Introduction to planning, scheduling and constraint satisfaction

Planning, scheduling and constraint satisfaction are important areas in artificial intelligence (AI). Many real-world problems are known as AI planning and scheduling problems, where resources must be allocated so as to optimize overall performance objectives. Therefore, solving these problems requires an adequate mixture of planning, scheduling and resource allocation to competing goal activities over time in the presence of complex state-dependent constraints. Constraint satisfaction plays also an important role to solve real-life problems, so that integrated techniques that manage planning and scheduling with constraint satisfaction remains necessary. This special issue on Planning, Scheduling and Constraint Satisfaction compiles a selection of papers of CAEPIA’2007 workshop on Planning, Scheduling and Constraint Satisfaction and COPLAS’2007: CP/ICAPS 2007 Joint Workshop on Constraint Satisfaction Techniques for Planning and Scheduling Problems. This issue presents novel advances on planning, scheduling, constraint programming/constraint satisfaction problems (CSPs) and many other common areas that exist among them. On the whole, this issue mainly focus on managing complex problems where planning, scheduling, constraint satisfaction and search must be combined and/or interrelated, which entails an enormous potential for practical applications and future research. Furthermore, this issue also includes a complete survey about constraint satisfaction, planning, scheduling and integration among these areas.     

Constraint satisfaction techniques in planning and scheduling

Over the last few years constraint satisfaction, planning, and scheduling have received increased attention, and substantial effort has been invested in exploiting constraint satisfaction techniques when solving real life planning and scheduling problems. Constraint satisfaction is the process of finding a solution to a set of constraints. Planning is the process of finding a sequence of actions that transfer the world from some initial state to a desired state. Scheduling is the problem of assigning a set of tasks to a set of resources subject to a set of constraints. In this paper, we introduce the main definitions and techniques of constraint satisfaction, planning and scheduling from the Artificial Intelligence point of view.     

Reasoning with Numeric and Symbolic Time Information

Representing and reasoning about time is fundamental in many applications of Artificial Intelligence as well as of other disciplines in computer science, such as scheduling, planning, computational linguistics, database design and molecular biology. The development of a domain-independent temporal reasoning system is then practically important. An important issue when designing such systems is the efficient handling of qualitative and metric time information. We have developed a temporal model, TemPro, based on the Allen interval algebra, to express and manage such information in terms of qualitative and quantitative temporal constraints. TemPro translates an application involving temporal information into a Constraint Satisfaction Problem (CSP). Constraint satisfaction techniques are then used to manage the different time information by solving the CSP. In order for the system to deal with real time applications or those applications where it is impossible or impractical to solve these problems completely, we have studied different methods capable of trading search time for solution quality when solving the temporal CSP. These methods are exact and approximation algorithms based respectively on constraint satisfaction techniques and local search. Experimental tests were performed on randomly generated temporal constraint problems as well as on scheduling problems in order to compare and evaluate the performance of the different methods we propose. The results demonstrate the efficiency of the MCRW approximation method to deal with under constrained and middle constrained problems while Tabu Search and SDRW are the methods of choice for over constrained problems.     

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.     

Production planning & scheduling: Computational feasibility of multi-criteria models of production, planning and scheduling

This paper surveys the applications of multi-criteria decision making (MCDM) methods to production planning, scheduling, and sequencing problems. The basic structure of the decision models are described by their objectives and the resulting models are classified by decision variables into the areas of Aggregate Production Planning, Disaggregate Production Planning, Production Scheduling, and Single Machine Sequencing. The problem sizes that have been solved are summarized to determine how practical it is to use MCDM.     

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。     

Domain-dependent distributed models for railway scheduling

Many combinatorial problems can be modelled as Constraint Satisfaction Problems (CSPs). Solving a general CSP is known to be NP-complete, so closure and heuristic search are usually used. However, many problems are inherently distributed and the problem complexity can be reduced by dividing the problem into a set of subproblems. Nevertheless, general distributed techniques are not always appropriate to distribute real-life problems. In this work, we model the railway scheduling problem by means of domain-dependent distributed constraint models, and we show that these models maintained better behaviors than general distributed models based on graph partitioning. The evaluation is focused on the railway scheduling problem, where domain-dependent models carry out a problem distribution by means of trains and contiguous sets of stations.     

