混合并行机调度问题的多目标优化模型及算法

针对生产工序的合并造成一种串并联共存的生产布局,研究了一种特殊的混合并行机调度问题,并考虑以最小化总流水时间和最小化总延迟工件数量为目标的多目标调度问题,建立了混合整数规划模型.针对模型特点,设计了一种改进的非支配排序遗传算法进行求解,采用基于启发式方法的初始种群生成方式以提高种群的质量和多样性,并引入一种局域搜索策略以改善求解算法所获得的非支配解的质量及分布性.通过对大量数值算例进行仿真实验,并与典型的多目标优化算法进行比较,结果表明所提出的模型和算法在收敛性、分布性及极端点质量方面均具有优势,能够较好的解决多目标混合并行机调度问题.     

A note on “Beam search heuristics for the single machine early/tardy scheduling problem with no machine idle time”

In a recent paper by Valente “Beam search heuristics for the single machine early/tardy scheduling problem with no machine idle time”’, Computers & Industrial Engineering, 55, 663–675, 2008, several beam search approaches are compared on a large set of instances of the total weighted earliness-tardiness problem on single machine with jobs independent weights and no machine idle time. That problem is denoted 1|nmit|_∑jhEj+_∑jwTj$1|\mathit{nmit}|{\sum }_j{\mathit{hE}}_j+{\sum }_j{\mathit{wT}}_j$. This note points out that the standard iterated dynasearch procedure applied to that problem outperforms all the literature heuristics. Based on these results and others obtained on similar problems, we conclude that dynasearch for its efficiency and simplicity, should be used as a benchmark for future heuristics on those types of single machine no idle time problems.     

改进蚁群算法求解同型机任务调度问题

针对并行与分布式系统中的同型机调度问题,提出了一种改进蚁群算法。结合问题具体特点,给出了蚂蚁分配方案的生成策略,设计了一种新颖的基于任务适合度的信息素表示方法,以实现信息素的有效累积;改进了状态转移规则,通过对阈值的自适应调整使算法能根据搜索进度确定查找区域;在对信息素全局更新前,对每轮迭代获得的最好解进行变邻域搜索,避免算法陷入局部最优,提高收敛速度。仿真结果表明,改进算法有较强的寻优能力和稳定的求解质量。     

Flexible job-shop scheduling with parallel variable neighborhood search algorithm

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. FJSP is NP-hard and mainly presents two difficulties. The first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on the machines. This paper proposes a parallel variable neighborhood search (PVNS) algorithm that solves the FJSP to minimize makespan time. Parallelization in this algorithm is based on the application of multiple independent searches increasing the exploration in the search space. The proposed PVNS uses various neighborhood structures which carry the responsibility of making changes in assignment and sequencing of operations for generating neighboring solutions. The results obtained from the computational study have shown that the proposed algorithm is a viable and effective approach for the FJSP.     

带释放时间的并行机调度问题的ILS & SS算法

研究工件带释放时间的两类并行机最小化总完成时间的调度问题.针对问题提出了一种新的基于变深度环交换邻域结构的Iterated local search(ILS)算法.1)提出了变深度环交换邻域结构.2)基于变深度环交换和传统Swap的混合邻域,提出了带有两种kick策略的ILS算法.3)为了加强ILS逃出局部最优的能力,将Scatter search (SS)搜索方法引入了ILS算法中;算法将当前最好解和次好解进行分散处理,再从处理后的解开始继续迭代.为了验证算法的有效性,对两类并行机问题分别随机产生100组数据进行试验.实验结果表明:对于同构并行机问题,引入SS的ILS算法的计算结果与下界的平均偏差为0.99%,而没有引入SS的ILS算法的为1.06%;对于无关并行机问题,引入SS搜索方法后,ILS算法的计算结果 改进了6.06%,并明显优于多点下降算法.     

并行机成组调度问题的启发式算法

研究了优化目标为总拖后/提前时间最小化的并行机成组调度问题,提出了一种三阶段启发式近似求解算法。首先把并行机问题看成单机问题,以最小化总拖后时间为优化目标排列工件的加工次序;然后将工件按第一阶段所求得的次序指派到最先空闲的并行的机器上;最后采用改进的GTW算法对各机器上的工件调度插入适当的空闲时间。计算表明该算法能够在很短的时间内给出大规模调度问题的近似最优解。     

A nature inspired intelligent water drops evolutionary algorithm for parallel processor scheduling with rejection

