Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm

Maintenance activities have been ignored in many studies on scheduling problems where all machines are assumed to be available without interruption in the planning horizon. However, in realistic situations, they might be unavailable due to preventive maintenance, basic maintenance or unforeseen breakdowns. In this paper, we simulate a condition-based maintenance (CBM) for flexible job shop scheduling problem (FJSP) and consider the combination of Sigmoid function and Gaussian distribution to improve the CBM simulation. This study proposes an improved imperialist competitive algorithm (ICA) for the FJSP scheduling problem with the objective of the makespan minimization. The performance of the proposed algorithm is enhanced with a hybridization of ICA with simulated annealing (SA), after diagnosing standard ICA disadvantages and shortcomings. This ICA also includes a simulation part to handle CBM requirements. Various parameters of the novel ICA are reviewed to calibrate the algorithm with the help of the Taguchi experimental design. Experimental results show the high performance of the novel ICA in comparison with the standard ICA. The obtained results demonstrate that the novel ICA is an effective algorithm for FJSP under CBM. Finally, the performance of ICA is evaluated compared to other popular algorithms.     

Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm

The traditional production scheduling problem considers performance indicators such as processing time, cost, and quality as optimization objectives in manufacturing systems; however, it does not take energy consumption or environmental impacts completely into account. Therefore, this paper proposes an energy-efficient model for flexible flow shop scheduling (FFS). First, a mathematical model for a FFS problem, which is based on an energy-efficient mechanism, is described to solve multi-objective optimization. Since FFS is well known as a NP-hard problem, an improved, genetic-simulated annealing algorithm is adopted to make a significant trade-off between the makespan and the total energy consumption to implement a feasible scheduling. Finally, a case study of a production scheduling problem for a metalworking workshop in a plant is simulated. The experimental results show that the relationship between the makespan and the energy consumption may be apparently conflicting. In addition, an energy-saving decision is performed in a feasible scheduling. Using the decision method, there could be significant potential for minimizing energy consumption.     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

A novel hybrid meta-heuristic algorithm for solving multi objective flexible job shop scheduling

Finding feasible scheduling that optimize all objective functions for flexible job shop scheduling problem (FJSP) is considered by many researchers. In this paper, the novel hybrid genetic algorithm and simulated annealing (NHGASA) is introduced to solve FJSP. The NHGASA is a combination of genetic algorithm and simulated annealing to propose the algorithm that is more efficient than others. The three objective functions in this paper are: minimize the maximum completion time of all the operations (makespan), minimize the workload of the most loaded machine and minimize the total workload of all machines. Pareto optimal solution approach is used in NHGASA for solving FJSP. Contrary to the other methods that assign weights to all objective functions to reduce them to one objective function, in the NHGASA and during all steps, problems are solved by three objectives. Experimental results prove that the NHGASA that uses Pareto optimal solutions for solving multi-objective FJSP overcome previous methods for solving the same benchmarks in the shorter computational time and higher quality.     

Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm

Most flexible job shop scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines may be unavailable due to maintenances, pre-schedules and so on. In this paper, we study the flexible job shop scheduling problem with availability constraints. The availability constraints are non-fixed in that the completion time of the maintenance tasks is not fixed and has to be determined during the scheduling procedure. We then propose a hybrid genetic algorithm to solve the flexible job shop scheduling problem with non-fixed availability constraints (fJSP-nfa). The genetic algorithm uses an innovative representation method and applies genetic operations in phenotype space in order to enhance the inheritability. We also define two kinds of neighbourhood for the problem based on the concept of critical path. A local search procedure is then integrated under the framework of the genetic algorithm. Representative flexible job shop scheduling benchmark problems and fJSP-nfa problems are solved in order to test the effectiveness and efficiency of the suggested methodology. Received: June 2005 /Accepted: December 2005     

A hybrid variable neighborhood search algorithm for solving the limited-buffer permutation flow shop scheduling problem with the makespan criterion

This paper investigates the limited-buffer permutation flow shop scheduling problem (LBPFSP) with the makespan criterion. A hybrid variable neighborhood search (HVNS) algorithm hybridized with the simulated annealing algorithm is used to solve the problem. A method is also developed to decrease the computational effort needed to implement different types of local search approaches used in the HVNS algorithm. Computational results show the higher efficiency of the HVNS algorithm as compared with the state-of-the-art algorithms. In addition, the HVNS algorithm is competitive with the algorithms proposed in the literature for solving the blocking flow shop scheduling problem (i.e., LBPFSP with zero-capacity buffers), and finds 54 new upper bounds for the Taillard's benchmark instances.     

