Fuzzy resource‐constrained project scheduling using taboo search algorithm

This paper proposes a mathematical model to deal with project scheduling problem under vagueness and a framework of a heuristic approach to fuzzy resource‐constrained project scheduling problem (F‐RCPSP) using heuristic and metaheuristic scheduling methods. Our approach is very simple to apply, and it does not require knowing the explicit form of the membership functions of the fuzzy activity times. We first identify two typical activity priority rules, namely, resource over time and minimum slack priority rules. They are used in the F‐RCPS problem and in the initial solution of Taboo search (TS) method. We improved the TS algorithm method for the solution of F‐RCPSP. Our objective is to check the performance of these rules and metaheuristic method in minimizing the project completion time for the F‐RCPS problems. In our study, we use trapezoidal fuzzy numbers (TraFNs) for activity times and activity‐on‐nodes (AON) representation and compute several project characteristics such as earliest, latest, and slack times in terms of TraFNs. The computational experiment shows that the performance of the proposed TS is better than the evaluation and light beam search algorithms in the literature. © 2012 Wiley Periodicals, Inc.     

Multi‐mode resource‐constrained project scheduling using modified variable neighborhood search heuristic

This paper aims at providing a fast near‐optimum solution to the multi‐mode resource‐constrained project scheduling problems (MRCPSPs), for projects with activities that have known deterministic renewable and nonrenewable resource requirements. The MRCPSP is known to be nondeterministic polynomial‐time hard and has been solved using various exact, heuristic, and meta‐heuristic procedures. In this paper, a modified variable neighborhood search heuristic algorithm is used as an advanced optimization technique that suits scheduling problems. For the experimental study, we have considered a standard set of 3929 multi‐mode benchmark instances from the project scheduling library with a range of projects comprising 10–30 activities. Moreover, for a better comparison, this research also considers a standard set of 4320 newly developed multi‐mode instances from MMLIB50, MMLIB100, and MMLIB+ datasets. With the limit of 50,000 schedules on these datasets, our proposed algorithm provides better makespan for 106, 34, and 1601 instances, respectively, which justifies the efficiency of the proposed algorithm, particularly for projects with a larger number of activities. The results reported in this paper can be used as a benchmark for other researchers to compare and improve.     

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.     

A multi-unit combinatorial auction based approach for decentralized multi-project scheduling

In industry, many problems are considered as the decentralized resource-constrained multi-project scheduling problem (DRCMPSP). Existing approaches encounter difficulties in dealing with large DRCMPSP cases while respecting the information privacy requirements of the project agents. In this paper, we tackle DRCMPSP by formulating it as a multi-unit combinatorial auction (Wellman et al. in Games Econ Behav 35(1):271–303, 2001), which does not require sensitive private project information. To handle the hardness of bidder valuation, we introduce the capacity query which uses different item capacity profiles to efficiently elicit valuation information from bidders. Based on the capacity query, we adopt two existing strategies (Gonen and Lehmann in Proceedings of the 2nd ACM conference on electronic commerce, pp 13–20, 2000) for solving multi-unit winner determination problems to find good allocations of the DRCMPSP auctions. The first strategy employs a greedy allocation process, which can rapidly find good allocations by allocating the bidder with the best answer after each query. The second strategy is based on a branch-and-bound process to improve the results of the first strategy, by searching for a better sequence of granting the bids from the bidders. Empirical results indicate that the two strategies can find good solutions with higher quality than state-of-the-art decentralized approaches, and scale well to large-scale problems with thousands of activities from tens of projects.     

Solving resource-constrained project scheduling problems: Conceptual validation of FLP formulation and efficient permutation-based ABC computation

In this paper, we propose two alternative approaches, applying the facility layout problem (FLP) concept and integrating the permutation-based artificial bee colony (PABC) algorithm, to effectively tackle the resource-constrained project scheduling problem (RCPSP). In the FLP formulation, the constraints are expressed to design the activities in the space constructed by resource and temporal restrictions, without violating the precedence relationships and overlaps between the activities. For dodging the difficulty of the FLP-based model to treat large-sized instances of NP-hard RCPSP, the permutation representation scheme of the PABC algorithm is in turn introduced utilizing the artificial bee colony (ABC) process to search the best solution for RCPSP. In the procedure, a crossover operator and an insert operator following the update equation of the ABC algorithm are devised to augment the effectiveness of computation, whereas a shift operator subject to the resource utilization ratio value is suggested to diversify the solutions. The makespan is then obtained and improved with the assistance of a serial scheduling scheme and a double justification skill. Subsequently, the computational experiments conducted substantiate the conceptual validity of the proposed facility layout formulation for RCPSP and the comprehensive simulation shows the effectiveness of the PABC algorithm for RCPSP.     

