A genetic algorithmic approach to multi-objective scheduling in a Kanban-controlled flowshop with intermediate buffer and transport constraints

In this paper, we consider the problem of extended permutation flowshop scheduling with the intermediate buffers. The Kanban flowshop problem considered involves dual-blocking by both part type and queue size acting on machines, as well as on material handling. The objectives considered in this study include the minimization of mean completion time of containers, mean completion time of part types, and the standard deviation of mean completion time of part types. An attempt is made to solve the multi-objective problem by using a proposed genetic algorithm, called the “non-dominated and normalized distance-ranked sorting multi-objective genetic algorithm” (NDSMGA). In order to evaluate the NDSMGA, we have made use of randomly generated flowshop scheduling problems with input and output buffer constraints in the flowshop. The non-dominated solutions for these problems are obtained from each of the existing methods, namely multi-objective genetic local search (MOGLS), elitist non-dominated sorting genetic algorithm (ENGA), gradual priority weighting genetic algorithm (GPWGA), modified MOGLS, and the NDSMGA. These non-dominated solutions are combined to obtain a net non-dominated solution set for a given problem. Contribution in terms of number of solutions to the net non-dominated solution set from each of these algorithms is tabulated, and the results reveal that a substantial number of non-dominated solutions are contributed by the NDSMGA.     

A genetic algorithmic approach to multi-objective scheduling in a kanban-controlled flowshop with intermediate buffer and transport constraints

In this paper, we consider the problem of extended permutation flowshop scheduling with the intermediate buffers. The Kanban flowshop problem considered involves dual-blocking by both part type and queue size acting on machines, as well as on material handling. The objectives considered in this study include the minimization of mean completion time of containers, mean completion time of part types, and the standard deviation of mean completion time of part types. An attempt is made to solve the multi-objective problem by using a proposed genetic algorithm, called the “non-dominated and normalized distanceranked sorting multi-objective genetic algorithm” (NDSMGA). In order to evaluate the NDSMGA, we have made use of randomly generated flowshop scheduling problems with input and output buffer constraints in the flowshop. The non-dominated solutions for these problems are obtained from each of the existing methods, namely multi-objective genetic local search (MOGLS), elitist non-dominated sorting genetic algorithm (ENGA), gradual priority weighting genetic algorithm (GPWGA), modified MOGLS, and the NDSMGA. These non-dominated solutions are combined to obtain a net non-dominated solution set for a given problem. Contribution in terms of number of solutions to the net non-dominated solution set from each of these algorithms is tabulated, and the results reveal that a substantial number of non-dominated solutions are contributed by the NDSMGA.     

A novel hybrid multi-objective shuffled frog-leaping algorithm for a bi-criteria permutation flow shop scheduling problem

This paper investigates a novel multi-objective model for a permutation flow shop scheduling problem that minimizes both the weighted mean earliness and the weighted mean tardiness. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, a new hybrid multi-objective algorithm based on shuffled frog-leaping algorithm (SFLA) and variable neighborhood search (VNS) is devised to find Pareto optimal solutions for the given problem. To validate the performance of the proposed hybrid multi-objective shuffled frog-leaping algorithm (HMOSFLA) in terms of solution quality and diversity level, various test problems are examined. Further, the efficiency of the proposed algorithm, based on various salient metrics, is compared against two well-known multi-objective genetic algorithms: NSGA-II and SPEA-II. Our computational results suggest that the proposed HMOSFLA outperforms the two foregoing algorithms, especially for large-sized problems.     

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.     

Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based discrete artificial bee colony algorithm for solving the multi-objective flexible job shop scheduling problem. In the hybrid algorithm, each solution corresponds to a food source, which composes of two components, i.e., the routing component and the scheduling component. Each component is filled with discrete values. A crossover operator is developed for the employed bees to learn valuable information from each other. An external Pareto archive set is designed to record the non-dominated solutions found so far. A fast Pareto set update function is introduced in the algorithm. Several local search approaches are designed to balance the exploration and exploitation capability of the algorithm. Experimental results on the well-known benchmark instances and comparisons with other recently published algorithms show the efficiency and effectiveness of the proposed algorithm.     