考虑特殊时间约束的混合流水车间调度

针对等待时间受限的准时制混合流水车间调度问题,建立其约束满足优化模型。考虑到模型具有二元变量的复杂性特点,将原问题分解为多能力流水车间调度和机器指派两个子问题。在对多能力流水车间调度问题的约束满足优化求解过程中嵌入邻域搜索,从而提高算法的收敛性。数据实验表明模型和算法是可行和有效的。     

云计算环境下的自适应资源管理技术综述

云环境下的自适应资源管理是当前云计算研究领域的热点问题,是云计算具备弹性扩展、动态分配和资源共享等特点的关键技术支撑,具有重要的理论意义和实用价值.其主要研究点包括:虚拟机放置优化算法,虚拟资源动态伸缩模型、多IDC间的全局云计算资源调度、全局资源配置及能力规划模型等.对云环境下自适应资源管理研究现状进行分析研究,并指出当前研究中存在的一些主要问题,同时进一步展望本领域未来的研究方向.     

Coordinating Mutually Exclusive Resources using GPGP

Hospital Patient Scheduling is an inherently distributed problem because of the way real hospitals are organized. As medical procedures have become more complex, and their associated tests and treatments have become interrelated, the current ad hoc patient scheduling solutions have been observed to break down. We propose a multi-agent solution using the Generalized Partial Global Planning (GPGP) approach that preserves the existing human organization and authority structures, while providing better system-level performance (increased hospital unit throughput and decreased patient stay time). To do this, we extend GPGP with a new coordination mechanism to handle mutually exclusive resource relationships. Like the other GPGP mechanisms, the new mechanism can be applied to any problem with the appropriate resource relationship. We evaluate this new mechanism in the context of the hospital patient scheduling problem, and examine the effect of increasing interrelations between tasks performed by different hospital units.     

流程工业计划调度技术研究与发展分析

计划调度系统是企业生产活动的组织和管理中心,是提高企业综合效益的有效途径,该文分析了流程工业计划调度系统特征,全面深入地研究了生产计划与调度问题的模型框架及求解技术,并针对目前流程工业计划调度研究中存在的问题,从系统结构、建模优化、智能求解等方面提出了流程企业计划调度技术的发展趋势,为流程企业的生产优化组织与运作提供了方法论的指导。     

REDOM: an OO language to define and on-line manipulate regulations in the resource (re)scheduling problem

In the class of (re)scheduling problems where humans constitute the main resource, the scheduling process is influenced by a great number of complex and frequently changing regulations. The complexity and the dynamic nature of these regulations impose the need for an efficient, flexible and user-friendly way to express and manage them. A solution to this problem, in the form of an object-oriented high-level language with semantics highly-tailored to the user needs, is presented. The language, called REDOM, can be applied to different scheduling application domains with a minimum degree of effort, because it is based on a generic meta-model of the resource scheduling problem. An application programming interface facilitates REDOM integration into existing scheduling systems. REDOM is currently being utilised by the DAYSY resource management system, that is implemented as a constraint satisfaction system based on a partial test-and-generate approach. The combination of REDOM and CHIP (Constraint Handling In Prolog), which was used for the implementation of the solution generation subsystem, resulted in a highly-efficient and flexible (re)scheduling system, well-accepted by users. © 1997 John Wiley & Sons, Ltd.     

分布式约束满足问题研究及其进展

近年来,随着网络技术的快速发展和广泛应用,人工智能领域中的诸多问题,如时序安排、计划编制、资源分配等,越来越多地以分布形式出现,从而形成一类多主体系统.相应地,求解该类问题的传统约束满足问题也发展为分布式约束满足问题,分布式约束满足已经成为多主体系统求解的一般框架.首先,简要介绍了分布式约束满足问题的基本概念,总结了该问题的基本算法及其改进算法,并对这些算法的效率和性能进行了比较分析.然后,讨论了近年来分布式约束满足问题的若干典型应用;最后,给出了分布式约束满足问题基本形式的扩展和今后的研究方向.分布式约束满足问题最新研究进展表明:今后的工作将着重于面向现实问题求解的理论研究,为实际应用提供坚实的理论基础.     

基于改进遗传算法的多天线地面站硬件资源分配方法

多天线卫星地面站硬件设备资源分配问题是一个基于约束满足的复杂资源组合优化问题。在考虑任务执行时间、地面站可见时间窗口、地面站设备接收能力和设备链路约束的情况下,对多天线地面站硬件资源分配问题建立了高可用模型。以加权任务执行总时间为目标,以经典遗传算法为基础,根据问题特点改进了相关遗传算子,在进行遗传变异的过程中,通过深度优先搜索算法确定单个染色体对应的最佳资源分配方案,同时利用启发式信息优化搜索过程。最后通过高可用算例仿真表明,所建模型和算法是合理有效的。     