Minimizing makespan in a flow shop with two batch-processing machines using simulated annealing

This paper aims at minimizing the makespan of two batch-processing machines in a flow shop. The processing times and the sizes of the jobs are known and non-identical. The machines can process a batch as long as its capacity is not exceeded. The processing time of a batch is the longest processing time among all the jobs in that batch. The problem under study is NP-hard for makespan objective. Consequently, a heuristic based on Johnson's algorithm and a simulated annealing (SA) algorithm is proposed. Random instances were generated to verify the effectiveness of the proposed approaches. The results obtained from SA were compared with the proposed heuristic and a commercial solver. The SA outperformed both the heuristic and the commercial solver. On larger problem instances, the heuristic outperformed the commercial solver.     

Reliability evaluation of a multistate flexible flow shop with stochastic capacity for multiple types of jobs

A flexible flow shop (FFS) is a general manufacturing system that has been studied by numerous researchers. Owing to maintenance, partial failure, the possibility of failure, unexpected situations, etc., the number of functioning machines in a stage should be represented by multiple levels. It is appropriate to regard the capacity in each stage (i.e., the number of machines in a stage) as stochastic. Unlike the previous research, which dealt with the FFS problems under the assumption of the fixed capacity, this paper extends the deterministic capacity to the stochastic case in every stage. The FFS with stochastic capacity is modeled as a multistate flexible flow shop network (MFFSN), where each edge denotes a stage with stochastic capacity and each node denotes a buffer. The addressed problem is to evaluate network reliability, the probability that the MFFSN can complete a customer's order composed of multiple types of jobs within a time threshold. An efficient algorithm integrating a systematic branch-and-bound approach is proposed to obtain the lower boundary vectors, in terms of a pair of capacity vectors generated from two estimated demand vectors. Two practical cases, a tile production system and an apparel manufacturing system, are presented to demonstrate the proposed algorithm and to discuss the changes in network reliability within different time thresholds, respectively.     

An Efficient Hybrid Algorithm for a Bi-objectives Hybrid Flow Shop Scheduling

This paper considers the problem of scheduling n independent jobs in g-stage hybrid flow shop environment. To address the realistic assumptions of the proposed problem, two additional traits were added to the scheduling problem. These include setup times, and the consideration of maximum completion time together with total tardiness as objective function. The problem is to determine a schedule that minimizes a convex combination of objectives. A procedure based on hybrid the simulated annealing; genetic algorithm and local search so-called HSA-GA-LS are proposed to handle this problem approximately. The performance of the proposed algorithm is compared with a genetic algorithm proposed in the literature on a set of test problems. Several performance measures are applied to evaluate the effectiveness and efficiency of the proposed algorithm in finding a good quality schedule. From the results obtained, it can be seen that the proposed method is efficient and effective.     

最优子种群遗传算法求解柔性流水车间调度问题

为了验证最优子种群遗传算法在解决柔性流水车间调度问题时相比于传统遗传算法的优越性,分析了柔性流水车间调度问题的特点,并运用一种新的编码方法和新的遗传算法求解了该问题。考虑到最优个体保护策略法对复杂问题容易使种群收敛陷入局部最优解,为了提高精度、加快较优个体的产生并避免陷入局部最优解,首先提出了一种合理、全面的编码方法,并运用最优子种群遗传算法来求解柔性流水车间调度问题。最后运用实例验证了最优子种群遗传算法的有效性、优越性和编码方式的合理性。     

