混合离散差分进化算法在单机批处理调度中的应用

本文研究单机批处理调度问题,批处理机有批次容量限制,批处理时间由每个批次所含作业中的最长作业处理时间决定。每个作业具有不同的大小、处理时间、提前拖期惩罚权重,所有作业具有公共交货期,且交货期无限晚。目标函数为最小化所有作业的加权提前拖期惩罚之和。该问题已被证明为NP难题,本研究找到了其最优解具有的一些性质,在此基础上利用它们提出了一种动态规划(DP)与差分进化(DE)算法相结合的混合离散差分进化(HDDE)算法来求解该问题,通过与传统的遗传算法、模拟退火算法和迭代贪婪算法进行对比,HDDE算法显示了更加强大的全局搜索能力。     

On the optimality of the TLS algorithm for solving the online-list scheduling problem with two job types on a set of multipurpose machines

In this paper we study the optimality of the TLS algorithm for solving the online scheduling problem of minimizing the makespan on a set of m multipurpose machines, where there are two different job types and each job type can only be processed on a unique subset of machines. The literature shows that the TLS algorithm is optimal for the special cases where either m=2 or where all processing times are restricted to unity. We show that the TLS algorithm is optimal also for the special cases where the job processing times are either job type or machine set dependent. For both cases, the optimality of the TLS algorithm is proven by showing that its competitive ratio matches the lower bound for any processing set and processing time parameters.     

Scheduling with machine cost and rejection

In this paper we consider the scheduling problem with machine cost and rejection penalties. For this problem, we are given a sequence of independent jobs, each being characterized by its processing time (size) and its penalty. No machine is initially provided, and when a job is revealed the algorithm has the option to purchase new machines. Right when a new job arrives, we have the following choices: (i) reject it, in which case we pay its penalty; (ii) non-preemptively process it on an existing machine, which contributes to the machine load; (iii) purchase a new machine, and assign it to this machine. The objective is to minimize the sum of the makespan, the cost for purchasing machines, and the total penalty of all rejected jobs. For the small job case, (where all jobs have sizes no greater than the cost for purchasing one machine, and which is the generalization of the Ski-Rental Problem) we present an optimal online algorithm with a competitive ratio of 2.     

基于改进遗传算法的置换装配线调度问题研究

企业的置换装配线调度问题（Permutation Assembly-line Scheduling Problem,PASP）是一类典型的NP-hard型生产调度问题,是现代集成制造系统CIMS极为关心的问题。该问题可以具体描述为n个工件要在m台机器上加工,每个工件需要经过m道工序,每道工序要求不同的机器,这n个工件通过m台机器的顺序相同,它们在每台机器上的加工顺序也相同,问题的主要目标是找到n个工件在每台机器上的最优加工顺序,使得最大完工时间最小。由于PASP问题的NP-hard性质,本文使用遗传算法对其进行求解。尽管遗传算法常用以求解调度问题,但其选择与交叉机制易导致局部最优及收敛慢。因此,本文提出基于区块挖掘与重组的改进遗传算法用于求解置换装配线调度问题。首先通过关联规则挖掘出不同的优秀基因,然后将具有较优结果的基因组合为优势区块,产生具优势的人工解,并引入高收敛性的局部搜索方法,提高搜索到最优解的机会与收敛效率。本文以OR-Library中Taillard标准测试例来验证改进遗传算法的求解质量与效率,结果证明：本文所提算法与其它求解调度问题的现有5种知名算法相比,不仅收敛速度较快,同时求解质量优于它们。     

On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan.Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while inthe non-clairvoyant on-line model, this processing requirement is notknown until the job is processed and completed.In both models, scheduling of a job is irrevocable.We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5/4 (preemptive) and 3/2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3/2 (preemptive and non-preemptive).     

