基于改进粒子群算法的资源受限项目进度研究

资源受限的项目进度问题是经典的NP-hard问题,在研究以往求解方法的基础上,应用一种新的群智能算法——粒子群算法,对粒子群优化算法的搜索能力进行改进,结合Gbest模型与Pbest模型的优点,提出使粒子在搜索的前期有较强的全局搜索能力,尽可能多地发现可能全局最优的种子,而在搜索的后期则具有较强的局部搜索能力,用提高算法的收敛速度和精度的复合最优模型粒子群算法对RCPSP问题进行了求解,最后用文献[8]中的算例进行了仿真实验,实验结果验证了此算法的可行性与优越性。     

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.     

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。     

求解RCPSP问题的带分布估计的差异演化算法

提出一种带分布估计的差异演化算法（DEED）用于求解资源受限项目调度问题（RCPSP）。该算法基于差异演化（DE）算法,利用分布估计算法（EDA）能够获得问题解空间的全局信息以及变量间的相互联系,以指导算法搜索过程,并对最优解的分布进行预测。DEED算法充分利用DE收敛速度快和EDA全局搜索优点。经标准问题库（PSPLIB）的单模式问题集验证,并与当前流行的算法进行比较,表明了DEED算法的有效性。     

资源约束项目调度研究综述

资源约束项目调度问题(RCPSP)研究资源的合理利用和项目活动的合理调度,实现既定目标的最优化,具有很强的工程背景,近年来得到了学术界和工业界的广泛关注.为此,介绍了RCPSP的数学模型以及多种问题的扩充,总结了相关理论,重点综述了RCPSP的算法,并归纳了若干应用进展.最后指出了有待进一步研究的方向和内容.     

基于资源缓存的应用快速切换技术

为了加快嵌入式智能终端多应用切换速度,提出了一种基于资源缓存的应用快速切换技术.设计了一种使用资源缓存代理机制的资源管理框架,缓存应用切换到后台运行时的资源状态,建立以最小化应用切换时间为目标的资源管理模型,并将该模型转化为多维多选择背包问题,为解决该问题分别提出基于穷举搜索和启发式方法的资源缓存算法.实验结果表明,基于穷举搜索的资源缓存算法复杂度虽高,但是可以求得应用切换时间问题的最优解;而与之相比,启发式的资源缓存算法可以在较短时间内求得次优解,更适合于嵌入式终端采用,以实现多应用间的快速切换.     

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.     

基于遗传算法的多模式资源约束项目调度问题研究*

为解决多模式资源约束项目调度问题,提出了一种混合遗传算法的求解方法。该算法采用二维编码方法来表示问题的解,基因的值表示任务的优先权和执行模式,每条染色体对应一个满足逻辑关系约束的可行任务排序,根据染色体所对应的任务调度顺序和执行模式序列可以获得一个满足资源约束的项目调度方案。应用该编码方法进行选择、交叉和变异等遗传操作,能够使搜索范围遍及整个问题解空间。实际应用表明,该算法能快速求得问题的最优解或近似最优解。     

蚁群算法求解多目标资源受限项目排程问题——结合不同排程法则的修正与比较

现有文献较多研究工期最小化的单目标项目排程问题,对于综合考虑项目总工期、总延迟时间、总延迟成本的多目标资源受限项目排程问题(RCPSP)还较少探讨。建构了一个多目标RCPSP模型,以蚁群算法(ACO)配合综合现有排程法则提出的局部启发式函数AM排程法则,修正得到AM_ACO演算法,设计出新的费洛蒙(Pheromone)更新方式,运用田口方法,测试分析ACO各项参数值。最后利用PSPLIB中的测试例题,比较验证AM_ACO演算法的求解品质与效率。比较结果证实AM_ACO演算法有较高的求解品质与效率。     

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%.     

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.     

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.     

