An Algorithm Based on Tabu Search for Satisfiability Problem

In this paper,a computationally effective algorithm based on tabu search for solving the satisfiability problem(TSSAT)is proposed.Some novel and efficient heuristic strategies for generating candidate neighborhood of the curred assignment and selecting varibables to be flipped are presented. Especially,the aspiration criterion and tabu list tructure of TSSAT are different from those of traditional tabu search.Computational experiments on a class of problem insteances show that,TSSAT,in a reasonable amount of computer time ,yields better results than Novelty which is currently among the fastest known.Therefore TSSAT is feasible and effective.     

Task-resource scheduling problem

Cloud computing is a new and rapidly emerging computing paradigm where applications,data and IT services are provided over the Internet.The task-resource management is the key role in cloud computing systems.Task-resource scheduling problems are premier which relate to the efficiency of the whole cloud computing facilities.Task-resource scheduling problem is NPcomplete.In this paper,we consider an approach to solve this problem optimally.This approach is based on constructing a logical model for the problem.Using this model,we can apply algorithms for the satisfiability problem(SAT) to solve the task-resource scheduling problem.Also,this model allows us to create a testbed for particle swarm optimization algorithms for scheduling workflows.     

Onk-positive satisfiability problem

An algorithm for solving the satisfiability problem is presented. It is proved that this algorithm solves 2-SAT and Horn-SAT in linear time andk-positive SAT (in which every clause contains at mostk positive literals) in timeO(|F|·ξ _n ^k ), where |F| is the length of inputF, n is the number of atoms occurring inF, and ξ _k is the greatest real number satisfying the equation . Compared with previous results, this nontrivial upper bound on time complexity could only be obtained fork-SAT, which is a subproblem ofk-positive SAT. Research partially supported by NSFC grant 221-4-1439. HUANG Xiong received his B.S. and M.S. degrees in computer science from Peking University in 1992 and 1995 respectively. Now he is a Ph.D. candidate in Beijing University of Aeronautics and Astronautics. His major research interests are design and analysis of algorithms, computational complexity, and satisfiability problem. LI Wei received his B.S. degree in mathematics from Peking University in 1966 and his Ph.D. degree in computer science from The University of Edinburgh in 1983. Since 1986, he has been a Professor in computer science at Beijing University of Aeronautics and Astronautics. He has published over 100 papers in the areas of concurrent programming languages, operational semantics, type theory, and logical foundation of artificial intelligence.     

Project scheduling under resource constraints: Application of the cumulative global constraint in a decision support framework

This paper concerns project scheduling under resource constraints. Traditionally, the objective is to find a unique solution that minimizes the project makespan, while respecting the precedence constraints and the resource constraints. This work focuses on developing a model and a decision support framework for industrial application of the cumulative global constraint. For a given project scheduling, the proposed approach allows the generation of different optimal solutions relative to the alternate availability of outsourcing and resources. The objective is to provide a decision-maker an assistance to construct, choose, and define the appropriate scheduling program taking into account the possible capacity resources. The industrial problem under consideration is modeled as a constraint satisfaction problem (CSP). It is implemented under the constraint programming language CHIP V5. The provided solutions determine values for the various variables associated to the tasks realized on each resource, as well as the curves with the profile of the total consumption of resources on time.     

可满足问题中的模型计数

模型计数问题是指计算给定问题的解的个数,这是一类比决策更困难的问题,也是人工智能领域研究的一个热点问题.对模型计数问题的研究不仅可以提高算法的求解效率,更能促进对问题困难本质的了解.以可满足问题（命题可满足（SAT）和约束可满足问题（CSP））为例,从精确算法和近似求解两方面综述了模型计数问题的研究现状,重点介绍了相关概念以及各个算法之间的优缺点,并提出了有待解决的开放性问题,对模型计数问题的研究予以了总结和展望.     

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.     

A two-machine flowshop scheduling problem with a separated maintenance constraint

This paper considers a two-machine flowshop scheduling problem with a separated maintenance constraint. This means that the machine may not always be available during the scheduling period. It needs a constant time to maintain the machine after completing a fixed number of jobs at most. The objective is to find the optimal job combinations and the optimal job schedule such that the makespan is minimized. The proposed problem has some practical applications, for example, in electroplating process, the electrolytic cell needs to be cleaned and made up a deficiency of medicine. In this paper, we propose a heuristic algorithm to solve this problem. Some polynomially solvable cases and computational experiments are also provided.     