An estimation of distribution algorithm for lot-streaming flow shop problems with setup times

Lot-streaming flow shops have important applications in different industries including textile, plastic, chemical, semiconductor and many others. This paper considers an n-job m-machine lot-streaming flow shop scheduling problem with sequence-dependent setup times under both the idling and no-idling production cases. The objective is to minimize the maximum completion time or makespan. To solve this important practical problem, a novel estimation of distribution algorithm (EDA) is proposed with a job permutation based representation. In the proposed EDA, an efficient initialization scheme based on the NEH heuristic is presented to construct an initial population with a certain level of quality and diversity. An estimation of a probabilistic model is constructed to direct the algorithm search towards good solutions by taking into account both job permutation and similar blocks of jobs. A simple but effective local search is added to enhance the intensification capability. A diversity controlling mechanism is applied to maintain the diversity of the population. In addition, a speed-up method is presented to reduce the computational effort needed for the local search technique and the NEH-based heuristics. A comparative evaluation is carried out with the best performing algorithms from the literature. The results show that the proposed EDA is very effective in comparison after comprehensive computational and statistical analyses.     

Efficient Algorithms for a Scheduling Problem and its Applications to Illicit Drug Market Crackdowns

We give polynomial time algorithms for a job scheduling problem. By duality we transform a special case of the drug market crackdown schedulingproblem to the above job scheduling problem and thus derive polynomial timealgorithms to the second problem. Finally, using the algorithm for the specialcase, we develop a quasipolynomial time approximation algorithm for thegeneral case of the drug market crackdown scheduling problem with monomialcost functions.     

一种差异工件单机批调度问题的蚁群优化算法

由于在利用蚁群算法构建差异工件(即工件有尺寸差异)单机批调度问题的解时,批的加工时间是不确定的.从而不能类似于经典调度问题的蚁群算法把批加工时间的倒数作为蚁群算法中的启发式信息,引入批的利用率和批的负载均衡率作为蚁群算法中的启发式信息,提出了JACO(ant colony optimization based a job sequence)和BACO(ant colony optimization based a batch sequence)两种蚁群优化算法.在算法JACO中,解的编码为工件序列,它对应着用BF(best fit)分批规则生成的调度方案,信息素代表工件间的排列顺序;在算法BACO中,解的编码为批序列,信息素代表工件间的批相关性,由此信息素通过中间信息素量来构造相应的解,并引入特定的局部优化策略,提高了算法的搜索效率.实验表明,与以往文献中的SA(simula-ted annealing)、GA(genetic algorithm)算法以及FFLPT(first-fit longest processing time)、BFLPT (best-fit longest processing time)启发式规则相比,算法JACO和BACO明显优于它们,且BACO算法比JACO算法效果更好.     

Single machine scheduling problems with subcontracting options

In this paper, we study a scheduling model as follows: there are n jobs which can be processed in house on a single machine or subcontracted to a subcontractor. If a job is subcontracted, its processing cost is different from the in-house cost and its delivery lead time is a stepwise function of the total processing time of outsourced jobs. Two objective functions are studied (1) to minimize the weighted sum of the maximal completion time and the total processing cost and (2) to minimize the weighted sum of the number of tardy jobs and the total processing cost. For the first problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm. For the second problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm for a special case.     

MINIMIZING TOTAL WEIGHTED COMPLETION TIME ON A SINGLE BATCH PROCESSING MACHINE

We study the problem of scheduling jobs on a single batch processing machine to minimize the total weighted completion time. A batch processing machine is one that can process a number of jobs simultaneously as a batch. The processing time of a batch is given by the processing time of the longest job in the batch. We present a branch and bound algorithm to obtain optimal solutions and develop lower bounds and dominance conditions. We also develop a number of heuristics and evaluate their performance through extensive computational experiments. Results show that two of the heuristics consistently generate high-quality solutions in modest CPU times.     