基于DCSP的煤矿应急救援资源调配方法

在大规模群体突发事件发生后,如何实时及有效地调配资源,是保障应急救援快速实施的关键。以煤矿应急救援为背景,探讨合适的资源调配方法。分布式约束满足问题(D(',SP-Distributed Constraint Satisfaction Problem)擅于表示及求解分布式环境下以协作性为主的问题,是一种解决具有信息分布、需求随环境动态变化等特点的资源调配问题的有效方法,而煤矿应急救援问题正好具有这样的特征。因此,采用DCSP方法来解决煤矿应急救援中的资源调配问题,抽取并构建了煤矿应急救援资源调配的模型,讨论了Agent模型和约束模型的定义,改进了MAWS(MAWS-Multiple Asynchronous Weak-commitment Search)算法。经实验验证,采用DCSP方法可在事故发生后的较短时间内做出有效的资源调配决策,减少资源送达到事故点的时间,为应急救援争取了大量救援时间,从而减少了煤矿事故发生后的人员伤亡和经济损失。     

A constraint programming formulation for planning: from plan scheduling to plan generation

Planning research is recently concerned with the resolution of more realistic problems as evidenced in the many works and new extensions to the Planning Domain Definition Language (PDDL) to better approximate real problems. Researchers’ works to push planning algorithms and capture more complex domains share an essential ingredient, namely the incorporation of new types of constraints. Adding constraints seems to be the way of approximating real problems: these constraints represent the duration of tasks, temporal and resource constraints, deadlines, soft constraints, etc., i.e. features that have been traditionally associated to the area of scheduling. This desired expressiveness can be achieved by augmenting the planning reasoning capabilities, at the cost of slightly deviating the planning process from its traditional implicit purpose, that is finding the causal structure of the plan. However, the resolution of complex domains with a great variety of different constraints may involve as much planning effort as scheduling effort (and perhaps the latter being more prominent in many problems). For this reason, in this paper we present a general approach to model those problems under a constraint programming formulation which allows us to represent and handle a wide range of constraints. Our work is based on the original model of , an optimal temporal planner, and it extends the ’s formulation to deal with more expressive constraints. We will show that our general formulation can be used for planning and/or scheduling, from scheduling a given complete plan to generating the whole plan from scratch. However, our contribution is not a new planner but a constraint programming formulation for representing highly-constrained planning + scheduling problems.     

Predicting phase transitions of binary constraint satisfaction problems with constraint graph information

Constraint satisfaction is at the core of many applications, such as scheduling. The study of phase transition has benefited algorithm selection and algorithm development in constraint satisfaction. Recent research provides evidence that constraint graph topology affects where phase transitions occur in constraint satisfaction problems. In this article, a new phase transition predictor which takes constraint graph information into consideration is proposed. The new predictor allows variation in the tightness of individual constraints and node degree variation in constraint graph. Experiments were conducted to study the usefulness of the new predictor on random binary constraint satisfaction problems. Results show that the new predictor is able to produce predictions as good as the state-of-the-art predictor in general, but do considerably better in sparsely constrained problems, particularly when the node degree variation in their constraint graphs is high.     

基于约束的调度研究和实现

运用约束程序设计(CP)思想和技术来调度正成为一个新兴的研究领域。文章首先对CP和调度的相关领域知识进行了简要介绍;然后按照CP所倡导的问题建模和问题求解相分离的思想,建立起一般理论调度问题的约束模型,并设计实现了一个基于约束的调度求解算法CBS-1;并对一些典型问题进行了实验,实验结果表明算法提高了约束调度求解的效率和通用性。     

Hybrid search for minimal perturbation in Dynamic CSPs

It is often the case that after a scheduling problem has been solved some small changes occur that make the solution of the original problem not valid. Solving the new problem from scratch can result in a schedule that is very different from the original schedule. In applications such as a university course timetable or flight scheduling, one would be interested in a solution that requires minimal changes for the users. The present paper considers the minimal perturbation problem. It is motivated by scenarios in which a Constraint Satisfaction Problem (CSP) is subject to changes. In particular, the case where some of the constraints are changed after a solution was obtained. The goal is to find a solution to the changed problem that is as similar as possible (e.g. includes minimal perturbations) to the previous solution. Previous studies proposed a formal model for this problem (Barták et al. 2004), a best first search algorithm (Ross et al. 2000), complexity bounds (Hebrard et al. 2005), and branch and bound based algorithms (Barták et al. 2004; Hebrard et al. 2005). The present paper proposes a new approach for solving the minimal perturbation problem. The proposed method interleaves constraint optimization and constraint satisfaction techniques. Our experimental results demonstrate the advantage of the proposed algorithm over former algorithms. Experiments were performed both on random CSPs and on random instances of the Meeting Scheduling Problem.