Inverse scheduling: two-machine flow-shop problem

We study an inverse counterpart of the two-machine flow-shop scheduling problem that arises in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find job sequence(s) for which the value of the makespan is minimum, in the inverse scheduling the exact values of processing times are unknown and they should be selected within given boundaries so that pre-specified job sequence(s) become optimal. We derive necessary and sufficient conditions of optimality of a given solution for the general case of the flow-shop problem when the job sequences on the machines can be different. Based on these conditions we prove that the inverse flow-shop problem is NP-hard even in the case of the same job sequence on both machines and produce a linear programming formulation for a special case which can be solved efficiently.     

Two-machine flow shop scheduling integrated with preventive maintenance planning

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.     

Parallel-machine scheduling to minimize tardiness penalty and power cost

Traditional research on machine scheduling focuses on job allocation and sequencing to optimize certain objective functions that are defined in terms of job completion times. With regard to environmental concerns, energy consumption becomes another critical issue in high-performance systems. This paper addresses a scheduling problem in a multiple-machine system where the computing speeds of the machines are allowed to be adjusted during the course of execution. The CPU adjustment capability enables the flexibility for minimizing electricity cost from the energy saving aspect by sacrificing job completion times. The decision of the studied problem is to dispatch the jobs to the machines as well as to determine the job sequence and processing speed of each machine with the objective function comprising of the total weighted job tardiness and the power cost. We give a formal formulation, propose two heuristic algorithms, and develop a particle swarm optimization (PSO) algorithm to effectively tackle the problem. Since the existing solution representations do not befittingly encode the decisions involved in the studied problem into the PSO algorithm, we design a tailored encoding scheme which can embed all decisional information in a particle. A computational study is conducted to investigate the performances of the proposed heuristics and the PSO algorithm.     

两机无等待流水车间调度问题的性质

针对两机无等待流水车间调度问题,提出目标函数最大完工时间最小化的快速算法,并给出算法的复杂度。分析两机无等待流水车间调度问题的排列排序性质,证明了两机无等待流水车间调度问题的可行解只存在于排列排序中,排列排序的最优解一定是两机无等待流水车间调度问题的最优解。最后研究了同时包含普通工件和无等待工件的两机流水车间调度问题的复杂性,为进一步研究两机无等待流水车间调度问题提供了理论依据。     

A novel hybrid PSO–GA meta-heuristic for scheduling of DAG with communication on multiprocessor systems

This work presents a novel hybrid meta-heuristic that combines particle swarm optimization and genetic algorithm (PSO–GA) for the job/tasks in the form of directed acyclic graph (DAG) exhibiting inter-task communication. The proposed meta-heuristic starts with PSO and enters into GA when local best result from PSO is obtained. Thus, the proposed PSO–GA meta-heuristic is different than other such hybrid meta-heuristics as it aims at improving the solution obtained by PSO using GA. In the proposed meta-heuristic, PSO is used to provide diversification while GA is used to provide intensification. The PSO–GA is tested for task scheduling on two standard well-known linear algebra problems: LU decomposition and Gauss–Jordan elimination. It is also compared with other states-of-the-art heuristics for known solutions. Furthermore, its effectiveness is evaluated on few large sizes of random task graphs. Comparative study of the proposed PSO-GA with other heuristics depicts that the PSO–GA performs quite effectively for multiprocessor DAG scheduling problem.     

柔性Flow-Shop调度的遗传算法优化

柔性Flow-shop调度问题（Flexible Flow-shop Scheduling Problem,FFSP）是一般Flow-shop调度问题的推广,由于在某些工序上存在并行机器,所以比一般的Flow-shop调度问题更复杂。为了有效地解决柔性Flow-shop调度问题,用遗传算法求解,给出了一种改进的编码方法,能够保证个体的合法性;并根据编码方法提出了矩阵解码方法。最后以某汽车发动机厂金加工车间的生产调度实例进行仿真,通过比较表明了算法的有效性。     

A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems

This paper presents a new, carefully designed algorithm for five bi-objective permutation flow shop scheduling problems that arise from the pairwise combinations of the objectives (i) makespan, (ii) the sum of the completion times of the jobs, and (iii) both, the weighted and non-weighted total tardiness of all jobs. The proposed algorithm combines two search methods, two-phase local search and Pareto local search, which are representative of two different, but complementary, paradigms for multi-objective optimization in terms of Pareto-optimality. The design of the hybrid algorithm is based on a careful experimental analysis of crucial algorithmic components of these two search methods. We compared our algorithm to the two best algorithms identified, among a set of 23 candidate algorithms, in a recent review of the bi-objective permutation flow-shop scheduling problem. We have reimplemented carefully these two algorithms in order to assess the quality of our algorithm. The experimental comparison in this paper shows that the proposed algorithm obtains results that often dominate the output of the two best algorithms from the literature. Therefore, our analysis shows without ambiguity that the proposed algorithm is a new state-of-the-art algorithm for the bi-objective permutation flow-shop problems studied in this paper.     

