An Arc-Consistency Algorithm for Dynamic and Distributed Constraint Satisfaction Problems

This paper presents the new DDAC4 algorithm for dynamic arc consistency enforcement in distributed constraint satisfaction problems (CSP). The algorithm is an adaptation of the well-known AC-4 algorithm to system settings where constraints can be added and deleted in concurrent processes. It is the first algorithm for arc-consistency enforcement in this system setting. Arc-consistency is achieved whenever the overall system reaches quiescence after a constraint is added or deleted.     

Filtering algorithms for the multiset ordering constraint

Constraint programming (CP) has been used with great success to tackle a wide variety of constraint satisfaction problems which are computationally intractable in general. Global constraints are one of the important factors behind the success of CP. In this paper, we study a new global constraint, the multiset ordering constraint, which is shown to be useful in symmetry breaking and searching for leximin optimal solutions in CP. We propose efficient and effective filtering algorithms for propagating this global constraint. We show that the algorithms maintain generalised arc-consistency and we discuss possible extensions. We also consider alternative propagation methods based on existing constraints in CP toolkits. Our experimental results on a number of benchmark problems demonstrate that propagating the multiset ordering constraint via a dedicated algorithm can be very beneficial.     

基于关联约束非二元弧一致性的约束满足问题求解

弧一致性算法在二元约束满足问题中取得了成功的应用,但并不能被有效泛化至预处理非二元约束满足问题(NCSP).本文提出了处理NCSP的关联约束非二元弧一致性算法.通过随机NCSP生成器产生问题实例,分别采用关联约束非二元弧一致性算法和非二元弧一致性算法进行预处理,并对预处理后的问题实例应用回溯算法进行求解.对比分析采用两种预处理算法和不采用预处理下回溯算法的求解性能,仿真实验结果表明关联约束非二元弧一致性算法可以有效地剔除冗余的约束元组和变量域值,使关联约束非二元弧一致性回溯算法具有更良好的鲁棒性.     

A Hybrid Algorithm for Compiling Equality Constraints and its Implementation

In this paper, we extend the language we proposed in [11] to make it possible to program arc-consistency algorithms. We also propose a hybrid algorithm that integrates the interval-consistency (IC) and arc-consistency (AC) algorithms. For a constraint, the algorithm checks IC when it is non-binary and checks AC when the constraint turns into binary. The algorithm is well-balanced. Its reduction cost is close to the IC checking algorithm, while its reduction power is close to the AC checking algorithm for most problems. The experimental results show that the hybrid algorithm may be a little slower than the IC checking algorithm for programs that do not require strong reduction power, but may be an order of magnitude faster than IC for other programs.     

Message delay and DisCSP search algorithms

Distributed constraint satisfaction problems (DisCSPs) are composed of agents, each holding its own variables, that are connected by constraints to variables of other agents. Due to the distributed nature of the problem, message delay can have unexpected effects on the behavior of distributed search algorithms on DisCSPs. This has been recently shown in experimental studies of asynchronous backtracking algorithms (Bejar et al., Artif. Intell., 161:117–148, 2005; Silaghi and Faltings, Artif. Intell., 161:25–54, 2005). To evaluate the impact of message delay on the run of DisCSP search algorithms, a model for distributed performance measures is presented. The model counts the number of non concurrent constraints checks, to arrive at a solution, as a non concurrent measure of distributed computation. A simpler version measures distributed computation cost by the non-concurrent number of steps of computation. An algorithm for computing these distributed measures of computational effort is described. The realization of the model for measuring performance of distributed search algorithms is a simulator which includes the cost of message delays. Two families of distributed search algorithms on DisCSPs are investigated. Algorithms that run a single search process, and multiple search processes algorithms. The two families of algorithms are described and associated with existing algorithms. The performance of three representative algorithms of these two families is measured on randomly generated instances of DisCSPs with delayed messages. The delay of messages is found to have a strong negative effect on single search process algorithms, whether synchronous or asynchronous. Multi search process algorithms, on the other hand, are affected very lightly by message delay.     

Nogood-FC for solving partitionable constraint satisfaction problems

Many real problems can be naturally modelled as constraint satisfaction problems (CSPs). However, some of these problems are of a distributed nature, which requires problems of this kind to be modelled as distributed constraint satisfaction problems (DCSPs). In this work, we present a distributed model for solving CSPs. Our technique carries out a partition over the constraint network using a graph partitioning software; after partitioning, each sub-CSP is arranged into a DFS-tree CSP structure that is used as a hierarchy of communication by our distributed algorithm. We show that our distributed algorithm outperforms well-known centralized algorithms solving partitionable CSPs.     

Parallel consistent labeling algorithms

Mackworth and Freuder have analyzed the time complexity of several constraint satisfaction algorithms.⁽¹⁾ Mohr and Henderson have given new algorithms, AC-4 and PC-3, for arc and path consistency, respectively, and have shown that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms.⁽²⁾ In this paper, we give parallel algorithms for solving node and arc consistency. We show that any parallel algorithm for enforcing are consistency in the worst case must have O(na) sequential steps, wheren is number of nodes, anda is the number of labels per node. We give several parallel algorithms to do arc consistency. It is also shown that they all have optimal time complexity. The results of running the parallel algorithms on a BBN Butterfly multiprocessor are also presented.This work was partially supported by NSF Grants MCS-8221750, DCR-8506393, and DMC-8502115.     