The satisfiability problem in regular CNF-formulas

 In this paper we deal with the propositional satisfiability (SAT) problem for a kind of multiple-valued clausal forms known as regular CNF-formulas and extend some known results from classical logic to this kind of formulas. We present a Davis–Putnam-style satisfiability checking procedure for regular CNF-formulas equipped with suitable data structures and prove its completeness. Then, we describe a series of experiments for regular random 3-SAT instances. We observe that, for the regular 3-SAT problem with this procedure, there exists a threshold of the ratio of clauses to variables such that (i) the most computationally difficult instances tend to be found near the threshold, (ii) there is a sharp transition from satisfiable to unsatisfiable instances at the threshold and (iii) the value of the threshold increases as the number of truth values considered increases. Instances in the hard part provide benchmarks for the evaluation of regular satisfiability solvers.     

Solving a real-time allocation problem with constraint programming

In this paper, we present an original approach (CPRTA for “Constraint Programming for solving Real-Time Allocation”) based on constraint programming to solve a static allocation problem of hard real-time tasks. This problem consists in assigning periodic tasks to distributed processors in the context of fixed priority preemptive scheduling. CPRTA is built on dynamic constraint programming together with a learning method to find a feasible processor allocation under constraints. Two efficient new approaches are proposed and validated with experimental results. Moreover, CPRTA exhibits very interesting properties. It is complete (if a problem has no solution, the algorithm is able to prove it); it is non-parametric (it does not require specific tuning) thus allowing a large diversity of models to be easily considered. Finally, thanks to its capacity to explain failures, it offers attractive perspectives for guiding the architectural design process.     

求解作业排序问题的一种改进修复约束满足算法

修复约束满足算法(修复法)是在完整初始解的基础上不断对变量进行修复,最终得到可行解.对此,提出一种求解flow shop排序问题的改进修复法(IRCS_WT),通过采用新的变量表达方式,设计了一种以启发式优化规则为指导的变量选择算法(LWT),并采用一种变量互换算法(LTEE)保证算法的全局搜索性能.将新算法应用于31个标准算例,与传统算法及遗传算法的优化结果进行比较,结果表明在相同运算时问下改进算法具有明显的优越性.     

Accelerating column generation for aircraft scheduling using constraint propagation

We discuss how constraint programming can improve the performance of a column generation solution process for the NP-hard Tail Assignment problem in aircraft scheduling. Combining a constraint model of a relaxed Tail Assignment problem with column generation, we achieve substantially improved performance. A generalized preprocessing technique based on constraint propagation is presented that can dramatically reduce the size of the flight network. We also present a heuristic preprocessing method based on the costs of connections, and show how constraint propagation can be used to improve fixing heuristics. Proof of concept is provided using real world Tail Assignment instances.     

An Iterative local-search framework for solving constraint satisfaction problem

In this article, we introduce a new solving framework based on using alternatively two local-search algorithms to solve constraint satisfaction and optimization problems. The technique presented is based on the integration of local-search algorithm as a mechanism to diversify the search instead of using a build on diversification mechanisms. Thus, we avoid tuning the multiple parameters to escape from a local optimum. This technique improves the existing methods: it is generic especially when the given problem can be expressed as a constraint satisfaction problem. We present the way the local-search algorithm can be used to diversify the search in order to solve real examination timetabling problems. We describe how the local-search algorithm can be used to assist any other specific local-search algorithm to escape from local optimality. We showed that such framework is efficient on real benchmarks for timetabling problems.     

Adapting the behavior of a job-shop scheduling system

Factory scheduling consists in assigning resources (e.g. machines) and start and end times to operations. Our work is concerned with the problems of schedule generation and schedule revision when unanticipated events occur on the factory floor. SONIA is a knowledge-based scheduling system provided with a blackboard architecture for coordinating the activation of various scheduling and analyzing knowledge sources. In this paper, we focus on the various behaviors these knowledge sources can have and we gather a collection of conclusions regarding the use of various backtracking strategies and the control of constraint propagation.     