Processing in a multi-machine batch manufacturing system with sequence dependent cost

Many workcells in batch manufacturing systems are populated with multiple, nonidentical machines that perform similar tasks. Because of the size of a batch when a job arrives, it may be uneconomical to set up two or more machines to process the same job simultaneously. An economic decision has to be made as regards which machine in the cell to assign the job. Likewise, many multi-operation jobs can be processed using one of several feasible operation sequences that may lead to different total manufacturing costs. The cost differences are the result of several factors, among which are processing time and cost dependencies between operations, fixturing requirements, and material handling requirements. When the workcell machine selection decision is considered along with the operation sequencing decision, determination of the best machine in a cell and the best operation sequence for the batch is a non-trivial task. In this paper, we address the problem of selecting the best machine within a cell and the best operation sequence for a batch when operation cost is machine and sequence dependent. The problem is modeled mathematically and solved using a heuristic algorithm. The performance of the algorithm is compared with that of an exact solution procedure.     

Decomposition algorithms for the integrated process planning and scheduling problem

There are several algorithms to solve the integrated process planning and scheduling (IPPS) problem (i.e., flexible job shop scheduling with process plan flexibility) in the literature. All the existing algorithms for IPPS are heuristic-based search methods and no research has investigated the use of exact solution methods for this problem. We develop several decomposition approaches based on the logic-based Benders decomposition (LBBD) algorithm. Our LBBD algorithm allows us to partition the decision variables in the IPPS problem into two models, master-problem and sub-problem. The master-problem determines process plan and operation-machine assignment, while the sub-problem optimizes sequencing and scheduling decisions. To achieve faster convergence, we develop two relaxations for the optimal makespan objective function and incorporate them into the master-problem. We analyze the performance and further enhance the algorithm with two ideas, a Benders optimality cut based on the critical path and a faster heuristic way to solve the sub-problem. 16 standard benchmark instances available in the literature are solved to evaluate and compare the performances of our algorithms with those of the state-of-the-art methods in the literature. The proposed algorithm either results in the optimal solution or improves the best-known solutions in all the existing instances, demonstrating its superiority to the existing state-of-the-art methods in literature.     

A genetic algorithm for scheduling on a single machine with set-up times and due dates

This paper presents a genetic algorithm for a single machine-scheduling problem with the objective of minimizing total tardiness. Each job has its own due date and the set-up times are sequence dependent. The parameters of the genetic algorithm are determined by a statistical method. For small problems, the solutions given by the proposed method are compared with solutions provided by a commercial package, and for larger problems, with those obtained by a heuristic proposed in the literature.     

Minimizing makespan in an ordered flow shop with?machine-dependent processing times

We consider a generalization of the proportionate flow shop problem with the makespan objective. Each job has a processing requirement and each machine has a characteristic value. In our case, we assume that the time a job occupies a machine is equal to the processing requirement of the job plus a setup time that is equal to the characteristic value of that machine. In this paper, we consider permutation schedules and show that the problem is solvable in polynomial time when the number of machines is fixed.     

Efficient Job Scheduling Algorithms with Multi-Type Contentions

In this paper, we consider an interesting generalization of the classic job scheduling problem in which each job needs to compete not only for machines but also for other types of resources. The contentions among jobs for machines and for resources could interfere with each other, which complicates the problem dramatically. We present a family of approximation algorithms for solving several variants of the problem by using a generic algorithmic framework. Our algorithms achieve a constant approximation ratio (i.e., 3) when there is only one type of resources or certain dependency relation exists among multiple types of resources. When the r resources are unrelated, the approximation ratio of our algorithm becomes k+2, where k≤ r is a constant depending on the problem instance. As an application, we also show that our techniques can be easily applied to optical burst switching (OBS) networks to design more efficient wavelength scheduling algorithms.This research was supported in part by an IBM faculty partnership award, and an IRCAF award from SUNY Buffalo.     

