Genetic algorithms with path relinking for the minimum tardiness permutation flowshop problem

In this work three genetic algorithms are presented for the permutation flowshop scheduling problem with total tardiness minimisation criterion. The algorithms include advanced techniques like path relinking, local search and a procedure to control the diversity of the population. We also include a speed up procedure in order to reduce the computational effort needed for the local search technique, which results in large CPU time savings. A complete calibration of the different parameters and operators of the proposed algorithms by means of a design of experiments approach is also given. We carry out a comparative evaluation with the best methods that can be found in the literature for the total tardiness objective, and with adaptations of other state-of-the-art methods originally proposed for other objectives, mainly makespan. All the methods have been implemented with and without the speed up procedure in order to test its effect. The results show that the proposed algorithms are very effective, outperforming the remaining methods of the comparison by a considerable margin.     

An ant colony optimization approach for the proportionate multiprocessor open shop

Multiprocessor open shop makes a generalization to classical open shop by allowing parallel machines for the same task. Scheduling of this shop environment to minimize the makespan is a strongly NP-Hard problem. Despite its wide application areas in industry, the research in the field is still limited. In this paper, the proportionate case is considered where a task requires a fixed processing time independent of the job identity. A novel highly efficient solution representation is developed for the problem. An ant colony optimization model based on this representation is proposed with makespan minimization objective. It carries out a random exploration of the solution space and allows to search for good solution characteristics in a less time-consuming way. The algorithm performs full exploitation of search knowledge, and it successfully incorporates problem knowledge. To increase solution quality, a local exploration approach analogous to a local search, is further employed on the solution constructed. The proposed algorithm is tested over 100 benchmark instances from the literature. It outperforms the current state-of-the-art algorithm both in terms of solution quality and computational time.

     

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。     

A heuristic to minimize total flow time in permutation flow shop

In this paper, we address an n-job, m-machine permutation flow shop scheduling problem for the objective of minimizing the total flow time. We propose a modification of the best-known method of Framinan and Leisten [An efficient constructive heuristic for flowtime minimization in permutation flow shops. Omega 2003;31:311–7] for this problem. We show, through computational experimentation, that this modification significantly improves its performance while not affecting its time-complexity.     

安装时间与次序相关的生产调度干扰管理研究

在安装时间和次序相关的单机调度问题中,为应对突发性的工件优先级变动造成的影响,构建了双目标重调度模型。原目标为生产的流程时间,扰动目标为工件的加工次序扰动。针对模型中的双目标,设计了基于有效解的两阶段混合启发式算法进行求解,在原目标和扰动目标之间进行权衡。混合算法第一阶段里,基于任意单个工件次序变化将双目标问题转化成单目标TSP问题,利用最近邻域和插入混合求得单目标问题的若干解,构成初始种群。第二阶段中基于非支配排序遗传算法在处理多目标问题上的优势,对初始种群进行扩展搜索,最后输出问题的有效前沿。通过数值试验运算比较分析若干针对有效解集的指标,验证了混合算法求得的解集在多样性和临近性上要优于单纯的非支配排序遗传算法。该混合算法可以有效地解决具有安装时间的加工次序扰动问题。     

An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem

In the no-idle flowshop, machines cannot be idle after finishing one job and before starting the next one. Therefore, start times of jobs must be delayed to guarantee this constraint. In practice machines show this behavior as it might be technically unfeasible or uneconomical to stop a machine in between jobs. This has important ramifications in the modern industry including fiber glass processing, foundries, production of integrated circuits and the steel making industry, among others. However, to assume that all machines in the shop have this no-idle constraint is not realistic. To the best of our knowledge, this is the first paper to study the mixed no-idle extension where only some machines have the no-idle constraint. We present a mixed integer programming model for this new problem and the equations to calculate the makespan. We also propose a set of formulas to accelerate the calculation of insertions that is used both in heuristics as well as in the local search procedures. An effective iterated greedy (IG) algorithm is proposed. We use an NEH-based heuristic to construct a high quality initial solution. A local search using the proposed accelerations is employed to emphasize intensification and exploration in the IG. A new destruction and construction procedure is also shown. To evaluate the proposed algorithm, we present several adaptations of other well-known and recent metaheuristics for the problem and conduct a comprehensive set of computational and statistical experiments with a total of 1750 instances. The results show that the proposed IG algorithm outperforms existing methods in the no-idle and in the mixed no-idle scenarios by a significant margin.     