Scheduling has become a popular area for artificial intelligence and expert system researchers during last decade. In this paper, a new metaheuristic algorithm entitled intelligent water drops (IWD) is adapted for solving a generalized kind of order scheduling problem where rejection of received orders is allowed with a penalty cost. At the beginning of production period, a set of orders are received by manufacturer. Due to capacity limit, the manufacturer can only process a subset of orders and has to decide to reject some of undesirable orders. The accepted orders are proceed to be scheduled by a set of identical parallel processors in shop floor. The objective is to select the best set of orders with high contribution in manufacturer's benefit and then find the appropriate schedule of accepted orders minimizing the number of tardy orders. To effectively solve the suggested problem, the Lexicographic utility function is customized to address different objectives and then an IWD algorithm, which is based on the process of the natural rivers and the interactions among water drops in a river, is devised. To further enhance the performance of basic IWD, an Iterated Local Search (ILS) heuristic is also incorporated into the main algorithm. To demonstrate the applicability of suggested problem and also show the effectiveness of enhanced IWD with ILS, a real-world application in commercial printing industry is presented and the performance of algorithm is compared with traditional algorithms like GA, DE and ACO.     

A two-stage stochastic programming model for the parallel machine scheduling problem with machine capacity

This paper proposes a two-stage stochastic programming model for the parallel machine scheduling problem where the objective is to determine the machines' capacities that maximize the expected net profit of on-time jobs when the due dates are uncertain. The stochastic model decomposes the problem into two stages: The first (FS) determines the optimal capacities of the machines whereas the second (SS) computes an estimate of the expected profit of the on-time jobs for given machines' capacities. For a given sample of due dates, SS reduces to the deterministic parallel weighted number of on-time jobs problem which can be solved using the efficient branch and bound of M’Hallah and Bulfin [16]. FS is tackled using a sample average approximation (SAA) sampling approach which iteratively solves the problem for a number of random samples of due dates. SAA converges to the optimum in the expected sense as the sample size increases. In this implementation, SAA applies a ranking and selection procedure to obtain a good estimate of the expected profit with a reduced number of random samples. Extensive computational experiments show the efficacy of the stochastic model.     

Ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times

This paper considers ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times. Two objects of minimizing the latest job completion time and minimizing the latest machine completion time are studied. For the first objective, we present the optimal algorithms for m = 2, 3, 4 machine cases. For m ≥ 5, we propose an algorithm with competitive ratio 2 - 1/(m - 1) while the lower bound is 5/3. For the second objective, the optimal algorithm is also given. Furthermore, for a special case, an algorithm with significantly improved competitive ratio is given.     

Parallel machine scheduling with splitting jobs by a hybrid differential evolution algorithm

The problem of parallel machine scheduling for minimizing the makespan is an open scheduling problem with extensive practical relevance. It has been proved to be non-deterministic polynomial hard. Considering a job’s batch size greater than one in the real manufacturing environment, this paper investigates into the parallel machine scheduling with splitting jobs. Differential evolution is employed as a solution approach due to its distinctive feature, and a new crossover method and a new mutation method are brought forward in the global search procedure, according to the job splitting constraint. A specific local search method is further designed to gain a better performance, based on the analytical result from the single product problem. Numerical experiments on the performance of the proposed hybrid DE on parallel machine scheduling problems with splitting jobs covering identical and unrelated machine kinds and a realistic problem are performed, and the results indicate that the algorithm is feasible and efficient.     

Search tree based approaches for parallel machine scheduling

This article compares two branching schemes for the parallel machine scheduling problem with release dates and tails. Both branching schemes can be used for either complete or incomplete search tree based algorithms. In particular, our study aims to prove the robustness of each of them for several search methods. We experimentally compare the efficiency of the two branching schemes when they are used in a branch-and-bound (BnB) method, in a limited discrepancy search, in a branch-and-greed (BnG) method or in a beam search (BS).     

A better online algorithm for the parallel machine scheduling to minimize the total weighted completion time

The identical parallel machine scheduling problem with the objective of minimizing total weighted completion time is considered in the online setting where jobs arrive over time. An online algorithm is proposed and is proven to be (2.5–1/2m)-competitive based on the idea of instances reduction. Further computational experiments show the superiority over other algorithms in the average performance.     

Parallel machine scheduling problems using memetic algorithms

In this paper, we investigate how to apply the hybrid genetic algorithms (the memetic algorithms) to solve the parallel machine scheduling problem. There are two essential issues to be dealt with for all kinds of parallel machine scheduling problems: job partition among machines and job sequence within each machine. The basic idea of the proposed method is that (a) use the genetic algorithms to evolve the job partition and then (b) apply a local optimizer to adjust the job permutation to push each chromosome climb to his local optima. Preliminary computational experiments demonstrate that the hybrid genetic algorithm outperforms the genetic algorithms and the conventional heuristics.     