修正免疫克隆约束多目标优化算法

针对约束多目标优化问题,提出修正免疫克隆约束多目标优化算法.该算法通过引进一个约束处理策略,用一个修正算法对个体的目标函数值进行修正,并对修正后的目标函数值采用免疫克隆算法进行优化,用一个精英种群对可行非支配解进行存储.该算法在优化过程中,既保留了非支配可行解,也充分利用了约束偏离值小的非可行解,同时引进整体克隆策略来提高解分布的多样性.通过对约束多目标问题的各项性能指标的测试以及和对比算法的比较可以看出:该算法在处理约束多目标优化测试问题时,所得解的多样性得到了一定的提高.同时,解的收敛性和均匀性也得到了一定的改进.     

项目优化调度的多智能体社会进化算法

结合多智能体系统、进化算法以及关系网模型,提出了一种多智能体社会进化算法用于求解项目活动的一个最优调度顺序以使整个工程的工期最短,每个智能体生存于环境中,为了增加自身能量将与其邻域展开竞争及协同操作,同时可利用自身的知识进行自学习来增加能量,根据项目优化调度的问题特点,设计了智能体的竞争行为、协同行为以及自学习行为,通过对PSPLIB中的标准问题进行测试,同时与其他启发式算法相比较的仿真实验结果表明该算法具有良好的性能,能在较短的时间内寻找到十分接近"最优解"的调度序列.     

Multi-skilled project scheduling with level-dependent rework risk; three multi-objective mechanisms based on cuckoo search

In many projects, multi-skilled workforces are able to perform different tasks with different quality levels. In this paper, a real-life version of the multi-skilled resource constrained project scheduling problem is investigated, in which the reworking risk of each activity depends on the assigned level of multi-skilled workforces. The problem is formulated mathematically as a bi-objective optimization model to minimize total costs of processing the activities and to minimize reworking risks of the activities, concurrently. In order to solve the resulting problem, three cuckoo-search-based multi-objective mechanisms are developed based on non-dominance sorting genetic algorithm, multi-objective particle swarm and multi-objective invasive weeds optimization algorithm. The parameters of the algorithms are tuned using the Taguchi method to improve the efficiency of the solution procedures. Furthermore, a competitive multi-objective invasive weeds optimization algorithm is used to evaluate the performance of the proposed methodologies. Finally, a priority based method is employed to compare the proposed algorithms in terms of different metrics.     

基于多目标优化策略的在线学习资源推荐方法

目前在线学习资源推荐较多采用单目标转化方法,推荐过程中对学习者偏好考虑相对不足,影响学习资源推荐精度.针对上述问题,文中提出基于多目标优化策略的在线学习资源推荐模型(MOSRAM),在学习者规划时间内,以同时获得学习者对学习资源类型偏好度最大和难度水平适应度最佳为优化目标,设计具有向邻居均值学习能力和探索新区域能力的多目标粒子群优化算法(NEMOPSO),提出以MOSRAM为核心的在线学习资源推荐方法(NEMOPSO-RA).不同问题规模下融合经典多目标优化算法的推荐方法对比实验表明,NEMOPSO-RA可以有效提高在线学习资源的推荐精度和推荐性能.     

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.     

An evolutionary algorithm with directed weights for constrained multi-objective optimization

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions.     

Multi-mode renewable resource-constrained allocation in PERT networks

This paper presents a hybrid metaheuristic algorithm (HMA) for Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP) in PERT networks. A PERT-type project, where activities require resources of various types with random duration, is considered. Each activity can be accomplished in one of several execution modes and each execution mode represents an alternative combination of resource requirements of the activity and its duration. The problem is to minimize the regular criterion namely project's makespan by obtaining an optimal schedule and also the amount of different resources assigned to each activity. The resource project scheduling model is strongly NP-hard, therefore a metaheuristic algorithm is suggested namely HMA. In order to validate the performance of new hybrid metaheuristic algorithm, solutions are compared with optimal solutions for small networks. Also the efficiency of the proposed algorithm, for real world problems, in terms of solution quality and CPU time, is compared to one of the well-known metaheuristic algorithms, namely Genetic Algorithm of Hartmann (GAH). The computational results reveal that the proposed method provides appropriate results for small networks and real world problems.