Symmetry Definitions for Constraint Satisfaction Problems

We review the many different definitions of symmetry for constraint satisfaction problems (CSPs) that have appeared in the literature, and show that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as an operation preserving the constraints. We refer to these as solution symmetries and constraint symmetries. We define a constraint symmetry more precisely as an automorphism of a hypergraph associated with a CSP instance, the microstructure complement. We show that the solution symmetries of a CSP instance can also be obtained as the automorphisms of a related hypergraph, the k-ary nogood hypergraph and give examples to show that some instances have many more solution symmetries than constraint symmetries. Finally, we discuss the practical implications of these different notions of symmetry.     

约束满足问题的预处理方法研究

搜索控制问题是大多数人工智能问题求解面临的一个根本间题,而约束满足是解决这一问题的常用方法之一它源于机器视觉领域中的情景标识任务,如今在人工智能的众多领域(如规划、调度、时序推理)中获得了广泛的应用,受到了人工智能界的高度重视.在近几期的UCAI和AAAI等国际人工智能会议上这方面的内容均占有一定的比重,《A币ficial In-telligence》杂志曾于1992年出了一期约束满足问题的专辑     

Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction

Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and propagated efficiently using lexicographic ordering, value symmetry breaking constraints are often difficult to formulate. In this paper, we propose two methods of using symmetry breaking constraints to tackle value symmetries. First, we show theoretically when value symmetries in one CSP correspond to variable symmetries in another CSP of the same problem. We also show when variable symmetry breaking constraints in the two CSPs, combined using channeling constraints, are consistent. Such results allow us to tackle value symmetries efficiently using additional CSP variables and channeling constraints. Second, we introduce value precedence, a notion which can be used to break a common class of value symmetries, namely symmetries of indistinguishable values. While value precedence can be expressed using inefficient if-then constraints in existing CSP solvers, we propose efficient propagation algorithms for implementing global value precedence constraints. We also characterize several theoretical properties of the value precedence constraints. Extensive experiments are conducted to verify the feasibility and efficiency of the two proposals.     

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.     

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.     

Reference,Synthesis and Constraint Satisfaction*

In this paper we discuss two kinds of constraint satisfaction problems that arise in the context of geometric modelling, In particular in the modification of 2-D wire-frame diagrams that are subject to an arbitrary number of geometrical and topological constraints. We argue that problems in this domain can be classified in two categories that we shall call problems of reference and problems of synthesis. Since Sutherland's Sketchpad program [16], a large number of systems have addressed constraint satisfaction in terms of the representation of constraints sets as equation systems, which in turn are solved by numerical methods like local propagation, relaxation and Gaussian elimination. Here, we present an alternative framework. We argue that conceptualising constraint satisfaction as symbolic rather than “numerical” problems helps to clarify the notion of “constraint”, simplify solution methods, and to explain the intuitive inferential processes underlying the modification of drawings in the course of interactive drafting sessions. The theory presented in this paper has been tested with an experimental computer program called Graflog [5, 8, 9, 10, 11, 12]. The program has been implemented during the last four years, and has evolved through several stages. The current version is implemented in terms of two Unix-processes connected by Unix-pipes. The first is a “C” program running X windows, and handles the external aspects of the interaction. The second is a Prolog program supporting the representational structures and interpreters of the system.     

When Ants Attack: Ant Algorithms for Constraint Satisfaction Problems

We describe an ant algorithm for solving constraint problems (Solnon 2002, IEEE Transactions on Evolutionary Computation 6(4): 347–357). We devise a number of variants and carry out experiments. Our preliminary results suggest that the best way to deposit pheromone and the best heuristics for state transitions may differ from current practice     

约束满足自适应神经网络求解车间调度问题

提出一种基于约求满足的自适应神经网络方法求解车间作业调度问题。在该算法中,神经网络在运行过程中能够根据问题的约束类型、约束满足情况、启发式规则的选择来自适应调节神经元之间的连接权值,从而求得问题的可行解。仿真实验证明了算法的有效性。     

Models for Global Constraint Applications

In this paper we give an overview of some industrial applications built using global constraints. We look at three systems from different application domains and show the core models used to express their constraints. We also consider different search strategies that have been applied and discuss some of the application aspects.     