A holonic approach to flexible flow shop scheduling under stochastic processing times

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. This paper presents a novel decomposition-based holonic approach (DBHA) for minimising the makespan of a flexible flow shop (FFS) with stochastic processing times. The proposed DBHA employs autonomous and cooperative holons to construct solutions. When jobs are released to an FFS, the machines of the FFS are firstly grouped by a neighbouring K-means clustering algorithm into an appropriate number of cluster holons, based on their stochastic nature. A scheduling policy, determined by the back propagation networks (BPNs), is then assigned to each cluster holon for schedule generation. For cluster holons of a low stochastic nature, the Genetic Algorithm Control (GAC) is adopted to generate local schedules in a centralised manner; on the other hand, for cluster holons of a high stochastic nature, the Shortest Processing Time Based Contract Net Protocol (SPT-CNP) is applied to conduct negotiations for scheduling in a decentralised manner. The combination of these two scheduling policies enables the DBHA to achieve globally good solutions, with considerable adaptability in dynamic environments. Computation results indicate that the DBHA outperforms either GAC or SPT-CNP alone for FFS scheduling with stochastic processing times.     

混合差分进化算法在舰载机出动调度中的应用

研究舰载机舰面航空保障问题,通过合理规划舰载机在舰面多阶段工位上的保障顺序和时序以提升舰载机的出动效率,并将问题抽象为考虑阶段转移时间的混合流水车间调度模型.针对传统智能算法求解混流车间问题时存在的搜索效率低和易陷入局部极值点的不足,提出了一种混合差分进化算法.为提升算法的求解效率,设计了基于先入先出和最先空闲机器原则的解码策略.其次,引入了交叉、变异参数的自适应控制策略以提升算法的全局搜索能力,并在算法框架中嵌入一种基于模拟退火的多邻域局部搜索策略.最后通过仿真验证了算法对求解舰载机出动调度问题具有较好的收敛性和鲁棒性.     

The economic lot scheduling problem in limited-buffer flexible flow shops: Mathematical models and a discrete fruit fly algorithm

This paper considers the lot scheduling problem in the flexible flow shop with limited intermediate buffers to minimize total cost which includes the inventory holding and setup costs. The single available mathematical model by Akrami et al. (2006) for this problem suffers from not only being non-linear but also high size-complexity. In this paper, two new mixed integer linear programming models are developed for the problem. Moreover, a fruit fly optimization algorithm is developed to effectively solve the large problems. For model’s evaluation, this paper experimentally compares the proposed models with the available model. Moreover, the proposed algorithm is also evaluated by comparing with two well-known algorithms (tabu search and genetic algorithm) in the literature and adaption of three recent algorithms for the flexible flow shop problem. All the results and analyses show the high performance of the proposed mathematical models as well as fruit fly optimization algorithm.     

Lexicographic optimization of a permutation flow shop scheduling problem with time lag constraints

This paper considers the permutation flow shop scheduling problem with minimal and maximal time lags. Time lags are defined as intervals of time that must exist between every pair of consecutive operations of a job. The objective is to hierarchically minimize two criteria, the primary criterion is the minimization of the number of tardy jobs and the secondary one minimizes the makespan. We propose a mixed integer mathematical programming formulation which can be solved with the subroutine CPLEX. We also propose several versions of simulated annealing algorithm to heuristically solve the problem. Computational experiments to compare the proposed procedures are presented and discussed.     

Minimizing total completion time in a two-stage hybrid flow shop with dedicated machines at the first stage

This paper considers a two-stage hybrid flow shop scheduling with dedicated machines at stage 1 with the objective of minimizing the total completion time. There exist two machines at stage 1 and one machine at stage 2. Each job must be processed on one of the two dedicated machines at stage 1 depending on the job type; subsequently, the job is processed on the single machine at stage 2.First, we introduce the problem and establish the complexity of the problem. For a special case in which the processing times on the machine at stage 2 are identical, an optimal solution is presented; for three special cases, we show that the decision version is unary NP-complete. For the general case, two simple and intuitive heuristics are introduced, and a worst case bound on the relative error is found for each of the heuristics. Finally, we empirically evaluate the heuristics, including an optimal algorithm for a special case.     

