一种求解无等待流水车间调度优化的启发式算法

提出了一种新的启发式算法,用于求解无等待流水车间调度问题的总流水时间指标。该算法命名为标准差启发,基于著名的NEH启发算法。首先阐述了总流水时间指标;其次描述了标准差启发算法的过程;最后用标准差启发算法求解标准实验案例,通过实验并与其他启发式算法比较,验证了标准差启发算法在求解无等待流水车间调度问题总流水时间指标的有效性。     

可重入混合流水车间调度的拉格朗日松弛算法

为了有效提升多重入车间的生产效率,考虑了实际生产中检查和修复过程对于逐层制造的可重入生产系统的重要性,提出了基于拉格朗日松弛算法的可重入混合流水车间的调度方法.首先进行了问题域的描述,并在此基础上以最小化加权完成时间为调度目标,建立数学规划模型.针对该调度问题提出了基于松弛机器能力约束的拉格朗日松弛算法,使松弛问题分解成工件级子问题,并使用动态规划方法建立递归公式,求解工件级子问题.随后,使用次梯度算法求解拉格朗日对偶问题.最后,对各种不同问题规模进行了仿真实验,结果表明,所提出的调度算法能够在合理的时间内获得满意的近优解.     

极小化时间表长的无等待流水车间调度

针对以时间表长最小为目标函数的无等待流水车间（No-Wait Flow Shop;NWFS）调度问题;提出了一个混合禁忌搜索算法（Hybrid Taboo Search;HTS）;以启发式算法产生的解作为初始解;通过禁忌搜索进一步提高解的质量。大量随机产生实例的实验结果表明:提出的HTS算法在总体性能上优于经典的RAJ、VNS和GASA算法;因此该算法具有可行性和优越性。     

一个求解无等待流水调度问题混合算法

针对以总完工时间最小为目标的无等待流水调度问题提出一个启发式算法和禁忌搜索算法相结合的混合禁忌搜索算法HTS(Hybrid Taboo Search):以启发式算法产生的解作为初始解,通过禁忌搜索提高解的质量.实验结果表明:提出的HTS性能上优于经典的RC1、RC2、PH1(p)和DS算法.     

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。     

基于约束传播的HFS调度研究

将约束传播技术同分枝定界法相结合求解优化目标为最小最大完工时间的混合流水车间调度问题。算法核心是根据资源松弛度确定关键阶段,通过在分枝定界算法中嵌入动态可调的开工时间窗口,用顺序传播、资源传播、上下游工序传播,动态修改每个操作的开工时间窗上下界,并在算法特点基础上给出相应的剪枝下界,以减小搜索空间,提高分枝定界法的优化能力。实验结果证明了算法的有效性。     

有准备时间无等待流水车间调度的搜索算法

利用迭代变化邻域搜索算法(IVNS)求解最小化总完工时间的有准备时间无等待流水车间调度问题. 设计局部搜索算法需要考虑3个关键因素：所用邻域、解评估和局部最优的克服. 因此,定义了3个较大规模邻域以扩大搜索范围. 为加速解评估,利用目标增量来避免重新计算每个解的目标函数值,使相邻解比较只需常量时间,NEH插入算法的时间复杂度降低一阶. IVNS通过切换邻域和扰动重启,来克服局部搜索易于陷入局部最优解的缺点. 通过与求解该问题的当前最好算法在5400个标准算上,以相同CPU时间进行的实算比较,实验结果统计分析验证了IVNS的寻优性能明显优于参照算法.     

基于目标增量的无等待流水调度快速迭代贪婪算法

最小化总完工时间无等待流水调度是典型的NP-完全问题,广泛存在于实际生产系统.改变传统求解调度序列目标函数的模式,提出目标增量法,通过目标函数变化量判断新解的优劣,大大降低算法所需计算时间;通过证明启发式算法基本操作的目标增量性质,设计两种基本目标增量法以快速评估新产生解的质量.提出快速迭代贪婪算法FIG(Fast Iterative Greedy algorithm)求解该问题,构造初始解生成算法,提出分段式重构局部搜索方法和迭代改进全局搜索策略以进一步提高解的质量.基于110个经典Benchmark实例,将提出的FIG算法与目前求解该问题较好的启发式算法PHlp和元启发式算法SRTS、DPSOvnd进行比较,实验结果表明FIG在性能上优于SRTS和PHlp,略逊于DPSOvnd;在效率上优于SRTS和DPSOvnd,略逊于PHlp.     

大规模无等待流水调度问题的邻域迭代搜索算法

在分析大规模无等待流水调度问题特点的基础上,提出了利用相邻工件间完工时间距离求最小化完工时间的方法;通过研究工件插入和工件对的交换对最小化完工时间的影响,提出一种邻域迭代搜索算法,该算法降低了求解完工时间的时间复杂度,大大提高了算法效率;为避免算法在邻域搜索过程中陷入局部最优,将变邻域结构算法的思想应用于其中.仿真结果表明,所提出的算法能高效率解决大规模无等待流水调度问题,所得结果令人满意.     