求解并行机拖期与能耗成本优化调度的混合教一学算法

针对加工时间可控的并行机调度,提出了一类考虑拖期与能耗成本优化的调度问题。首先对调度问题进行了问题描述,并建立了整数线性规划模型以便于CPLEX求解。为了快速获得问题的满意解,提出了一种混合教-学算法。结合问题的性质,设计了编码与解码方法以克服标准教-学算法无法直接适用于离散问题的缺点。同时,构建了基于变邻域搜索的局部搜索算子以强化混合算法的搜索性能。最后,对加工时间可控的并行机调度问题进行了仿真实验,测试结果验证了本文构建的整数线性规划模型和混合算法的可行性和有效性。     

Unrelated parallel machine scheduling with setup times using simulated annealing

This paper presents a scheduling problem for unrelated parallel machines with sequence-dependent setup times, using simulated annealing (SA). The problem accounts for allotting work parts of L jobs into M parallel unrelated machines, where a job refers to a lot composed of N items. Some jobs may have different items while every item within each job has an identical processing time with a common due date. Each machine has its own processing times according to the characteristics of the machine as well as job types. Setup times are machine independent but job sequence dependent. SA, a meta-heuristic, is employed in this study to determine a scheduling policy so as to minimize total tardiness. The suggested SA method utilizes six job or item rearranging techniques to generate neighborhood solutions. The experimental analysis shows that the proposed SA method significantly outperforms a neighborhood search method in terms of total tardiness.     

Selection of cutting conditions for power constrained parallel machine scheduling

Most previous studies on machining optimization focused on aspects related to machining efficiency and economics, without accounting for environmental considerations. Higher cutting speed is usually desirable to maximize machining productivity, but this requires a high power load peak. In Taiwan, electricity prices rise sharply if instantaneous power demand exceeds contract capacity. Many studies over the previous decades have examined production scheduling problems. However, most such studies focused on well-defined jobs with known processing times. In addition, traditional sequencing and scheduling models focus primarily on economic objectives and largely disregard environmental issues raised by production scheduling problems. This study investigates a parallel machine scheduling problem for a manufacturing system with a bounded power demand peak. The challenge is to simultaneously determine proper cutting conditions for various jobs and assign them to machines for processing under the condition that power consumption never exceed the electricity load limit. A two-stage heuristic approach is proposed to solve the parallel machine scheduling problem with the goal of minimizing makespan. The heuristic performance is tested by distributing 20 jobs over 3 machines with four possible cutting parameter settings.     

单机调度问题对偶集结迭代算法

具有到达时间约束、目标为最小化加权完工时间之和的单机调度问题是一个典型的NP-hard问题,采用时间下标建模的线性规划松弛方法可提供一个很强的下界,但优化求解存在维数困难.为此,本文提出了一种对偶集结优化策略,通过选择一个衰减集结矩阵集结对偶乘子变量,利用对偶理论获得模型的约束集结,从而降低计算复杂度.同时分析了集结模型的结构特性,并提出一种迭代算法来改善下界.仿真结果表明对偶集结迭代算法能够减少计算时间,同时改善下界性能,适用于大规模调度问题.     

Search heuristics for a parallel machine scheduling problem with ready times and due dates

We consider a problem of scheduling orders on identical parallel machines. An order can be released after a given ready time and must be completed before its due date. An order is split into multiple jobs (batches) and a job is processed on one of the parallel machines. The objective of the scheduling problem is to minimize the holding costs of orders including work-in-process as well as finished job inventories. We suggest two local search heuristics, simulated annealing and taboo search algorithms, for the problem. Performance of the suggested algorithms is tested through computational experiments on randomly generated test problems.     

求解异构并行机调度问题的混合多目标教-学优化算法

以异构并行机调度问题为研究对象,考虑了一类以优化总加权完工时间和加权延误总和的调度问题。首先,基于问题描述构建了该问题的混合整数规划模型。其次,提出了混合多目标教-学优化算法。在算法设计中,结合问题的特点设计序列编码方法,并采用分解技术来实现多目标调度问题的求解。此外,该算法通过融合多种交叉算子来定义个体进化过程,并通过与变邻域搜索算法的混合来提升其优化效果。最后,给出了仿真实验与分析,测试结果验证了多目标教-学优化算法求解该调度问题的优越性。     

Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems

This research compares the performance of various heuristics and one metaheuristic for unrelated parallel machine scheduling problems. The objective functions to be minimized are makespan, total weighted completion time, and total weighted tardiness. We use the least significant difference (LSD) test to identify robust heuristics that perform significantly better than others for a variety of parallel machine environments with these three performance measures. Computational results show that the proposed metaheuristic outperforms other existing heuristics for each of the three objectives when run with a parameter setting appropriate for the objective.