基于动态规划的资源受限随机工序调度

为解决资源受限条件下的随机工序调度问题,该文提出一种基于离散随机动态系统描述的加工时间离散随机分布且同时具有不兼容和多种可更新资源约束的资源受限项目调度模型,使得在满足资源约束和工序约束的前提下,总的平均加工时间最短。该系统研究了动态规划算法求解该问题的方法。通过实例,验证了该方法的有效性和可行性。     

基于双层规划的容器云资源动态配置算法

本文分析容器云资源动态配置决策问题,通过定义容器云资源的调度任务,求解得到容器云资源调度时间;利用容器云资源调度任务的最短时间矩阵,获取容器云资源调度所需的条件。在双层规划条件下,求解容器云资源调度的目标函数和约束函数;考虑到用户的任务情况和云数据中心的云资源状况,在虚拟机上构建一个到物理主机的矩阵,通过构建容器云资源动态配置结果在优化时的目标函数,结合约束条件,实现容器云资源的动态配置。实验结果表明,资源动态配置算法不仅可以提高容器云资源的利用率,还可以减少配置完成时间,具有更好的动态配置性能。     

Genetic algorithm for the resource-constrained project scheduling problem

We consider the resource-constrained project scheduling problem with respect to the makespan minimization criterion. The problem accounts for technological constraints of activities precedence together with resource constraints. We propose a genetic algorithm with two versions of crossovers based on the idea of most rational use of constrained resources. The crossovers uses a heuristic that takes into account the degree of criticality for the resources, which is derived from the solution of a relaxed problem with a constraint on accumulative resources. A numerical experiment with examples from the PCPLIB library has shown that the proposed algorithm has competitive quality. For some examples from the j120 test series the best known solutions were improved and for j60 (50 000 and 500 000 iterations) and for j120 (500 000 iterations) we have obtain the best average deviations of the solutions from the critical path value.     

柔性工时约束下项目调度及其蚁群算法

针对软件工程项目调度问题,在考虑加班工时的情况下,提出了柔性工时约束下项目调度问题的数学模型,并设计了相应的蚁群算法。模型对项目人力资源的特殊性进行了分析,指出项目人力资源是一种特殊的可更新资源,在允许加班的情况下,人力资源构成特殊的柔性工时约束。针对所设计的数学模型,在并行项目进度生成机制基础上设计了蚁群算法,并通过算例进行验证与分析。     

约束进化算法及其应用研究综述

约束优化问题广泛存在于科学研究和工程实践中,其对应的约束优化进化算法也成为了进化领域的重要研究方向。约束优化进化算法的本质问题是如何有效地利用不可行解和可行解的信息,平衡目标函数和约束条件,使得算法更加高效。首先对约束优化问题进行定义;然后详细分析了目前主流的约束进化算法,同时,基于不同的约束处理机制,将这些机制分为约束和目标分离法、惩罚函数法、多目标优化法、混合法和其他算法,并对这些方法进行了详细的分析和总结;接着指出约束进化算法亟待解决的问题,并明确指出未来需要进一步研究的方向;最后对约束进化算法在工程优化、电子和通信工程、机械设计、环境资源配置、科研领域和管理分配等方面的应用进行了介绍。     

考虑胜任力水平的研发项目群人力资源调度

在资源受限项目调度问题中,将可更新资源进一步拓展为具有胜任力差异的人力资源,建立考虑胜任力差异的人力资源受限项目调度问题模型,该模型是对传统多模式资源约束项目调度问题（MRCPSP）更接近研发项目群实际的扩展。提出了衡量人员胜任力的参数及估算公式,以多项目总工期和总成本最小化为双目标,建立相应的数学优化模型。按双目标重要性排序,依次对工期最优及成本最优的单目标优化问题求解。根据模型的约束条件将多项目初始网络图转化为几种单项目初始网络图,利用枚举算法给出满足约束条件的可行解集,再设计基于动态规划思想的算法进行分阶段寻优。数值实验表明,考虑了胜任力差异的数学优化模型在求解质量方面具有良好性能。     