基于深度强化学习与迭代贪婪的流水车间调度优化

流水车间调度是应用背景最为广泛的调度问题,其智能算法研究具有重要的学术意义和应用价值.以最小化最大完工时间为目标,提出求解流水车间调度的一种基于深度强化学习与迭代贪婪算法的框架.首先,设计一种新的编码网络对问题进行建模,解决了传统模型受问题规模影响而难以扩展的缺陷,并利用强化学习训练模型以获取优良输出结果;然后,提出一种带反馈机制的迭代贪婪算法,以网络的输出结果为初始解,协同利用多种局部操作提高搜索能力,并根据性能反馈调节各操作的使用,进而获得最终的调度解.仿真结果和统计对比表明,所提出的深度强化学习与迭代贪婪融合的算法能够取得更好的性能.     

差异工件流水车间批调度问题的求解

针对流水车间批调度问题,提出一种基于群智能算法的求解思路。结合问题具体特点,给出工件集合的分批策略,设计了将Palmer和Best Fit（BF）分批规则相结合的分批方法;在批排序阶段,提出了一种改进的微粒群算法;在粒子初始生成阶段,通过引入NEH启发式算法改进了粒子的初始化质量;在全局最佳位置更新前,通过变邻域搜索优化了算法的局部搜索能力,避免了算法陷入局部最优。仿真实验表明,改进后的算法优于传统的微粒群算法和NEH启发式算法。     

直觉模糊集相似度遗传算法求解多目标车间调度问题

为了提高高维多目标置换流水车间调度问题的求解质量,提出基于直觉模糊集相似度的遗传算法(similarity of intuitionistic fuzzy sets GA,SIFS_GA).算法中分别将参考解和Pareto解映射为参考解直觉模糊集和Pareto解直觉模糊集.计算两个集合之间的直觉模糊相似度,用以判断Pareto解的优劣.以直觉模糊集相似度值引导多目标遗传算法进化.对6个CEC标准测试集与10个流水车间调度测试实例进行仿真实验,结果表明SIFS_GA算法性能优于常用的多目标优化算法,且可以有效解决多目标置换流水车间调度问题,尤其在解决规模较大的问题上是一种有效方法.     

求解job shop调度问题的量子粒子群优化算法*

针对粒子群优化算法搜索空间有限、容易出现早熟现象的缺陷,提出将量子粒子群优化算法用于求解作业车间调度问题。求解时,将每个调度按照一定的规则编码为一个矩阵,并以此矩阵作为算法中的粒子;然后根据调度目标确定目标函数,并按照量子粒子群优化算法的进化规则在调度空间内搜索最优解。仿真实例结果证明,该算法具有良好的全局收敛性能和快捷的收敛速度,调度效果优于遗传算法和粒子群优化算法。     

离散微粒群算法求解批量流水线调度问题

提出了解决批量流水线调度问题的离散微粒群优化算法。该算法采用了基于工序的编码方式,设计了新的粒子生成公式,从而使微粒群算法可以直接应用于调度问题。同时,针对微粒群算法容易陷入局部最优的缺陷,将其与模拟退火算法结合,得到了改进的微粒群优化算法。仿真实验表明了上述算法的有效性。     

基于GA-PSO的天基预警系统资源调度方法

为解决天基预警系统中的卫星资源调度问题,从预警任务特点出发,在对预警任务进行分解的基础上,建立了资源调度模型．结合传统遗传算法（GA）和粒子群算法（PSO）的优点,采用一种混合遗传粒子群（GA-PSO）算法来求解资源调度问题．该算法在解决粒子编解码问题的前提下,将遗传算法的遗传算子应用于粒子群算法,改善了粒子群算法的寻优能力．实验结果表明,提出的算法能有效解决多目标探测时天基预警系统的资源调度问题,调度结果优于传统粒子群算法和遗传算法．     

遗传算法求解多目标柔性Job-shop问题

本文描述了基于可变机器约束的多目标柔性Job-shop调度问题模型,并应用一种改进的遗传算法进行求解。我们采用了表示工序先后顺序及机器选择的二维编码方式,以多目标优化函数为度量,通过三种遗传操作扩展后代的多样性和算法的搜索空间。仿真结果验证了该算法能有效解决多目标优化问题。     