基于种群迭代贪婪算法无等待流水车间调度

针对无等待流水车间调度问题,提出一种基于种群迭代的改进贪婪算法解决以最小化最大完工时间为目标的此类问题。首先,采用改进NEH(Nawaz–Enscore–Ham)算法提升初始种群的质量,提高种群的多样性,并得出初始解,确定最优个体;其次,采用种群迭代贪婪算法对确定的种群序列进行破坏与重新构建,将新序列插入指定位置,并对获得的候选方案进行本地搜索,获得新的解决方案,同时取代劣势解决方案;最后,通过仿真实例将种群迭代贪婪算法与其他智能优化算法在平均相对偏差率、最佳相对偏差率、算法收敛性上进行对比,结果表明种群迭代贪婪算法求解所提问题的高效性和稳定性。     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.     

具有混合动态约束的生产系统优化调度新算法

研究具有混合动态约束的生产系统优化调度问题.在Lagrange松弛法框架下,求解包含混合动态约束的子问题仍然十分复杂,许多算法只能求得子问题的近似解,降低了Lagrange松弛法的有效性.文中提出了一种新的离散状态定义方法,解除了子问题中离散决策变量与连续决策变量的耦合.在此基础上结合动态规划思想,提出了一种新算法,在保证整体最优性的前提下,可以同时对离散和连续状态分别寻优,对算法复杂性进行了初步分析,新算法效率高且可以得到子问题的精确解.电力系统调度问题的数值算例验证了新算法的有效性.     

Scheduling a hybrid flowshop with batch production at the last stage

In this paper, we address the problem of scheduling n$n$ jobs in an s$s$-stage hybrid flowshop with batch production at the last stage with the objective of minimizing a given criterion with respect to the completion time. The batch production at stage s$s$ is referred to as serial batches by Hopp and Spearman where the processing time of a batch is equal to the sum of the processing times of all jobs included in it. This paper establishes an integer programming model and proposes a batch decoupling based Lagrangian relaxation algorithm for this problem. In this algorithm, after capacity constraints are relaxed by Lagrangian multipliers, the relaxed problem is decomposed based on a batch, unlike the commonly used job decoupling, so that it can be decomposed into batch-level subproblems, each for a specific batch. An improved forward dynamic programming algorithm is then designed for solving these subproblems where all operations within a batch form an in-tree structure and the precedence relations exist not only between the operations of a job but between the jobs in this batch at the last stage. A computational comparison is provided for the developed algorithm and the commonly used Lagrangian relaxation algorithm which, after capacity constraints and precedence relations within a batch are relaxed, decomposes the relaxed problem into job-level subproblems and solves the subproblems by using dynamic programming. Numerical results show that the designed Lagrangian relaxation method provides much better schedules and converges faster for small to medium sized problems, especially for larger sized problems.     

A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is presented in which precedence constraints are relaxed to the objective function by introducing Lagrangian multipliers, unlike the commonly used method of relaxing capacity constraints. In this way the relaxed problem can be decomposed into machine type subproblems, each of which corresponds to a specific stage. A dynamic programming algorithm is designed for solving parallel identical machine subproblems where jobs may have negative weights. The multipliers are then iteratively updated along a subgradient direction. The new algorithm is computationally compared with the commonly used Lagrangian relaxation algorithms which, after capacity constraints are relaxed, decompose the relaxed problem into job level subproblems and solve the subproblems by using the regular and speed-up dynamic programming algorithms, respectively. Numerical results show that the new Lagrangian relaxation method produces better schedules in much shorter computation time, especially for large-scale problems.     

带运输考虑的多阶段动态可重入混合流水车间调度

可重入混合流水车间调度允许一个工件多次进入某些加工阶段,它广泛出现在许多工业制造过程中,如半导体制造、印刷电路板制造等.本文研究了带运输时间的多阶段动态可重入混合流水车间问题,目标是最小化总加权完成时间.针对该问题,建立了整数规划模型,进而基于工件解耦方式提出了两种改进的拉格朗日松弛(LR)算法.在这些算法中,设计了动态规划的改进策略以加速工件级子问题的求解,提出了异步次梯度法以得到有效的乘子更新方向.测试结果说明了所提出的两种改进算法在解的质量和运行时间方面均优于常规LR算法,两种算法都能在可接受的计算时间内得到较好的近优解.     

A faster polynomial algorithm for 2-cyclic robotic scheduling

This paper addresses the 2-cyclic identical part scheduling in a no-wait robotic flowshop where exactly two parts enter and two parts leave the production line during each cycle. This problem was previously proved to be polynomially solvable in O(N⁸log N) time, where N is the number of tanks in the production line. This paper proposes an improved algorithm with reduced complexity O(N⁵log N).     

Automatic structural identification and relaxation for integer programming

This research investigates the automatic identification of typical embedded structures in the Integer Programming (IP) models and automatic transformation of the problem to an adequate Lagrangian problem which can provide tight bounds within the acceptable run time. For this purpose, the structural distinctivenesses of variables, constants, blocks of terms, and constraint chunks are identified to specify the structure of the IP model. To assist the identification of the structural distinctiveness, the representation by the knowledge based IP model formulator, UNIK-IP, is adopted. To reason for the structural identification, the hybrid of bottom-up, top-down, and case-based approaches are proposed. A system UNIK-RELAX is developed to implement the approaches proposed in this research.     

Scheduling of thermal units with a nonlinear load flow network model

We describe a formulation of the thermal unit commitment problem that includes AC network constraints, which allows taking into account VAr production as a criterion for generator commitment for the first time. The formulation makes it possible to use the Lagrangian Relaxation technique as a solution algorithm even though the network constraints are not linear. Although the solution method is computationally intensive, the problem exhibits a separation structure and a price coordination schedule that suggest several ways of improving the performance. Preliminary test results are reported.