A class of hypothesis-test-based genetic algorithms for flow shop scheduling with stochastic processing time

As an important optimisation problem with a strong engineering background, stochastic flow shop scheduling with uncertain processing time is difficult because of inaccurate objective estimation, huge search space, and multiple local minima, especially NP-hardness. As an effective meta-heuristic, genetic algorithms (GAs) have been widely studied and applied in scheduling fields, but so far seldom for stochastic cases. In this paper, a hypothesis-test method, an effective methodology in statistics, is employed and incorporated into a GA to solve the stochastic flow shop scheduling problem and to avoid premature convergence of the GA. The proposed approach is based on statistical performance and a hypothesis test. It not only preserves the global search ability of a GA, but it can also reduce repeated searches for those solutions with similar performance in a statistical sense so as to enhance population diversity and achieve better results. Simulation results based on some benchmarks demonstrate the feasibility and effectiveness of the proposed method by comparison with traditional GAs. The effects of some parameters on the performance of the proposed algorithms are also discussed .     

Developing two multi-objective evolutionary algorithms for the multi-objective flexible job shop scheduling problem

The aim of this paper is to study multi-objective flexible job shop scheduling problem (MOFJSP). Flexible job shop scheduling problem is a modified version of job shop scheduling problem (JSP) in which an operation is allowed to be processed by any machine from a given set of capable machines. The objectives that are considered in this study are makespan, critical machine work load, and total work load of machines. In the literature of the MOFJSP, since this problem is known as an NP-hard problem, most of the studies have developed metaheuristic algorithms to solve it. Most of them have integrated their objective functions and used an integrated single-objective metaheuristic algorithm though. In this study, two new version of multi-objective evolutionary algorithms including non-dominated sorting genetic algorithm and non-dominated ranking genetic algorithm are adapted for MOFJSP. These algorithms use new multi-objective Pareto-based modules instead of multi-criteria concepts to guide their process. Another contribution of this paper is introducing of famous metrics of the multi-objective evaluation to literature of the MOFJSP. A new measure is also proposed. Finally, through using numerous test problems, calculating a number of measures, performing different statistical tests, and plotting different types of figures, it is shown that proposed algorithms are at least as good as literature’s algorithm.     

Solving a multi-objective job shop scheduling problem with sequence-dependent setup times by a Pareto archive PSO combined with genetic operators and VNS

In this paper, we present a combination of particle swarm optimization (PSO) and genetic operators for a multi-objective job shop scheduling problem that minimizes the mean weighted completion time and the sum of the weighted tardiness/earliness costs, simultaneously. At first, we propose a new integer linear programming for the given problem. Then, we redefine and modify PSO by introducing genetic operators, such as crossover and mutation operators, to update particles and improve particles by variable neighborhood search. Furthermore, we consider sequence-dependent setup times. We then design a Pareto archive PSO, where the global best position selection is combined with the crowding measure-based archive updating method. To prove the efficiency of our proposed PSO, a number of test problems are solved. Its reliability based on some comparison metrics is compared with a prominent multi-objective genetic algorithm (MOGA), namely non-dominated sorting genetic algorithm II (NSGA-II). The computational results show that the proposed PSO outperforms the above MOGA, especially for large-sized problems.     

A GRASP heuristic for the multi-objective permutation flowshop scheduling problem

This paper presents a multi-objective greedy randomized adaptive search procedure (GRASP)-based heuristic for solving the permutation flowshop scheduling problem in order to minimize two and three objectives simultaneously: (1) makespan and maximum tardiness; (2) makespan, maximum tardiness, and total flowtime. GRASP is a competitive metaheuristic for solving combinatorial optimization problems. We have customized the basic concepts of GRASP algorithm to solve a multi-objective problem and a new algorithm named multi-objective GRASP algorithm is proposed. In order to find a variety of non-dominated solutions, the heuristic blends two typical approaches used in multi-objective optimization: scalarizing functions and Pareto dominance. For instances involving two machines, the heuristic is compared with a bi-objective branch-and-bound algorithm proposed in the literature. For instances involving up to 80 jobs and 20 machines, the non-dominated solutions obtained by the heuristic are compared with solutions obtained by multi-objective genetic algorithms from the literature. Computational results indicate that GRASP is a promising approach for multi-objective optimization.     