A multi-objective particle swarm for a flow shop scheduling problem

Flow shop problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider a bi-criteria permutation flow shop scheduling problem, where weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in strong sense, an effective multi-objective particle swarm (MOPS), exploiting a new concept of the Ideal Point and a new approach to specify the superior particle's position vector in the swarm, is designed and used for finding locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm, i.e. SPEA-II. The computational results show that the proposed MOPS performs better than the genetic algorithm, especially for the large-sized problems.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

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.     

A novel discrete artificial bee colony algorithm for the hybrid flowshop scheduling problem with makespan minimisation

The hybrid flowshop scheduling (HFS) problem with the objective of minimising the makespan has important applications in a variety of industrial systems. This paper presents an effective discrete artificial bee colony (DABC) algorithm that has a hybrid representation and a combination of forward decoding and backward decoding methods for solving the problem. Based on the dispatching rules, the well-known NEH heuristic, and the two decoding methods, we first provide a total of 24 heuristics. Next, an initial population is generated with a high level of quality and diversity based on the presented heuristics. A new control parameter is introduced to conduct the search of employed bees and onlooker bees with the intention of balancing the global exploration and local exploitation, and an enhanced strategy is proposed for the scout bee phase to prevent the algorithm from searching in poor regions of the solution space. A problem-specific local refinement procedure is developed to search for solution space that is unexplored by the honey bees. Afterward, the parameters and operators of the proposed DABC are calibrated by means of a design of experiments approach. Finally, a comparative evaluation is conducted, with the best performing algorithms presented for the HFS problem under consideration, and with adaptations of some state-of-the-art metaheuristics that were originally designed for other HFS problems. The results show that the proposed DABC performs much better than the other algorithms in solving the HFS problem with the makespan criterion.     

An iterated local search with multiple perturbation operators and time varying perturbation strength for the aircraft landing problem

Landing aircraft safely is an important operation that air traffic controllers have to deal with on a daily basis. For each arriving aircraft a runway and a landing time must be allocated. If these allocations can be done in an efficient way, it could give the airport a competitive advantage. The Aircraft Landing Problem (ALP) aims to minimize the deviation from a preferred target time of each aircraft. It is an NP-hard problem, meaning that we may have to resort to heuristic methods as exact methods may not be suitable, especially as the problem size increases. This paper proposes an iterated local search (ILS) algorithm for the ALP. ILS is a single solution based search methodology that successively invokes a local search procedure to find a local optimum solution. A perturbation operator is used to modify the current solution in order to escape from the local optimum and to provide a new solution for the local search procedure. As different problems and/or instances have different characteristics, the success of the ILS is highly dependent on the local search, the perturbation operator(s) and the perturbation strength. To address these issues, we utilize four perturbation operators and a time varying perturbation strength which changes as the algorithm progresses. A variable neighborhood descent algorithm is used as our local search. The proposed ILS generates high quality solutions for the ALP benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both solution quality and computational time. Moreover, the proposed ILS produces new best results for some instances.     

用混合遗传算法求解物流配送路径优化问题的研究

论文建立了物流配送路径优化问题的数学模型,并针对遗传算法在局部搜索能力方面的不足,提出将爬山算法与遗传算法相结合,从而构造了求解物流配送路径优化问题的混合遗传算法,并进行了实验计算。计算结果表明,用混合遗传算法求解物流配送路径优化问题,可以在一定程度上克服遗传算法在局部搜索能力方面的不足和爬山算法在全局搜索能力方面的不足,从而得到质量较高的解。     

Two new robust genetic algorithms for the flowshop scheduling problem

The flowshop scheduling problem (FSP) has been widely studied in the literature and many techniques for its solution have been proposed. Some authors have concluded that genetic algorithms are not suitable for this hard, combinatorial problem unless hybridization is used. This work proposes new genetic algorithms for solving the permutation FSP that prove to be competitive when compared to many other well known algorithms. The optimization criterion considered is the minimization of the total completion time or makespan (_Cmax$C_{\max }$). We show a robust genetic algorithm and a fast hybrid implementation. These algorithms use new genetic operators, advanced techniques like hybridization with local search and an efficient population initialization as well as a new generational scheme. A complete evaluation of the different parameters and operators of the algorithms by means of a Design of Experiments approach is also given. The algorithm's effectiveness is compared against 11 other methods, including genetic algorithms, tabu search, simulated annealing and other advanced and recent techniques. For the evaluations we use Taillard's well known standard benchmark. The results show that the proposed algorithms are very effective and at the same time are easy to implement.     