The power of ants in solving Distributed Constraint Satisfaction Problems

Distributed Constraint Satisfaction (DCSP) has long been considered an important area of research for artificial intelligence and multi-agent systems. Also, Ant Colony Optimization (ACO) is an important evolutionary method for solving various optimization problems. This paper demonstrates the power of ants in solving DCSPs and describes a new approach for such a solution, showing how it differs from previous ACO-based DCSP solvers. The presented algorithm is designed to provide the special requirements that are important in the distributed form of Constraint Satisfaction Problem (CSP). The paper describes the important criteria for distributed CSP and then demonstrates how the presented algorithm stands out over similar DCSP solvers considering these criteria. Finally, the proposed approach is evaluated on random binary problems. The practical results show that this method, in most of the cases, outperforms the Asynchronous Backtracking Algorithm (ABT) and Distributed Breakout Algorithm (DBA) two important algorithms in this field of research.     

Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems

We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or heavy tails. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavy-tailed behavior. Furthermore, for harder problem instances, we observe long tails on the left-hand side of the distribution, which is indicative of a non-negligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavy-tailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis.     

A Connectionist Approach for Solving Large Constraint Satisfaction Problems

An efficient neural network technique is presented for the solution of binary constraint satisfaction problems. The method is based on the application of a double-update technique to the operation of the discrete Hopfield-type neural network that can be constructed for the solution of such problems. This operation scheme ensures that the network moves only between consistent states, such that each problem variable is assigned exactly one value, and leads to a fast and efficient search of the problem state space. Extensions of the proposed method are considered in order to include several optimisation criteria in the search. Experimental results concerning many real-size instances of the Radio Links Frequency Assignment Problem demonstrate very good performance.     

Solving Mixed and Conditional Constraint Satisfaction Problems

Constraints are a powerful general paradigm for representing knowledge in intelligent systems. The standard constraint satisfaction paradigm involves variables over a discrete value domain and constraints which restrict the solutions to allowed value combinations. This standard paradigm is inapplicable to problems which are either:(a) mixed, involving both numeric and discrete variables, or(b) conditional,¹ containing variables whose existence depends on the values chosen for other variables, or(c) both, conditional and mixed.We present a general formalism which handles both exceptions in an integral search framework. We solve conditional problems by analyzing dependencies between constraints that enable us to directly compute all possible configurations of the CSP rather than discovering them during search. For mixed problems, we present an enumeration scheme that integrates numeric variables with discrete ones in a single search process. Both techniques take advantage of enhanced propagation rule for numeric variables that results in tighter labelings than the algorithms commonly used. From real world examples in configuration and design, we identify several types of mixed constraints, i.e. constraints defined over numeric and discrete variables, and propose new propagation rules in order to take advantage of these constraints during problem solving.     

Stochastic Constraint Programming: A Scenario-Based Approach

To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. We provide a semantics for stochastic constraint programs based on scenario trees. Using this semantics, we can compile stochastic constraint programs down into conventional (non-stochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Van Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as portfolio diversification, agricultural planning and production/inventory management.     

Increasing Constraint Propagation by Redundant Modeling: an Experience Report

This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as sub-models. Channeling constraints allow the sub-models to cooperate during constraint solving by propagating constraints freely amongst the sub-models. This extra level of pruning and propagation activities becomes the source of execution speedup. real-life nurse rostering system. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and well-known n-queens problem, while the second case study applies our method in the design and construction of a real-life nurse rostering system. Experimental results provide empirical evidence in line with our prediction.     

Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems

There are two main solving schemas for constraint satisfaction and optimization problems: i) search, whose basic step is branching over the values of a variables, and ii) dynamic programming, whose basic step is variable elimination. Variable elimination is time and space exponential in a graph parameter called induced width, which renders the approach infeasible for many problem classes. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables may reduce drastically the search tree size.In this paper we introduce BE-BB(k), a hybrid general algorithm that combines search and variable elimination. The parameter k controls the tradeoff between the two strategies. The algorithm is space exponential in k. Regarding time, we show that its complexity is bounded by k and a structural parameter from the constraint graph. We provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in constraint satisfaction, Max-CSP and Weighted CSP. Especially in optimization tasks, the advantage of our approach over plain search can be overwhelming.     

基于约束满足的Job-Shop调度算法研究

文章在分析Job-Shop调度问题的基础上,引入约束满足方法来研究Job-Shop的调度问题。首先建立基于CSP的JSS模型,然后针对该模型设计了调度算法框架,仿真结果证明该调度算法是可行和有效的。     

用遗传算法解决条件约束问题的一种新思路及其在TTP问题中的应用

文章提出了在遗传算法中使用染色体分段方法解决条件约束问题的一种新思路,并将其运用于TTP问题,取得了较好的效果。