Hybrid discrete particle swarm optimization for multi-objective flexible job-shop scheduling problem

Flexible job-shop problem has been widely addressed in literature. Due to its complexity, it is still under consideration for research. This paper addresses flexible job-shop scheduling problem (FJSP) with three objectives to be minimized simultaneously: makespan, maximal machine workload, and total workload. Due to the discrete nature of the FJSP problem, conventional particle swarm optimization (PSO) fails to address this problem and therefore, a variant of PSO for discrete problems is presented. A hybrid discrete particle swarm optimization (DPSO) and simulated annealing (SA) algorithm is proposed to identify an approximation of the Pareto front for FJSP. In the proposed hybrid algorithm, DPSO is significant for global search and SA is used for local search. Furthermore, Pareto ranking and crowding distance method are incorporated to identify the fitness of particles in the proposed algorithm. The displacement of particles is redefined and a new strategy is presented to retain all non-dominated solutions during iterations. In the presented algorithm, pbest of particles are used to store the fixed number of non-dominated solutions instead of using an external archive. Experiments are performed to identify the performance of the proposed algorithm compared to some famous algorithms in literature. Two benchmark sets are presented to study the efficiency of the proposed algorithm. Computational results indicate that the proposed algorithm is significant in terms of the number and quality of non-dominated solutions compared to other algorithms in the literature.     

An effective hybrid particle swarm optimization for no-wait flow shop scheduling

The no-wait flow shop scheduling that requires jobs to be processed without interruption between consecutive machines is a typical NP-hard combinatorial optimization problem, and represents an important area in production scheduling. This paper proposes an effective hybrid algorithm based on particle swarm optimization (PSO) for no-wait flow shop scheduling with the criterion to minimize the maximum completion time (makespan). In the algorithm, a novel encoding scheme based on random key representation is developed, and an efficient population initialization, an effective local search based on the Nawaz-Enscore-Ham (NEH) heuristic, as well as a local search based on simulated annealing (SA) with an adaptive meta-Lamarckian learning strategy are proposed and incorporated into PSO. Simulation results based on well-known benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed hybrid algorithm.     

求解车间调度问题的改进型自适应遗传算法

针对作业车间调度问题,以最小化完工时间为目标,借鉴内分泌激素调节机制,提出了一种新颖的改进型自适应遗传算法.通过引入自适应交叉概率和变异概率因子,克服了传统的遗传算法在解决生产调度问题时存在的搜索精度低和收敛性难以控制等问题,并在Microsoft Visual C++6.0中实现了该算法.通过一个10工件、10机器作...     

An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling

Process planning and scheduling are two major sub-systems in a modern manufacturing system. In traditional manufacturing system, they were regarded as the separate tasks to perform sequentially. However, considering their complementarity, integrating process planning and scheduling can further improve the performance of a manufacturing system. Meanwhile, the multiple objectives are needed to be considered during the realistic decision-making process in a manufacturing system. Based on the above requirements from the real manufacturing system, developing effective methods to deal with the multi-objective integrated process planning and scheduling (MOIPPS) problem becomes more and more important. Therefore, this research proposes a multi-objective genetic algorithm based on immune principle and external archive (MOGA-IE) to solve the MOIPPS problem. In MOGA-IE, the fast non-dominated sorting approach used in NSGA-II is utilized as the fitness assignment scheme and the immune principle is exploited to maintain the diversity of the population and prevent the premature condition. Moreover, the external archive is employed to store and maintain the Pareto solutions during the evolutionary process. Effective genetic operators are also designed for MOIPPS. To test the performance of the proposed algorithm, three different scale instances have been employed. And the proposed method is also compared with other previous algorithms in literature. The results show that the proposed algorithm has achieved good improvement and outperforms the other algorithms.     

Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm

Flow shop scheduling problems have gained wide attention both in practical and academic fields. In this paper, we consider a multi-objective no-wait flow shop scheduling problem by minimizing the weighted mean completion time and weighted mean tardiness simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, an effective immune algorithm (IA) is proposed for searching locally the Pareto-optimal frontier for the given problem. To validate the performance of the proposed algorithm in terms of solution quality and diversity level, various test problems are carried out and the efficiency of the proposed algorithm, based on some comparison metrics, is compared with a prominent multi-objective genetic algorithm, i.e., strength Pareto evolutionary algorithm II (SPEA-II). The computational results show that the proposed IA outperforms the above genetic algorithm, especially for large problems.     

A hybrid EDA with ACS for solving permutation flow shop scheduling

This paper proposes a hybrid estimation of distribution algorithm (EDA) with ant colony system (ACS) for the minimization of makespan in permutation flow shop scheduling problems. The core idea of EDA is that in each iteration, a probability model is estimated based on selected members in the iteration along with a sampling method applied to generate members from the probability model for the next iteration. The proposed algorithm, in each iteration, applies a new filter strategy and a local search method to update the local best solution and, based on the local best solution, generates pheromone trails (a probability model) using a new pheromone-generating rule and applies a solution construction method of ACS to generate members for the next iteration. In addition, a new jump strategy is developed to help the search escape if the search becomes trapped at a local optimum. Computational experiments on Taillard’s benchmark data sets demonstrate that the proposed algorithm generated high-quality solutions by comparing with the existing population-based search algorithms, such as genetic algorithms, ant colony optimization, and particle swarm optimization.     