Estimation of distribution algorithms using Gaussian Bayesian networks to solve industrial optimization problems constrained by environment variables

Many real-world optimization problems involve two different subsets of variables: decision variables, and those variables which are not present in the cost function but constrain the solutions, and thus, must be considered during optimization. Thus, dependencies between and within both subsets of variables must be considered. In this paper, an estimation of distribution algorithm (EDA) is implemented to solve this type of complex optimization problems. A Gaussian Bayesian network is used to build an abstraction model of the search space in each iteration to identify patterns among the variables. As the algorithm is initialized from data, we introduce a new hyper-parameter to control the influence of the initial data in the decisions made during the EDA execution. The results show that our algorithm improves the cost function more than the expert knowledge does.

     

Effective heuristics for the blocking flowshop scheduling problem with makespan minimization

The blocking flowshop scheduling problem with makespan criterion has important applications in a variety of industrial systems. Heuristics that explore specific characteristics of the problem are essential for many practical systems to find good solutions with limited computational effort. This paper first presents two simple constructive heuristics, namely weighted profile fitting (wPF) and PW, based on the profile fitting (PF) approach of McCormick et al. [Sequencing in an assembly line with blocking to minimize cycle time. Operations Research 1989;37:925-36] and the characteristics of the problem. Then, three improved constructive heuristics, called PF-NEH, wPF-NEH, and PW-NEH, are proposed by combining the PF, wPF, and PW with the enumeration procedure of the Nawaz-Enscore-Ham (NEH) heuristic [A heuristic algorithm for the m-machine, n-job flow shop sequencing problem. OMEGA-International Journal of Management Science 1983;11:91-5] in an effective way. Thirdly, three composite heuristics i.e., PF-NEH_LS, wPF-NEH_LS, and PW-NEH_LS, are developed by using the insertion-based local search method to improve the solutions generated by the constructive heuristics. Computational simulations and comparisons are carried out based on the well-known flowshop benchmarks of Taillard [Benchmarks for basic scheduling problems. European Journal of Operation Research 1993;64:278-85] that are considered as blocking flowshop instances. The results show that the presented constructive heuristics perform significantly better than the existing ones, and the proposed composite heuristics further improve the presented constructive heuristics by a considerable margin. In addition, 17 new best-known solutions for Taillard benchmarks with large scale are found by the presented heuristics.     

A heuristic algorithm for minimizing maintenance workforce level

We develop a heuristic algorithm for minimizing the workforce level required to accommodate all the maintenance jobs requested within a specific time interval. Each maintenance job has its own release and due dates as well as the required man-days, and must be scheduled in a noninterrupted time interval, i.e. without preemption. However, the duration of each job is not fixed, but to be determined within a specific range. We show that this problem can be seen as a variant of the two-dimensional bin-packing problem with some additional constraints. We develop a non-linear mixed integer programming model for the proposed problem, and employ some well-known bin-packing algorithms to develop an efficient heuristic algorithm. In order to evaluate the performance of the proposed heuristic, we present a computationally efficient scheme for getting a good lower bound for the actual minimum. The computational experiment shows that the proposed heuristic algorithm performs quite satisfactorily in practice.     

The flexible blocking job shop with transfer and set-up times

The Flexible Blocking Job Shop (FBJS) considered here is a job shop scheduling problem characterized by the availability of alternative machines for each operation and the absence of buffers. The latter implies that a job, after completing an operation, has to remain on the machine until its next operation starts. Additional features are sequence-dependent transfer and set-up times, the first for passing a job from a machine to the next, the second for change-over on a machine from an operation to the next. The objective is to assign machines and schedule the operations in order to minimize the makespan. We give a problem formulation in a disjunctive graph and develop a heuristic local search approach. A feasible neighborhood is constructed, where typically a critical operation is moved (keeping or changing its machine) together with some other operations whose moves are “implied”. For this purpose, we develop the theoretical framework of job insertion with local flexibility, based on earlier work of Gröflin and Klinkert on insertion. A tabu search that consistently generates feasible neighbor solutions is then proposed and tested on a larger test set. Numerical results support the validity of our approach and establish first benchmarks for the FBJS.     

The no-wait job shop with regular objective: a method based on optimal job insertion

The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.     

The permutation flow shop problem with blocking. A tabu search approach

This paper develops a fast tabu search algorithm to minimize makespan in a flow shop problem with blocking. Some properties of the problem associated with the blocks of jobs have been presented and discussed. These properties allow us to propose a specific neighbourhood of algorithms. Also, the multimoves are used that consist in performing several moves simultaneously in a single iteration and guide the search process to more promising areas of the solutions space, where good solutions can be found. It allow us to accelerate the convergence of the algorithm. Besides, a dynamic tabu list is proposed that assists additionally to avoid being trapped at a local optimum. The proposed algorithms are empirically evaluated and found to be relatively more effective in finding better solutions than attained by the leading approaches in a much shorter time. The presented ideas can be applied in many local search procedures.     

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.