基于改进NSGA-II算法求解多目标资源受限项目调度问题

资源受限项目调度问题(resource constrained project scheduling problem, RCPSP)要求在满足相关约束的条件下安排各活动开始时间,从而达到某一目标的最优,具有很强的应用背景,并受到众多学者的广泛关注.经典的RCPSP模型以最小化项目工期为单一目标,忽略了资源使用率等因素对项目整体的影响,使其与实际应用仍有较大差距.基于经典的RCPSP模型,引入最优资源均衡为另一目标,将模型扩展为多目标模型,丰富了RCPSP模型的应用场景.同时,考虑到新模型中各活动间存在大量的控制关系,使用传统的启发式多目标算法需要耗费大量的时间对不可行解进行判断,求解性能较低,提出一种新的算法框架NSGA-IIs.该算法框架基于活动间控制关系将各活动分成若干子集,并在初始化和交叉变异等阶段以子集为基本单位产生新的个体,能够较好地避免不可行解的产生,提高算法的效率.使用解集覆盖度作为评价指标,通过实例数据集的实验表明,与已有的求解RCPSP的经典算法相比,所提出的算法具有明显的优越性.     

不确定资源受限项目调度研究综述

不确定资源受限项目调度问题(RCPSP)是研究在不确定环境和有限资源约束下如何合理安排项目活动,以实现既定目标的最优化.不确定RCPSP具有很强的工程背景,在学术和应用上均具有很高的研究价值,但存在大规模、强约束、多极小、多目标和不确定等诸多复杂性,求解非常困难.为此,介绍了不确定RCPSP的数学描述和几种具体形式,重点综述了不确定RCPSP的算法进展,并归纳了相关的应用成果,最后指出了有待进一步研究的若干方向和内容.     

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.     

蚁群算法在资源受限项目调度问题中的应用

资源受限的项目调度问题(RCPSP,Resource-ConstrainedProjectSchedulingProblems)已经被证明是一种NP-hard的组合优化问题,随着问题规模的增大,使用经典的数学方法如数学规划等方法,已经很难解决问题。论文提出了一种用于求解资源受限的项目调度问题的蚁群算法。针对资源受限的项目调度问题的具体特点,提出了蚂蚁巡游网络图的动态生成方式,信息素的表示及更新方式,以及启发信息的计算方法。针对PSPLIB中的测试集对算法中的主要参数进行了优化,最后,使用PSPLIB中的四种测试集对算法进行了测试,计算结果表明了算法的有效性。     

求解资源受限项目调度问题的约束规划/数学规划混合算法

利用约束规划（constraintprogramming,CP）与数学规划（mathematicalprogramming,MP）结合的方法求解调度问题已经获得了一些较好的研究成果,正成为调度问题研究领域的一个新的热点研究方向．本文针对求解资源受限项目调度问题（RCPSP）的整数规划模型,设计了基于CP技术的问题和模型预处理方法,证明了整数规划模型的有效不等式定理,提出了通过将项目子网络图转化为加权最大团问题求解后获得有效不等式的方法．引用标准问题库PSPLIB中的一组典型问题进行求解实验,结果表明本文提出的有效不等式可以明显改进模型的求解质量和时间性能．论文最后对实验结果进行了深入讨论,讨论了未来的研究方向．     

RCPSP中现金流优化问题的HGA方法

针对网络进度计划中财务方面对项目管理的影响 ,研究资源受限项目调度问题 (RCPSP)中网络现金流的优化问题。提出以网络净现值最大作为网络现金流优化的目标 ,建立了带有贴现率的非线性整数规划模型 ,采用遗传算法与模拟退火算法相结合的混合式遗传算法进行求解。仿真实例表明了方法的合理性和有效性。     

协同震荡搜索混沌粒子群求解资源受限项目调度问题

针对求解资源受限项目调度问题(RCPSP),提出了协同震荡搜索混沌粒子群(CSCPSO)算法。算法围绕种群粒子吸引子建立双向协同震荡搜索机制,该机制一方面使粒子向吸引子收敛,另一方面使粒子震荡调整自身与吸引子相邻维度大小关系不一致的维度,提升算法的搜索精度和种群的多样性。项目调度采用基于粒子的拓扑排序和串行项目进度生成机制,保证项目调度解决方案满足资源约束和紧前约束。采用具体算例对算法进行检验,结果表明该算法在求解RCPSP的精度和稳定性方面表现更优。     

考虑柔性资源能力差异的项目调度问题

在资源受限项目调度问题中,将可再生资源进一步拓展为具有能力差异的柔性资源,建立考虑能力差异的柔性资源受限项目调度问题模型,该模型是对传统资源约束项目调度问题（RCPSP）更接近实际的拓展。为了求解该模型,提出一种基于活动序列表示的粒子群算法,在粒子解码过程中运用了基于优先规则的柔性资源-能力分配算法,在此基础上详细介绍了改进的串行调度生成方案与改进的并行调度生成方案、算法框架、选择性粒子更新方法。通过在改造的项目调度测试问题集上进行数值实验,证明了算法的可行性和有效性,其中使用改进串行调度生成方案与最匹配资源优先规则的粒子群算法具有较好的求解性能。     