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 multi-agent system for distributed multi-project scheduling: An auction-based negotiation approach

Simultaneously running multiple projects are quite common in industries. These projects require local (always available to the concerned project) and global (shared among the projects) resources that are available in limited quantity. The limited availability of the global resources coupled with compelling schedule requirements at different projects leads to resource conflicts among projects. Effectively resolving these resource conflicts is a challenging task for practicing managers. This paper proposes a novel distributed multi-agent system using auctions based negotiation (DMAS/ABN) approach for resolving the resource conflicts and allocating multiple different types of shared resources amongst multiple competing projects. The existing multi-agent system (MAS) using auction makes use of exact methods (e.g. dynamic programming relaxation) for solving winner determination problem to resolve resource conflicts and allocation of single unit of only one type of shared resource. Consequently these methods fail to converge for some multi-project instances and unsuitable for real life large problems. In this paper the multi-unit combinatorial auction is proposed and winner determination problem is solved by efficient new heuristic.The proposed approach can solve complex large-sized multi-project instances without any limiting assumptions regarding the number of activities, shared resources or the number of projects. Additionally our approach further allows to random project release-time of projects which arrives dynamically over the planning horizon. The DMAS/ABN is tested on standard set of 140 problem instances. The results obtained are benchmarked against the three state-of-the-art decentralized algorithms and two existing centralized methods. For 82 of 140 instances DMAS/ABN found new best solutions with respect to average project delay (APD) and produced schedules on an average 16.79% (with maximum 57.09%) lower APD than all the five methods for solving the same class of problems.     

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.     

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.     

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。     

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.     

项目资源均衡研究综述

作为一类经典的项目调度问题,资源均衡研究的是如何通过安排活动来均衡整个项目周期内资源的使用.资源均衡问题因其重要的理论价值和应用背景,一直是项目调度领域的重点研究课题.鉴于此,对国内外项目资源均衡的研究成果进行了系统性总结与梳理:介绍了资源均衡问题的数学模型和常用的测试问题库;综述了求解资源均衡问题的各类算法;总结了资源均衡问题的一些扩展问题和应用情况.最后指出了未来进一步的研究方向.     

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.     

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.     

Solving project scheduling problems with resource constraints via an event list-based evolutionary algorithm

There are various scheduling problems with resource limitations and constraints in the literature that can be modeled as variations of the Resource Constrained Project Scheduling Problem (RCPSP). This paper proposes a new solution representation and an evolutionary algorithm for solving the RCPSP. The representation scheme is based on an ordered list of events, that are sets of activities that start (or finish) at the same time. The proposed solution methodology, namely SAILS, operates on the event list and relies on a scatter search framework. The latter incorporates an Adaptive Iterated Local Search (AILS), as an improvement method, and integrates an event-list based solution combination method. AILS utilizes new enriched neighborhoods, guides the search via a long term memory and applies an efficient perturbation strategy. Computational results on benchmark instances of the literature indicate that both AILS and SAILS produce consistently high quality solutions, while the best results are derived for most problem data sets.     

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。     

An evolutionary implicit enumeration procedure for solving the resource‐constrained project scheduling problem

This paper presents a procedure for solving the resource‐constrained project scheduling problem. It consists of an implicit enumeration module and a genetic algorithm. If the procedure is provided access to all of its required computational resources of the problem at hand, it guarantees the optimality of the produced solution. In contrast, and in the case of limited access to computational resources, the procedure gradually moves the root of the search‐tree downward, and consequently prunes part of the search space, trading speed with precision effectively. In the cases where speed has been traded with precision, and the guarantee of optimality has been lost, the final schedule created by the implicit enumeration module is used as a template whose modified instances fill an initial pool of a genetic algorithm to improve the proposed solution. The procedure has been applied to 2040 benchmark instances. The results are promising; whereas for all small‐ and some medium‐sized instances, the procedure has found and guaranteed optimal solutions, for other instances, whose optimal solutions cannot be guaranteed within the limit of computational resources, it has produced high‐quality solutions.     

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.     

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。     

Chaos-based improved immune algorithm (CBIIA) for resource-constrained project scheduling problems

This paper introduces a novel meta-heuristic, the chaos-based improved immune algorithm (CBIIA), for solving resource-constrained project scheduling problems (RCPSP). In RCPSP the activities of a project have to be scheduled with the objective of minimizing total makespan subject to both temporal and resource constraints. The proposed CBIIA is based on the traits of an artificial immune system, chaotic generator and parallel mutation. CBIIA is different from the traditional immune algorithm in its initialization and hypermutation mechanism. Initialization in CBIIA is done by using chaotic generator (Logistic, Tent, and Sinusoidal) instead of conventional random number generator (RNG). The hypermutation is performed by parallel mutation (PM) operator rather than point mutation. Parallel mutation comprises two mutation strategies viz. Gaussian and Cauchy. Gaussian strategy is utilized for small step mutation and Cauchy strategy is for large step mutation. In order to demonstrate the efficacy of the proposed algorithm, Patterson’s test suites are worked out. This study aims at developing an alternative and more efficient optimization methodology and opening the application of variants of artificial immune system for solving the RCPSP.