带尺寸约束的二机流水车间生产运输协调博弈调度问题

研究二机流水车间生产运输协调调度问题,当工件在第1台机器加工完成后,由1台带有容量限制的运输车分批次运输到第2台机器加工,运输过程考虑工件尺寸约束,目标函数为最小化最大完工时间.考虑到源于不同客户的工件对机器及运输设备的竞争,以工件为博弈方,工件在生产运输过程中等待时间为策略,各工件完工时间为收益,建立非合作博弈模型.通过将问题转化为马尔可夫决策过程,设计线性逼近值函数的Q-learning算法求解纳什均衡调度.实验结果表明Q-learning算法求得的纳什均衡调度具有较好的全局最优性,从而能够在满足客户的利益下,提高企业的生产效率,实现客户与企业的双赢.     

A note on “Two-machine flow-shop scheduling with rejection” and its link with flow-shop scheduling and common due date assignment

In a recent paper by Shabtay and Gasper “Two-machine flow-shop scheduling with rejection, Computers and Operations Research”, forthcoming, doi:10.1016/j.cor.2011.05.023, several complexity and approximation results are proposed for a two-criteria two-machine flow-shop scheduling problem with rejection. The two criteria to be minimized are the makespan the total rejection cost. This note positions the contribution of such results with respect to the contributions of the literature on common due date assignment and flow-shop scheduling not considered in the work of Shabtay and Gasper.     

图形处理中一类 Flow-shop 问题的改进算法

考虑图形处理中的一类两台处理器上的Flow-shop调度问题, 目标是极小化最早完工时间. 每个任务包含两道工序, 第一道工序可以在两台处理器中的任何一台上处理, 而第二道则只能在第二台处理器上处理, 且必须在第一道工序完工之后才能进行. 对该问题, 设计了一个改进的多项式时间近似算法, 在绝对性能方面, 该算法的最坏情况界为3/2; 而从实例计算的平均效果方面, 该算法所得的结果比原有的贪婪算法所得的结果要好20% 左右.     

Neural network and genetic algorithm-based hybrid approach to expanded job-shop scheduling

The expanded job-shop scheduling problem (EJSSP) is a practical production scheduling problem with processing constraints that are more restrictive and a scheduling objective that is more general than those of the standard job-shop scheduling problem (JSSP). A hybrid approach involving neural networks and genetic algorithm (GA) is presented to solve the problem in this paper. The GA is used for optimization of sequence and a neural network (NN) is used for optimization of operation start times with a fixed sequence.

After detailed analysis of an expanded job shop, new types of neurons are defined to construct a constraint neural network (CNN). The neurons can represent processing restrictions and resolve constraint conflicts. CNN with a gradient search algorithm, gradient CNN in short, is applied to the optimization of operation start times with a fixed processing sequence. It is shown that CNN is a general framework representing scheduling problems and gradient CNN can work in parallel for optimization of operation start times of the expanded job shop.

Combining gradient CNN with a GA for sequence optimization, a hybrid approach is put forward. The approach has been tested by a large number of simulation cases and practical applications. It has been shown that the hybrid approach is powerful for complex EJSSP.     

A new genetic algorithm for lot-streaming flow shop scheduling with limited capacity buffers

Lot-streaming is the process of splitting a job (lot) into a number of smaller sublots to allow the overlapping of operations between successive machines in a multi-stage production system. The use of sublots usually results in substantially shorter job completion times for the corresponding schedule. A new genetic algorithm (NGA) is proposed for an n-job, m-machine, lot-streaming flow shop scheduling problem with equal size sublots and limited capacity buffers with blocking in which the objective is to minimize total earliness and tardiness penalties. NGA replaces the selection and mating operators of genetic algorithms (GAs), which often lead to premature convergence, by new operators (marriage and pregnancy operators) and also adopts the idea of inter-chromosomal dominance and individuals’ similarities. Extensive computational experiments have been conducted to compare the performance of NGA with that of GA. The results show that, on the average, NGA outperforms GA by 9.86 % in terms of objective function value for medium to large-scale lot-streaming flow-shop scheduling problems.     

求解混合流水车间调度问题的分布估计算法

针对混合流水车间调度问题(Hybrid flow-shop scheduling problem, HFSP)的特点, 设计了基于排列的编码和解码方法, 建立了描述问题解空间的概率模型, 进而提出了一种有效的分布估计算法(Estimation of distribution algorithm, EDA). 该算法基于概率模型通过采样产生新个体, 并基于优势种群更新概率模型的参数. 同时, 通过实验设计方法对算法参数设置进行了分析并确定了有效的参数组合. 最后, 通过基于实例的数值仿真以及与已有算法的比较验证了所提算法的有效性和鲁棒性.