考虑资源转移时间的资源受限项目调度问题的算法

现有项目调度问题的研究一般假设资源在任务间转移不需要时间,但这一假设与很多实际情况不相符,本文在资源受限项目调度问题（Resource-constrained project scheduling problem,RCPSP）中引入资源转移时间,以最小化项目工期为目标,建立了考虑资源转移时间的资源受限项目调度问题的数学模型.为改善遗传算法在局部搜索能力方面的不足,提出将分支定界法与遗传算法相结合,构造了一种内嵌分支定界寻优搜索的遗传算法,在保证算法全局搜索能力的前提下提升局部精确搜索能力.同时,对于遗传算法,为了适应算法结构提出了一种基于任务绝对顺序的编码策略.数据实验表明,对于小规模问题可获得近似精确解,对于大规模问题相较现有文献所提算法,在算法求解精度上可提升10%.     

采用优先规则的粒子群算法求解RCPSP

优先规则是解决大规模资源受限的项目调度问题（Resource-Constrained Project Scheduling Problem,RCPSP）强有力的方法,但是单一的优先规则的往往仅在某些特定的问题上表现出良好的性能。以粒子群算法为基础,提出了基于优先规则编码的粒子群算法（Priority Rule based Particle Swarm Optimization,PRPSO）,求解资源受限的项目调度问题。该方法能够通过粒子群算法搜索优先规则和调度生成方案的组合。分别对PRPSO采用串行调度方案、并行调度方案和混合调度方案时,不同任务数和资源强度的问题实例进行了分析。通过对PSPLIB进行测试,结果表明该方法与其它基于优先规则的启发式方法相比有较低的偏差率,因而有较好的性能。     

基于关键链的资源受限项目调度新方法

针对资源受限项目调度问题（RCPSPs）的实际需求建立了多目标优化调度模型，综合运用现有研究成果，设计了基于关键链的项目调度方法。该方法首先采用基于优先规则的启发式算法生成工期最小的近优项目计划，再在该计划中嵌入输入缓冲和项目缓冲，保证项目计划在非确定环境下的稳定执行。论文引用RCPSPs的标准问题库PSPLIB中大量案例对算法进行了的仿真试验，结果表明本文方法较传统项目调度方法有很大改进，论文最后对仿真结果进行了深入讨论，并指出了未来的研究方向。     

Deep reinforcement learning for solving resource constrained project scheduling problems with resource disruptions

The resource-constrained project scheduling problem (RCPSP) is encountered in many fields, including manufacturing, supply chain, and construction. Nowadays, with the rapidly changing external environment and the emergence of new models such as smart manufacturing, it is more and more necessary to study RCPSP considering resource disruptions. A framework based on reinforcement learning (RL) and graph neural network (GNN) is proposed to solve RCPSP and further solve the RCPSP with resource disruptions (RCPSP-RD) on this basis. The scheduling process is formulated as sequential decision-making problems. Based on that, Markov decision process (MDP) models are developed for RL to learn scheduling policies. A GNN-based structure is proposed to extract features from problems and map them to action probability distributions by policy network. To optimize the scheduling policy, proximal policy optimization (PPO) is applied to train the model end-to-end. Computational results on benchmark instances show that the RL-GNN algorithm achieves competitive performance compared with some widely used methods.     

A hybrid evolutionary algorithm for the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) is an NP-hard optimization problem. RCPSP is one of the most important and challenging problems in the project management field. In the past few years, many researches have been proposed for solving the RCPSP. The objective of this problem is to schedule the activities under limited resources so that the project makespan is minimized. This paper proposes a new algorithm for solving RCPSP that combines the concepts of negative selection mechanism of the biologic immune system, simulated annealing algorithm (SA), tabu search algorithm (TS) and genetic algorithm (GA) together. The performance of the proposed algorithm is evaluated and compared to current state-of-the-art metaheuristic algorithms. In this study, the benchmark data sets used in testing the performance of the proposed algorithm are obtained from the project scheduling problem library. The performance is measured in terms of the average percentage deviation from the critical path lower bound. The experimental results show that the proposed algorithm outperforms the state-of-the-art metaheuristic algorithms on all standard benchmark data sets.     

A multi-agent system for the decentralized resource-constrained multi-project scheduling problem

A restart evolution strategy (RES) for the resource‐constrained project scheduling problem (RCPSP), as well as its integration in a multi‐agent system (MAS) for solving the decentralized resource‐constrained multi‐project scheduling problem (DRCMPSP) will be presented. To evaluate the developed approach, problem instances of the RCPSP taken from the literature with up to 300 activities are used, as well as 80 generated instances of the DRCMPSP, with up to 20 projects and with up to 120 activities each. For 73 instances of the RCPSP, the RES found better solutions than the best ones found so far. In addition, the MAS is suitable for solving large multi‐project instances decentrally. The results for the DRCMPSP instances show that the presented decentralized MAS is competitive with a central solution approach.     