相接行凸约束网络的快速识别算法

约束网络为计算机科学中的许多问题提供了一种有效的表示方法.一般而言,约束满足问题是NP完全的.然而,许多实际问题通常对约束的结构或形式施加了特殊的限制,从而能够高效地加以解决.迄今,为了识别易处理约束类,人们对特殊的约束或约束网络方面进行了许多研究.相接行凸(connected row-convex,简称CRC)约束网络是Deville等人提出的一类易处理问题.为了给该类问题寻求有效的快速识别算法,在CRC约束网络相关工作基础上,提出了CRC约束矩阵的标准型.在分析CRC约束矩阵的标准型性质的基础上,利用行凸(row-convex,简称RC)约束网络的判定,结合PQ树(由P节点和Q节点构成的树)的性质和矩阵的索引表示法,给出了CRC约束网络的快速识别算法.该算法的时间复杂度为O(n³d²),其中,n为约束网络涉及的变量数,d为各变量的定义域中最大定义域的大小.该时间复杂度达到该类问题的最佳时间复杂度,从而为实际的CRC约束满足问题的求解提供了可行的方法.     

Saving Support-Checks Does Not Always Save Time

Arc-consistency algorithms are the workhorse of backtrackers that maintain arc-consistency (MAC). This paper will provide experimental evidence that, despite common belief to the contrary, it is not always necessary for a good arc-consistency algorithm to have an optimal worst-case time-complexity. Sacrificing this optimality allows MAC solvers that (1) do not need additional data structures during search, (2) have an excellent average time-complexity, and (3) have a space-complexity that improves significantly on that of MAC solvers that have optimal arc-consistency components. Results will be presented from an experimental comparison between MAC-2001, MAC-3 _d and related algorithms. MAC-2001 has an arc-consistency component with an optimal worst-case time-complexity, whereas MAC-3 _d does not. MAC-2001 requires additional data structures during search, whereas MAC-3 _d does not. MAC-3 _d has a O(e+nd) of space-complexity, where n is the number of variables, d the maximum domain size, and e the number of constraints. We shall demonstrate that MAC-2001's space-complexity is O(edmin(n,d)). Our experimental results indicate that MAC-2001 was slower than MAC-3 _d for easy and hard random problems. For real-world problems things were not as clear.     

Customer satisfaction‐aware scheduling for utility maximization on geo‐distributed data centers

With the increasingly growing amount of service requests from the world‐wide customers, the cloud systems are capable of providing services while meeting the customers' satisfaction. Recently, to achieve the better reliability and performance, the cloud systems have been largely depending on the geographically distributed data centers. Nevertheless, the dollar cost of service placement by service providers (SP) differ from the multiple regions. Accordingly, it is crucial to design a request dispatching and resource allocation algorithm to maximize net profit. The existing algorithms are either built upon energy‐efficient schemes alone, or multi‐type requests and customer satisfaction oblivious. They cannot be applied to multi‐type requests and customer satisfaction‐aware algorithm design with the objective of maximizing net profit. This paper proposes an ant‐colony optimization‐based algorithm for maximizing SP's net profit (AMP) on geographically distributed data centers with the consideration of customer satisfaction. First, using model of customer satisfaction, we formulate the utility (or net profit) maximization issue as an optimization problem under the constraints of customer satisfaction and data centers. Second, we analyze the complexity of the optimal requests dispatchment problem and rigidly prove that it is an NP‐complete problem. Third, to evaluate the proposed algorithm, we have conducted the comprehensive simulation and compared with the other state‐of‐the‐art algorithms. Also, we extend our work to consider the data center's power usage effectiveness. It has been shown that AMP maximizes SP net profit by dispatching service requests to the proper data centers and generating the appropriate amount of virtual machines to meet customer satisfaction. Moreover, we also demonstrate the effectiveness of our approach when it accommodates the impacts of dynamically arrived heavy workload, various evaporation rate and consideration of power usage effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.     

Cycle Flow Formulation of Optimal Network Flow Problems and Respective Distributed Solutions

In this paper, we use the cycle basis from graph theory to reduce the size of the decision variable space of optimal network flow problems by eliminating the aggregated flow conservation constraint. We use a minimum cost flow problem and an optimal power flow problem with generation and storage at the nodes to demonstrate our decision variable reduction method. The main advantage of the proposed technique is that it retains the natural sparse/decomposable structure of network flow problems. As such, the reformulated problems are still amenable to distributed solutions. We demonstrate this by proposing a distributed alternating direction method of multipliers (ADMM) solution for a minimum cost flow problem. We also show that the communication cost of the distributed ADMM algorithm for our proposed cycle-based formulation of the minimum cost flow problem is lower than that of a distributed ADMM algorithm for the original arc-based formulation.      