求解柔性流水车间调度问题的高效分布估算算法

针对最小化最大完工时间的柔性流水车间调度,利用事件建模思想,线性化0-1混合整数规划模型,使得小规模调度问题通过Cplex可以准确求解,同时设计了高效分布估算算法来求解大规模调度问题.该算法采用的是一种新颖的随机规则解码方式,工件排序按选定的规则安排而机器按概率随机分配.针对分布估算算法中的概率模型不能随种群中个体各位置上工件的更新而自动调整的缺点,提出了自适应调整概率模型,该概率模型能提高分布估算算法的收敛质量和速度.同时为提高算法局部搜索能力和防止算法陷入局部最优,设计了局部搜索和重启机制.最后,采用实验设计方法校验了高效分布估算算法参数的最佳组合.算例和实例测试结果都表明本文提出的高效分布估算算法在求解质量和稳定性上均优于遗传算法、引力搜索算法和经典分布估算算法.     

A neural network model and algorithm for the hybrid flow shop scheduling problem in a dynamic environment

A hybrid flow shop (HFS) is a generalized flow shop with multiple machines in some stages. HFS is fairly common in flexible manufacturing and in process industry. Because manufacturing systems often operate in a stochastic and dynamic environment, dynamic hybrid flow shop scheduling is frequently encountered in practice. This paper proposes a neural network model and algorithm to solve the dynamic hybrid flow shop scheduling problem. In order to obtain training examples for the neural network, we first study, through simulation, the performance of some dispatching rules that have demonstrated effectiveness in the previous related research. The results are then transformed into training examples. The training process is optimized by the delta-bar-delta (DBD) method that can speed up training convergence. The most commonly used dispatching rules are used as benchmarks. Simulation results show that the performance of the neural network approach is much better than that of the traditional dispatching rules.This revised version was published in June 2005 with corrected page numbers.     

混合文化优化算法及在车间调度中的应用

针对文化算法收敛速度慢、易陷入局部最优解以及种群多样性少的问题,本文对文化算法进行优化设计,提出一种将带有精英保留策略的遗传算法(GA)和模拟退火算法(SA)纳入文化算法(CA)框架的混合优化算法.此算法基于协同进化的思想,算法分为下层种群空间和上层信念空间,两个空间采用了相同的进化机制,但使用不同的参数.在文化算法的基础上加入带有精英保留策略的遗传算法,使种群中的优秀个体直接进入下一代,以此提高收敛速度;加入模拟退火算法,利用其具有突变的特点,概率性的跳出局部最优并接受劣质解,以此增加种群多样性.函数优化结果证明了算法的有效性,将此算法用于求解最小化最大完工时间的流水车间调度问题,仿真结果显示,此算法在收敛速度和精度方面都优于其他几个具有代表性的算法.     

一类含同工件流水线调度问题的优化研究

流水线调度问题是具有很强工程背景的典型NP完全问题,当其含有同工件时,批量和排序的相关性使得问题的求解更为复杂。文章有机结合模拟退火的概率突跳性和遗传算法的并行搜索结构,提出了处理一类含同工件流水线调度问题的混合优化策略。算法不仅能够动态缩小搜索空间以提高搜索效率,而且在保优策略的基础上利用重升温技术来增强克服陷入局部极小的能力,其有效性和快速性通过仿真得到了验证。     

An exact and a simulated annealing algorithm for simultaneously determining flow path and the location of P/D stations in bidirectional path

In this paper, we present two algorithms to design flow path and the location of its pickup and delivery (P/D) stations simultaneously in a block layout for Automated Guided Vehicles (AGVs). We develop two algorithms to solve this problem. The first one is a cutting-plane algorithm to solve the mixed integer linear program that models the problem. The second one is a Simulated Annealing (SA) approach which solves the problem heuristically to a near best solution. Computational results show the performance of both algorithms.