复杂反应约束的流程优化调度问题及求解

由于化工流程的生产过程涉及复杂的化学反应,因此,在研究化工流程中的调度问题的时候需要考虑其化学反应所带来的影响因素;这就使得调度的数学模型的建立变得非常的困难。本文针对中小型合成氨流程中的调度问题进行研究,分析合成氨反应的温度、压力、环境等影响因素建立调度的数学模型,采用基于微粒群算法的多目标优化方法对该流程进行优化调度,其结果表明所建的模型具有很好的收敛性和稳定性。     

Pharmacy duty scheduling problem

In this study, we define the pharmacy duty scheduling problem, which requires a subset of pharmacies to be on duty on national holidays, at weekends, and at nights, in order to be able to satisfy the emergency medicine needs. We model the pharmacy duty scheduling problem as a multiperiod p‐median problem with special side constraints, and analyze the computational complexity. We propose a Tabu Search heuristic and develop lower bound (LB) algorithms. We test the performance of mathematical models, Tabu Search heuristic, and the LBs on randomly generated instances. We analyze the current system in ?zmir, the third largest city in Turkey, with a population of 3.5 million, and apply solution methods. Our results show that the proposed Tabu Search algorithm suggests improvements on the current system.     

Production management as a constraint satisfaction problem

Production management problems can be quite straightforwardly presented as constraint satisfaction problems, where values for some variables are searched for under a set of constraints. A combination of an operation and a resource is usually interpreted as the variable, and a time window is usually interpreted as the value to be searched for. This convention is challenged. A case is considered where the most appropriate interpretation treats the combination of a resource and a time window as the variable, and an operation as the value. A third possible interpretation is also briefly covered, where the combination of an operation and a time window is the variable, and the resource is the value.     

多文字可满足SAT问题的相变点上界

可满足(SAT)问题是指：是否存在一组布尔变元赋值,使得随机合取范式(CNF)公式中每个子句至少有1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,使得随机CNF公式中每个子句至少有2个文字为真。此问题仍然是一个NP难问题。定义约束密度α为CNF公式子句数与变元数之比,对该问题的相变点上界α^*进行了研究。如果α>α^*,则多文字可满足SAT问题高概率不可满足。通过一阶矩一个简单的推断,可以证明α^*=-ln 2/ln(1-(k+1)/2^k),当k=3时,α^*=1。利用Kirousis等人的局部最大值技术,提升了多文字可满足3-SAT问题的相变点上界α^*=0.7193。最后,选择了大量数据进行实验验证,结果表明,理论结果与实验结果相吻合。     

Scheduling trains as a blocking parallel-machine job shop scheduling problem

In this paper, the train scheduling problem is modelled as a blocking parallel-machine job shop scheduling (BPMJSS) problem. In the model, trains, single-track sections and multiple-track sections, respectively, are synonymous with jobs, single machines and parallel machines, and an operation is regarded as the movement/traversal of a train across a section. Due to the lack of buffer space, the real-life case should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold the train until next section on the routing becomes available. Based on literature review and our analysis, it is very hard to find a feasible complete schedule directly for BPMJSS problems. Firstly, a parallel-machine job-shop-scheduling (PMJSS) problem is solved by an improved shifting bottleneck procedure (SBP) algorithm without considering blocking conditions. Inspired by the proposed SBP algorithm, feasibility satisfaction procedure (FSP) algorithm is developed to solve and analyse the BPMJSS problem, by an alternative graph model that is an extension of the classical disjunctive graph models. The proposed algorithms have been implemented and validated using real-world data from Queensland Rail. Sensitivity analysis has been applied by considering train length, upgrading track sections, increasing train speed and changing bottleneck sections. The outcomes show that the proposed methodology would be a very useful tool for the real-life train scheduling problems.     

On optimizing the satisfiability (SAT) problem

1IntroductionThesatisfiability(SAT)problemistodeterminewhetherthereexistsanassignmentofvaluesin{0,1}toasetofBooleanvariables{x1,xm}thatmakesaconjunctivenormalform(CNF)formulatrue.ThesatisfiabilityproblemofaCNFformulawithatmostlliteralsineachclauseiscalledthel-SATproblem.Theoretically,for>3,theSATproblemisawell-knownNP-completeproblem.Andthus,thereexistsnopolynomialtimealgorithmfortheSATproblemontheassumptionthatPNP.Ontheotherhand,theSATproblemisfundamentalinsolvingmanypracticalprob…