非平衡有向网络下带约束的连续时间分布式优化算法设计EI北大核心CSCD

本文基于权重不平衡有向网络,对一类分布式约束优化问题进行研究,其中全局目标函数等于具有李普希兹梯度的强凸目标函数之和,并且每个智能体的状态都有一个局部约束集.每个智能体仅知道自身的局部目标函数和非空约束集.本文的目标是用分布式方法求解该问题的最优解.针对优化问题,提出了一种新的分布式投影梯度连续时间协调算法,利用拉普拉斯矩阵的零特征值对应的左特征向量消除了图的不平衡性.在某些假设下,结合凸分析理论和李雅普诺夫稳定性理论,证明了算法能够获得问题的最优解.最后,通过仿真验证了算法的有效性.     

The distributed constraint satisfaction problem: formalization andalgorithms

We develop a formalism called a distributed constraint satisfaction problem (distributed CSP) and algorithms for solving distributed CSPs. A distributed CSP is a constraint satisfaction problem in which variables and constraints are distributed among multiple agents. Various application problems in distributed artificial intelligence can be formalized as distributed CSPs. We present our newly developed technique called asynchronous backtracking that allows agents to act asynchronously and concurrently without any global control, while guaranteeing the completeness of the algorithm. Furthermore, we describe how the asynchronous backtracking algorithm can be modified into a more efficient algorithm called an asynchronous weak-commitment search, which can revise a bad decision without exhaustive search by changing the priority order of agents dynamically. The experimental results on various example problems show that the asynchronous weak-commitment search algorithm is, by far more, efficient than the asynchronous backtracking algorithm and can solve fairly large-scale problems     

一种基于分布式约束满足的资源优化模型*

分布式约束满足作为分布式人工智能领域的一个重要分支,在许多领域均得到了广泛应用。针对Web服务事务协调过程中的资源优化问题,在分布式逃逸算法的基础上提出了一种基于分布式约束满足的资源优化模型,并通过仿真实验证实了模型及其算法的收敛性和优化性。     

基于约束图分片求解DCOP的Agent组织结构

MAS中许多分布式推理问题可以建模为分布式约束优化问题(DCOP),解决DCOP的分布式算法已经成为MAS中的重要基础.已有的Adopt等算法通过对等的Agent之间的平等协商完成求解,强调了异步通信、分布计算与对解质量的保证,在求解问题的组织结构方面仍有改进余地.可以采用一种基于分散与集中相结合的思路,基于对约束图分片的方法及核心结点、通信主干道等概念,构造新颖的Agent组织结构,完成DCOP问题的异步、分布求解.在该组织结构下求解DCOP的算法可在效率、适应动态性方面得到改善,并将一个Agent一个变量和一个Agent多个变量的DCOP求解方法统一起来.     

Approximated consistency for the automatic recording constraint

We introduce the automatic recording constraint (ARC) that can be used to model and solve scheduling problems where tasks may not overlap in time and the tasks linearly exhaust some resource. Since achieving generalized arc-consistency for the ARC is NP-hard, we develop a filtering algorithm that achieves approximated consistency only. Numerical results show the benefits of the new constraint on three out of four different types of benchmark sets for the automatic recording problem. On these instances, run-times can be achieved that are orders of magnitude better than those of the best previous constraint programming approach.     

Discrete optimisation based on the combined use of reinforcement and constraint satisfaction schemes

A new approach is presented for finding near-optimal solutions to discrete optimisation problems that is based on the cooperation of two modules: an optimisation module and a constraint satisfaction module. The optimisation module must be able to search the problem state space through an iterative process of sampling and evaluating the generated samples. To evaluate a generated point, first a constraint satisfaction module is employed to map that point to another one satisfying the problem constraints, and then the cost of the new point is used as the evaluation of the original one. The scheme that we have adopted for testing the effectiveness of the method uses a reinforcement learning algorithm in the optimisation module and a general deterministic constraint satisfaction algorithm in the constraint satisfaction module. Experiments using this scheme for the solution of two optimisation problems indicate that the proposed approach is very effective in providing feasible solutions of acceptable quality.     

分布式遗传退火算法求解分布式配置问题

利用分布式约束满足的方法求解分布式配置问题时,在过约束和欠约束条件下都不能得到令人满意的结果,文中将分布式配置问题抽象为分布式组合最优化问题,把遗传退火算法扩展到分布式计算环境以求解分布式配置问题,以SOAP为基础搭建实验平台,在各种约束情况下,文中算法都给出了令人满意的实验结果,可见分布式遗传退火算法可以求解各种约束条件下的分布式配置问题。     

分布式问题求解中的妥协策略

基于多agent系统的分布式约束满足(CSP)问题的求解进程依赖于agent间的有效交互。该文针对着色问题(GCP)的分布式求解,提出了agent妥协的概念。通过妥协,两个相邻agent改变了各自原有的局部目标,实现了相邻约束的满足。模拟实验表明,妥协策略有助于提高分布式GCP问题的求解性能。该文还讨论了不同的妥协实现方式对性能的影响。