飞机着陆调度排序算法的设计与实现

航空管制员必须为同时到达的每一架飞机计算着陆时间，使整体费用最小，同时还要注意一些硬性的限制条件。在某一时刻，给定管制员视野内的飞机数量，可以公式化为约束最优化问题，从而应用一定的算法来解决。该文提出了基于分枝定界的飞机着陆调度排序算法——ASAL，实验证明通过该算法能够很好地解决飞机着陆调度优化问题。     

知识化制造环境下航空发动机装配线调度及自重构

航空发动机装配工序数量多、工序间装配约束复杂. 当产品需求变化时, 人工调整存在响应速度慢、装配效率低等问题. 以最小化产品完工成本、工序提前期惩罚成本及班组重构成本加权和为目标, 建立了航空发动机装配线调度和装配班组自重构优化模型. 提出一种新的基于工序局部最优排序的分解算法, 将调度问题分解为单个装配组上工序顺序优化问题. 设计了一种工序后向插入搜索策略. 最后提出装配线调度及自重构集成优化算法. 通过数值试验,验证了模型与算法的有效性.     

Aviation maintenance technician scheduling with personnel satisfaction based on interactive multi-swarm bacterial foraging optimization

This study focuses on the challenges of aviation maintenance technician (AMT) scheduling and constructs a model based on personnel satisfaction and the parallel execution of aircraft maintenance tasks. To obtain the scheduling scheme from the constructed NP-hard model, an interactive multi-swarm bacterial foraging optimization (IMSBFO) algorithm is proposed using multi-swarm coevolution, structural recombination, and three information interactive mechanisms among individuals. Moreover, considering the distributed feature of the AMT scheduling problem, a specific mechanism is designed to convert continuous solution to a binary AMT scheduling scheme. Finally, a series of comparative experiments highlight the efficiency and superiority of our proposed IMSBFO algorithm, and the optimal scheduling scheme owns the delicate balance between the work and rest time.     

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.     

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.     

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。     

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.     

An evolutionary algorithm for the resource-constrained project scheduling problem with minimum and maximum time lags

In this paper, we present an evolutionary algorithm (EVA) for solving the resource-constrained project scheduling problem with minimum and maximum time lags (RCPSP/max). EVA works on a population consisting of several distance-order-preserving activity lists representing feasible or infeasible schedules. The algorithm uses the conglomerate-based crossover operator, the objective of which is to exploit the knowledge of the problem to identify and combine those good parts of the solution that have really contributed to its quality. In a recent paper, Valls et al. (European J. Oper. Res. 165, 375–386, 2005) showed that incorporating a technique called double justification (DJ) in RCPSP heuristic algorithms can produce a substantial improvement in the results obtained. EVA also applies two double justification operators DJmax and DJU adapted to the specific characteristics of problem RCPSP/max to improve all solutions generated in the evolutionary process. Computational results in benchmark sets show the merit of the proposed solution method.     

A heuristic algorithm to minimize total weighted tardiness on a single machine with release times

This paper attempts to solve a single machine‐scheduling problem, in which the objective function is to minimize the total weighted tardiness with different release dates of jobs. To address this scheduling problem, a heuristic scheduling algorithm is presented. A mathematical programming formulation is also formulated to validate the performance of the heuristic scheduling algorithm proposed herein. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. Overall, this algorithm can find the optimal solutions for 2200 out of 2400 randomly generated problems (91.67%). For the most complicated 20 job cases, it requires less than 0.0016 s to obtain an ultimate or even optimal solution. This heuristic scheduling algorithm can therefore efficiently solve this kind of problem.     