A swarm optimization approach for flexible flow shop scheduling with multiprocessor tasks

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (C_max). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.     

An improved hybrid multi-objective parallel genetic algorithm for hybrid flow shop scheduling with unrelated parallel machines

In this paper, we address the hybrid flow shop scheduling problems with unrelated parallel machines, sequence-dependent setup times and processor blocking to minimize the makespan and maximum tardiness criteria. Since the problem is strongly NP-hard, we propose an effective algorithm consisting of independent parallel genetic algorithms by dividing the whole population into multiple subpopulations. Each subpopulation will be assigned with different weights to search for optimal solutions in different directions. To further cover the Pareto solutions, each algorithm is combined with a novel local search step and a new helpful procedure called Redirect. The proposed Redirect procedure tries to help the algorithm to overcome the local optimums and to further search the solution space. When a population stalls over a local optimum, at first, the algorithm tries to achieve a better solution by implementing the local search step based on elite chromosomes. As implementing the local search step is time-consuming, we propose a method to speed up the searching procedure and to further increase its efficiency. If the local search step failed to work, then the Redirect procedure changes the direction and refreshes the population. Computational experiments indicate that our proposed improving procedures are thriving in achieving better solutions. We have chosen two measures to evaluate the performance of our proposed algorithms. The obtained results clearly reveal the prosperity of our proposed algorithm considering both measures we have chosen.     

An intelligent hybrid meta-heuristic for solving a case of no-wait two-stage flexible flow shop scheduling problem with unrelated parallel machines

This paper addresses the problem of no-wait two-stage flexible flow shop scheduling problem (NWTSFFSSP) considering unrelated parallel machines, sequence-dependent setup times, probable reworks and different ready times to actualize the problem. The performance measure used in this study is minimizing maximum completion time (makespan). Because of the complexity of addressed problem, we propose a novel intelligent hybrid algorithm [called hybrid algorithm (HA)] based on imperialist competitive algorithm (ICA) which are combined with simulated annealing (SA), variable neighborhood search (VNS) and genetic algorithm (GA) for solving the mentioned problem. The hybridization is carried out to overcome some existing drawbacks of each of these three algorithms and also for increasing the capability of ICA. To achieve reliable results, Taguchi approach is used to define robust parameters' values for our proposed algorithm. A simulation model is developed to study the performance of our proposed algorithm against ICA, SA, VNS, GA and ant colony optimization (ACO). The results of the study reveal the relative superiority of HA studied. In addition, potential areas for further researches are highlighted.     

考虑节能的改进多目标樽海鞘群算法TFT-LCD面板阵列制程调度问题

TFT-LCD面板生产的阵列制程是可重入混合流水车间调度问题,采用一种改进多目标樽海鞘群算法对其进行优化求解。构建以最大完工时间、总拖期时间和总耗能为优化目标的数学规划模型;针对该问题结构特点,对基本多目标樽海鞘群算法进行了一系列改进操作,包括基于升序排列的随机键编码、PS方法解码、基于Lévy飞行的领导者个体位置更新方式,以及外部档案中非支配个体的变邻域搜索操作,并采用田口方法进行算法参数设置;最后通过对基准算例的数值实验,将改进多目标樽海鞘群算法与基本多目标樽海鞘群算法、多目标粒子群优化算法、快速非支配排序遗传算法进行对比,实验结果表明了改进多目标樽海鞘群算法的有效性。     

无成组技术条件下流水车间调度的多目标优化

针对有工件组调整时间的流水车间调度问题,提出了无成组技术假设条件下的多目标优化模型,并设计了一种进化计算与局部搜索结合的混合遗传算法.模型的目标函数是最小化最大完工时间和最大拖期.在局部搜索过程中,根据问题的特征定义了两种邻域结构,采取两阶段搜索策略,以提高算法的优化搜索效率.进化过程中,采用基于个体的累计排序数和密度值的适应度分配方法,以保持群体多样性,并采取精英保留策略,以保证解的收敛性.通过测试问题和实际问题的实验以及与其他算法的比较,验证了所提模型和算法的有效性.