase transitions

This paper analyzes the resolution complexity of two random constraint satisfaction problem (CSP) models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families of CSPs and CNF formulas hard to solve, which can be useful in the experimental evaluation of CSP and SAT algorithms, but also propose models with both many hard instances and exact phase transitions. Finally, conclusions are presented, as well as a detailed comparison of Model RB/RD with the Hamiltonian cycle problem and random 3-SAT, which, respectively, exhibit three different kinds of phase transition behavior in NP-complete problems.     

A Mixed Closure-CSP Method for Solving Scheduling Problems

Scheduling problems can be viewed as a set of temporal metric and disjunctive constraints and so they can be formulated in terms of CSP techniques. In the literature, there are CSP-based methods which sequentially interleave search efforts with the application of consistency enforcing mechanisms and variable/ordering heuristics. Therefore, the number of backtrackings needed to obtain a solution is reduced. In this paper, we propose a new method that effectively integrates the CSP process into a limited closure process: not by interleaving them but rather as a part of the same process. Such an integration allows us to define more informed heuristics. These heuristics are used to limit the complete closure process to a maximum number of disjunctions, thereby reducing its complexity while at the same time reducing the search space. Some open disjunctive solutions can be maintained in the CSP process, limiting the number of backtrackings necessary, and avoiding having to know all the problem constraints in advance. Our experiments with flow-shop and job-shop instances show that this approach obtains a feasible solution/optimal solution without having to use backtracking in most cases. We also analyze the behaviour of our algorithm when some constraints are known dynamically and we demonstrate that it can provide better results than a pure CSP process.     

Approximating Satisfiable Satisfiability Problems

We study the approximability of the Maximum Satisfiability Problem (MAX SAT) and of the boolean k -ary Constraint Satisfaction Problem (MAX k CSP) restricted to satisfiable instances. For both problems we improve on the performance ratios of known algorithms for the unrestricted case. Our approximation for satisfiable MAX 3CSP instances is better than any possible approximation for the unrestricted version of the problem (unless P=NP). This result implies that the requirement of perfect completeness weakens the acceptance power of non-adaptive PCP verifiers that read 3 bits. We also present the first non-trivial results about PCP classes defined in terms of free bits that collapse to P. Received August 1997; revised February 1999.     

Solution Techniques for Constraint Satisfaction Problems: Advanced Approaches

Conventional techniques for the constraint satisfaction problem (CSP)have had considerable success in their applications. However,there are many areas in which the performance of the basic approachesmay be improved. These include heuristic ordering of certain tasksperformed by the CSP solver, hybrids which combine compatible solutiontechniques and graph based methods which exploit the structure of theconstraint graph representation of a CSP. Also, conventionalconstraint satisfaction techniques only address problems with hardconstraints (i.e. each of which are completely satisfied or completelyviolated, and all of which must be satisfied by a validsolution). Many real applications require a more flexible approachwhich relaxes somewhat these rigid requirements. To address theseissues various approaches have been developed. This paper attempts asystematic review of them.