资源约束项目的改进差分进化参数控制及双向调度算法

针对资源约束项目调度组合优化难题,提出一种改进的动态差分进化参数控制及双向调度算法.通过参数时变衰减与个体优劣评价,自适应控制个体进化参数,提高算法的收敛性能、勘探与开发最优解的能力;基于动态差分进化(Dynamic differential evolution, DDE),提出一种双向调度算法,使用满足任务时序约束的优先数编码、交替正向反向调度,结合标准化编码调整与精英保留的种群随机重建策略,建立了一种高效稳健的双向编码调整机制.通过著名的项目调度问题库(Project scheduling problem library, PSPLIB)中实例集测试,并与其他文献算法比较最优解平均偏差率,验证了所提算法的有效性与优越性.     

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.     

差分进化混合粒子群算法求解项目调度问题*

针对求解资源受限项目调度问题（RCPSP）,提出了基于差分进化（DE）的混合粒子群算法（PSODE）。通过在PSO种群和DE种群之间建立一种信息交流机制,使信息能够在两个种群中传递,以避免个体因错误的信息判断而陷入局部最优点。采用标准测试函数和具体算例进行检验,结果表明PSODE算法可以较好地解决RCPS问题。     

面向航空发动机的知识化制造系统拖期调度与自重构

针对某航空发动机装配线装配效率低、工人分配不合理等问题,建立面向航空发动机的知识化制造系统拖期调度和班组自重构优化模型.提出一种启发式算法,实现生产调度与班组配置的协同优化.在算法调度层中,针对航空发动机装配过程存在复杂约束这一特点,证明与产品拖期优化目标相关的工序排序性质,设计相应工序调整算法,给出工序在并行装配组上的初始分配方案和优化方案.在重构层,根据系统负载平衡的原则优化各装配班中装配组的数量.仿真实验结果表明了模型和所提出算法的有效性.     

Two-machine flowshop scheduling with bicriteria problem

This paper attempts to solve a two-machine flowshop bicriteria scheduling problem with release dates for the jobs, in which the objective function is to minimize a weighed sum of total flow time and makespan. To tackle this scheduling problem, an integer programming model with N²+3N variables and 5N constraints where N is the number of jobs, is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, a heuristic scheduling algorithm is presented. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. The average solution quality of the heuristic algorithm is above 99% and is much better than that of the SPT rule as a benchmark. A 15-job case requires only 0.018 s, on average, to obtain an ultimate or even optimal solution. The heuristic scheduling algorithm is a more practical approach to real world applications than the integer programming model.     

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.     

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%.     

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.     

An efficient hybrid genetic algorithm to solve assembly line balancing problem with sequence-dependent setup times

In this paper the setup assembly line balancing and scheduling problem (SUALBSP) is considered. Since this problem is NP-hard, a hybrid genetic algorithm (GA) is proposed to solve the problem. This problem involves assigning the tasks to the stations and scheduling them inside each station. A simple permutation is used to determine the sequence of tasks. To determine the assignment of tasks to stations, the algorithm is hybridized using a dynamic programming procedure. Using dynamic programming, at any time a chromosome can be converted to an optimal solution (subject to the chromosome sequence).     

An integrated selection and scheduling for disjunctive network problems

In network optimization problems, the application of conventional integrated selection and scheduling solution methods becomes complicated when the size of the problems, such as real life project management, assembly and transportation problems, get bigger. These kinds of problems often consist of disjunctive networks with alternative subgraphs. Traditionally, in order to handle alternative subgraphs in a disjunctive network, researchers consider first selection and then solution (scheduling) of the problem sequentially. However, the use of traditional approaches result in the loss of the problem structural integrity. When the approach losses its integrated structure, the network problem also losses its integrity. Therefore, these two issues, i.e. selection and scheduling, have to be considered together. To provide a new approach to maintain the problem integrity, we proposed an integrated genetic algorithm for solving this selection and scheduling problems together using a multi-stage decision approach. In this study, two newly defined problems with different disjunctive networks and different characteristics, i.e. resource constrained multiple project scheduling (rc-mPSP) models with alternative projects and variable activity times, and U-shaped assembly line balancing (uALB) models with alternative subassemblies, have been solved using the proposed solution approach to highlight the applicability and performance of the proposed solution approach.