基于混沌粒子群算法的项目调度干扰问题研究

针对资源受限项目调度问题中的干扰情况进行了界定, 面向几种干扰问题建立了相应的资源受限项目调度干扰模型和混沌粒子群求解算法, 对项目网络图干扰、任务干扰和资源干扰三种干扰问题进行仿真计算, 验证了算法和模型的有效性, 为决策者在干扰事件发生后及时对原最优调度计划作出调整给出了方向。     

Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities

Research concerning project planning under uncertainty has primarily focused on the stochastic resource-constrained project scheduling problem (stochastic RCPSP), an extension of the basic RCPSP, in which the assumption of deterministic activity durations is dropped. In this paper, we introduce a new variant of the RCPSP, for which the uncertainty is modeled by means of resource availabilities that are subject to unforeseen breakdowns. Our objective is to build a robust schedule that meets the project deadline and minimizes the schedule instability cost, defined as the expected weighted sum of the absolute deviations between the planned and the actually realized activity starting times during project execution. We describe how stochastic resource breakdowns can be modeled, which reaction is recommended, when a resource infeasibility occurs due to a breakdown, and how one can protect the initial schedule from the adverse effects of potential breakdowns. An extensive computational experiment is used to show the relative performance of the proposed proactive and reactive strategies. It is shown that protection of the baseline schedule, coupled with intelligent schedule recovery, yields significant performance gains over the use of deterministic scheduling approaches in a stochastic setting. This research has been supported by project OT/03/14 of the Research Fund of K.U.Leuven, project G.0109.04 of the Research Programme of the Fund for Scientific Research, Flanders (Belgium) (F.W.O.-Vlaanderen) and project NB/06/06 of the National Bank of Belgium.     

An adaptive genetic algorithm for demand-driven and resource-constrained project scheduling in aircraft assembly

Scheduling of aircraft assembling activities is proven as a non-deterministic polynomial-time hard problem; which is also known as a typical resource-constrained project scheduling problem (RCPSP). Not saying the scheduling of the complex assemblies of an aircraft, even for a simple product requiring a limited number of assembling operations, it is difficult or even infeasible to obtain the best solution for its RCPSP. To obtain a high quality solution in a short time frame, resource constraints are treated as the objective function of an RCPSP, and an adaptive genetic algorithm (GA) is proposed to solve demand-driven scheduling problems of aircraft assembly. In contrast to other GA-based heuristic algorithms, the proposed algorithm is innovative in sense that: (1) it executes a procedure with two crossovers and three mutations; (2) its fitness function is demand-driven. In the formulation of RCPSP for aircraft assembly, the optimizing criteria are the utilizations of working time, space, and operators. To validate the effectiveness of the proposed algorithm, two encoding approaches have been tested with the real data of demand.     

人工蜂群算法求解资源受限项目调度问题

针对资源受限项目调度问题,提出了一种基于人工蜂群算法的优化方法。人工蜂群算法中每个食物源的位置代表一种项目任务的优先权序列,每个食物源的位置通过扩展串行调度机制转换成可行的调度方案,迭代中由三种人工蜂执行不同的操作来实现全局最优解的更新。实验结果表明,人工蜂群算法是求解资源受限项目调度问题的有效方法,同时扩展调度机制的引入可以加速迭代收敛的进程。     

Particle swarm optimization with justification and designed mechanisms for resource-constrained project scheduling problem

The studied resource-constrained project scheduling problem (RCPSP) is a classical well-known problem which involves resource, precedence, and temporal constraints and has been applied to many applications. However, the RCPSP is confirmed to be an NP-hard combinatorial problem. Restated, it is hard to be solved in a reasonable time. Therefore, there are many metaheuristics-based schemes for finding near optima of RCPSP were proposed. The particle swarm optimization (PSO) is one of the metaheuristics, and has been verified being an efficient nature-inspired algorithm for many optimization problems. For enhancing the PSO efficiency in solving RCPSP, an effective scheme is suggested. The justification technique is combined with PSO as the proposed justification particle swarm optimization (JPSO), which includes other designed mechanisms. The justification technique adjusts the start time of each activity of the yielded schedule to further shorten the makespan. Moreover, schedules are generated by both forward scheduling particle swarm and backward scheduling particle swarm in this work. Additionally, a mapping scheme and a modified communication mechanism among particles with a designed gbest ratio (GR) are also proposed to further improve the efficiency of the proposed JPSO. Simulation results demonstrate that the proposed JPSO provides an effective and efficient approach for solving RCPSP.