A branch-and-price-and-check model for the vehicle routing problem with location congestion

This paper considers a vehicle routing problem with pickup and delivery, time windows and location congestion. Locations provide a number of cumulative resources that are utilized by vehicles either during service (e.g., forklifts) or for the entirety of their visit (e.g., parking bays). Locations can become congested if insufficient resources are available, upon which vehicles must wait until a resource becomes available before proceeding. The problem is challenging from a computational standpoint since it incorporates the vehicle routing problem and the resource-constrained project scheduling problem. The main contribution of this paper is a branch-and-price-and-check model that uses a branch-and-price algorithm that solves the underlying vehicle routing problem, and a constraint programming subproblem that checks the feasibility of the location resource constraints, and then adds combinatorial nogood cuts to the master problem if the resource constraints are violated. Experimental results show the benefits of the branch-and-price-and-check approach.     

Uncertain project scheduling problem with resource constraints

Project scheduling problem is to make a schedule for allocating the loans to a project such that the total cost and the completion time of the project are balanced under some constraints. This paper presents an uncertain project scheduling problem, of which both the duration times and the resources allocation times are uncertain variables. An uncertain programming model with multiple objectives is obtained, whose first objective is to minimize the total cost, and second objective is to minimize the overtime. Genetic algorithm is employed to solve the proposed uncertain project scheduling model, and its efficiency is illustrated by a numerical experiment.     

An optimal resources scheduling strategy on multimedia cloud computing under multi- device constraint

In view of the problem of inaccurate scheduling by using traditional resource scheduling method, because the method is mainly based on extracting and classifying the resource features to make scheduling, ignoring the effect of the feature relevance between the resources on the scheduling results. This paper presents a model for multimedia cloud resource scheduling based on multi- device constraint. In this method the objective function is no longer constrained only by the CPU computing capacity and the minimized completion time, but to achieve a minimum time-consuming of CPU, memory and other peripherals operation are considered as the scheduling objectives. Then the utilization of solving constrained jointly is employed to obtain the mapping relationship of the optimal virtual and physical machine. Moreover, a regressive dimensionality reduction algorithm is designed for this scheduling model to solve the high dimensional problems aroused by multi-device constraints. Simulation results show that the improved algorithm has a better performance than the traditional algorithm, has a good efficiency and has a certain convergence.     

An architecture for workflow scheduling under resource allocation constraints

Research on specification and scheduling of workflows has concentrated on temporal and causality constraints, which specify existence and order dependencies among tasks. However, another set of constraints that specify resource allocation is also equally important. The resources in a workflow environment are agents such as person, machine, software, etc. that execute the task. Execution of a task has a cost and this may vary depending on the resources allocated in order to execute that task. Resource allocation constraints define restrictions on how to allocate resources, and scheduling under resource allocation constraints provide proper resource allocation to tasks. In this work, we provide an architecture to specify and to schedule workflows under resource allocation constraints as well as under the temporal and causality constraints. A specification language with the ability to express resources and resource allocation constraints and a scheduler module that contains a constraint solver in order to find correct resource assignments are core and novel parts of this architecture.     

基于广义资源日历约束的项目资源调配优化问题

资源受限项目调度问题(RCPSP)是最具代表性的项目调度问题之一,针对实际情况中考虑资源投入的必要性,建立一种以资源投入为变量的基于广义资源日历约束的项目调度优化模型.首先,引入组合优先关系的概念对广义资源日历的概念和具体内容进行整合和完善,为了避免传统网络图在表示组合优先关系时出现的网络循环等弊端,使用节点表示活动开始和结束的瞬时状态改进节点网络图;其次,考虑活动优先关系、活动持续时间、不可更新资源总量和资源日历约束,以项目工期最短和项目成本最小为优化目标,运用CP优化器求解所建立的多目标优化模型;最后,通过设计仿真算例并进行数值实验验证模型的准确性和高效性.     