考虑分时电价的多目标批调度问题蚁群算法求解

对同时优化电力成本和制造跨度的多目标批处理机调度问题进行了研究,设计了两种多目标蚁群算法,基于工件序的多目标蚁群算法(J-PACO,Job-based Pareto Ant Colony Optimization)和基于成批的多目标蚁群算法(B-PACO,Batch-based Pareto Ant Colony Optimization)对问题进行求解分析。由于分时电价中电价是时间的函数,因而在传统批调度进行批排序的基础上,需要进一步确定批加工时间点以测定电力成本。提出的两种蚁群算法分别将工件和批与时间线相结合进行调度对此类问题进行求解。通过仿真实验将两种算法对问题的求解进行了比较,仿真实验表明B-PACO算法通过结合FFLPT(First Fit Longest Processing Time)启发式算法先将工件成批再生成最终方案,提高了算法搜索效率,并且在衡量算法搜索非支配解数量的Q指标和衡量非支配集与Pareto边界接近程度的HV指标上,均优于J-PACO算法。     

Batch-Processing Scheduling with Setup Times

The problem is to minimize the total weighted completion time on a single batch-processing machine with setup times. The machine can process a batch of at most B jobs at one time, and the processing time of a batch is given by the longest processing time among the jobs in the batch. The setup time of a batch is given by the largest setup time among the jobs in the batch. This batch-processing problem reduces to the ordinary uni-processor scheduling problem when B = 1. In this paper we focus on the extreme case of B = +, i.e. a batch can contain any number of jobs. We present in this paper a polynomial-time approximation algorithm for the problem with a performance guarantee of 2. We further show that a special case of the problem can be solved in polynomial time.     

面向成套订单问题的工艺规划与排序的集成研究

本文从工艺规划与排序的集成优化角度研究了成套订单问题^[1],克服了单独研究工艺规划和排序局部优化的局限性.文章中考虑了同一工件内部各道工序之间存在的优先加工限制,以及工件在不同机器上加工需要转移时间和工序间接连加工需要机器调整时间的情况,建立了成套订单问题的集成排序模型,并提出了针对求解大规模问题的基于遗传算法的启发式算法,最后通过一个算例对所研究的集成排序问题和所提出的算法进行了说明,计算结果表明了算法的有效性.     

A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling

In the multiprocessor scheduling problem to minimize the total job completion time, an optimal schedule can be obtained by the shortest processing time rule and the completion time of each job in the schedule can be used as a guarantee for scheduling revenue. However, in practice, some jobs will not arrive at the beginning of the schedule but are delayed and their delayed arrival times are given to the decision-maker for possible rescheduling. The decision-maker can choose to reject some jobs in order to minimize the total operational cost that includes three cost components: the total rejection cost of the rejected jobs, the total completion time of the accepted jobs, and the penalty on the maximum tardiness for the accepted jobs, for which their completion times in the planned schedule are their virtual due dates. This novel rescheduling problem generalizes several classic NP-hard scheduling problems. We first design a pseudo-polynomial time dynamic programming exact algorithm and then, when the tardiness can be unbounded, we develop it into a fully polynomial time approximation scheme. The dynamic programming exact algorithm has a space complexity too high for truthful implementation; we propose an alternative to integrate the enumeration and the dynamic programming recurrences, followed by a depth-first-search walk in the reschedule space. We implemented the alternative exact algorithm in C and conducted numerical experiments to demonstrate its promising performance.

     

On single machine scheduling with resource constraint

The single machine scheduling with resource constraint is a nonlinear combinatorial optimization problem in cloud computing applications. Given a set of jobs and certain resource, the problem is to find a permutation of jobs and a distribution of resource to optimize certain objective function. The processing time of each job is a nonlinear function with respect to the resource assigned to it. In this paper, we propose a naive algorithm and study a subproblem in the algorithm that suppose the permutation of jobs is also given, how to find a resource distribution to minimize the total weighted flow time. We found a polynomial-time optimal solution for a special case and an approximation solution in general case.