考虑多类型时间依赖资源约束的敏捷卫星调度优化

随着现代空间科技的迅猛发展, 光学遥感图像数据的应用需求越来越广泛, 大力推动了光学对地观测卫星的发展. 然而, 由于高昂的发射成本的约束, 对地观测卫星的资源是有限的, 远远无法满足各类数据需求. 因此, 提高对地观测卫星的使用效率, 提高其任务执行率, 具有非常重要的应用价值. 本文聚焦于敏捷对地观测卫星的任务调度问题, 即在给定的调度周期内, 对有限的卫星资源制定合理的任务调度方案, 在满足一定星上资源约束下, 最大化观测任务收益. 该问题难点在于星上的资源是非常有限的, 例如存储图像数据的固存资源、用于采集数据和卫星姿态切换的能量资源及执行任务活动耗费的时间资源. 需要注意的是, 能量消耗量和时间消耗量依赖于任务的执行时间, 这是敏捷卫星相对传统的非敏捷卫星独有的特性. 不同任务场景对不同类型资源的需求不同, 多种资源约束互相耦合, 资源约束具有时间依赖特性, 这些难点无疑极大地增加了卫星调度的求解难度. 为高效地求解该问题,本文构建了多类型时间依赖资源约束的敏捷卫星调度整数规划模型, 并针对问题特性提出了一种基于自适应选择因子的迭代局部搜索启发式算法. 自适应选择因子综合考虑了目标收益、资源消耗量、资源约束的松弛量, 采用动态变化的资源重要度, 能快速自适应地根据当前场景下各种类型的资源数据使用量来确定最佳局部搜索方向, 从而在有限时间内找到高质量的解. 实验结果证明, 本文所提出的算法在多种情况下相比当前最好算法求解效果显著更优. 此外, 算法独有的自适应选择因子相比传统的选择因子的求解质量更高, 这是因为所设计的自适应选择因子兼顾了目标收益和资源消耗量之间权衡关系的同时, 采用动态变化的资源重要度准确捕捉了资源需求的迫切程度.     

Distributed constraint optimization with MULBS: A case study on collaborative meeting scheduling

This paper introduces MULBS, a new DCOP (distributed constraint optimization problem) algorithm and also presents a DCOP formulation for scheduling of distributed meetings in collaborative environments. Scheduling in CSCWD can be seen as a DCOP where variables represent time slots and values are resources of a production system (machines, raw-materials, hardware components, etc.) or management system (meetings, project tasks, human resources, money, etc). Therefore, a DCOP algorithm must find a set of variable assignments that maximize an objective function taking constraints into account. However, it is well known that such problems are NP-complete and that more research must be done to obtain feasible and reliable computational approaches. Thus, DCOP emerges as a very promising technique: the search space is decomposed into smaller spaces and agents solve local problems, collaborating in order to achieve a global solution. We show with empirical experiments that MULBS outperforms some of the state-of-the-art algorithms for DCOP, guaranteeing high quality solutions using less computational resources for the distributed meeting scheduling task.     

多维动态规划在对地观测卫星调度中的应用

对地观测卫星调度问题是指如何利用有限卫星资源,在时间、空间等多约束条件下提高对地观测任务执行效率,是一个多约束条件下的目标满足问题.多维动态规划是针对多维约束任务将有限资源进行合理分配、高效调度的有效方法.它以缩短任务完成时间为目标,通过先求解一系列子问题,再处理子问题间关系求得问题最终解,避免了计算的复杂性,又满足了时效性要求.针对卫星对地观测任务约束变量多的特点,将多维动态规划应用到对地观测卫星调度问题中,是解决该问题在时效性要求条件下的有效方法,其可行性通过想定任务在文章中得到证明.     

On periodic resource scheduling for continuous-media databases

The Enhanced Pay-Per-View (EPPV) model for providing continuous-media services associates with each continuous-media clip a display frequency that depends on the clip's popularity. The aim is to increase the number of clients that can be serviced concurrently beyond the capacity limitations of available resources, while guaranteeing a constraint on the response time. This is achieved by sharing periodic continuous-media streams among multiple clients. The EPPV model offers a number of advantages over other data-sharing schemes (e.g., batching), which make it more attractive to large-scale service providers. In this paper, we provide a comprehensive study of the resource-scheduling problems associated with supporting EPPV for continuous-media clips with (possibly) different display rates, frequencies, and lengths. Our main objective is to maximize the amount of disk bandwidth that is effectively scheduled under the given data layout and storage constraints. Our formulation gives rise to -hard combinatorial optimization problems that fall within the realm of hard real-time scheduling theory. Given the intractability of the problems, we propose novel heuristic solutions with polynomial-time complexity. We also present preliminary experimental results for the average case behavior of the proposed scheduling schemes and examine how they compare to each other under different workloads. A major contribution of our work is the introduction of a robust scheduling framework that, we believe, can provide solutions for a variety of realistic EPPV resource-scheduling scenarios, as well as any scheduling problem involving regular, periodic use of a shared resource. Based on this framework, we propose various interesting research directions for extending the results presented in this paper. Received June 9, 1998 / Accepted October 13, 1998     

Algorithms for propagating resource constraints in AI planning and scheduling: Existing approaches and new results

This paper summarizes the main existing approaches to propagate resource constraints in Constraint-Based scheduling and identifies some of their limitations for using them in an integrated planning and scheduling framework. We then describe two new algorithms to propagate resource constraints on discrete resources and reservoirs. Unlike most of the classical work in scheduling, our algorithms focus on the precedence relations between activities rather than on their absolute position in time. They are efficient even when the set of activities is not completely defined and when the time window of activities is large. These features explain why our algorithms are particularly suited for integrated planning and scheduling approaches. All our algorithms are illustrated with examples. Encouraging preliminary results are reported on pure scheduling problems as well as some possible extensions of our framework.     

An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem

We present an optimal solution procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem. In this problem, we assume the constrained renewable resources are limited to very expensive equipments and machines that are used in other projects and are not available in all periods of time of a project. In other words, for each resource, there is a dictated ready date as well as a due date such that no resource can be available before its ready date but the resources are permitted to be used after their due dates by paying penalty cost depending on the resource type. We also assume that only one unit of each resource type is available and no activity needs more than it for execution. The objective is to determine a schedule with minimal total weighted resource tardiness penalty costs. For this purpose, we present a branch-and-bound algorithm in which the branching scheme starts from a graph representing a set of conjunctions (the classical finish-start precedence constraints) and disjunctions (introduced by the resource constraints). In the search tree, each node is branched to two child nodes based on the two opposite directions of each undirected arc of disjunctions. Selection sequence of undirected arcs in the search tree affects the performance of the algorithm. Hence, we developed different rules for this issue and compare the performance of the algorithm under these rules using a randomly generated benchmark problem set.     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.     

Fast GA-based project scheduling for computing resources allocation in a cloud manufacturing system

Cloud manufacturing is becoming an increasingly popular enterprise model in which computing resources are made available on-demand to the user as needed. Cloud manufacturing aims at providing low-cost, resource-sharing and effective coordination. In this study, we present a genetic algorithm (GA) based resource constraint project scheduling, incorporating a number of new ideas (enhancements and local search) for solving computing resources allocation problems in a cloud manufacturing system. A newly generated offspring may not be feasible due to task precedence and resource availability constraints. Conflict resolutions and enhancements are performed on newly generated offsprings after crossover or mutation. The local search can exploit the neighborhood of solutions to find better schedules. Due to its complex characteristics, computing resources allocation in a cloud manufacturing system is NP-hard. Computational results show that the proposed GA can rapidly provide a good quality schedule that can optimally allocate computing resources and satisfy users’ demands.