Genetic algorithms for job shop scheduling problems with alternative routings

The purpose of this research is to solve a general job shop problem with alternative machine routings. We consider four performance measures: mean flow time, makespan, maximum lateness, and total absolute deviation from the due dates. We first develop mixed-integer linear programming (MILP) formulations for the problems. The MILP formulations can be used either to compute optimal solutions for small-sized problems or to test the performance of existing heuristic algorithms. In addition, we have developed a genetic algorithm that can be used to generate relatively good solutions quickly. Further, computational experiments have been performed to compare the solution of the MILP formulations with that of existing algorithms.     

改进遗传算法求解多时间约束的柔性作业车间调度问题

将加工时间、调整时间和移动时间分别作为独立时间因素考虑到柔性作业车间调度模型中,建立以最大完工时间最小、总调整时间最小、总移动时间最小为目标的考虑多时间约束的柔性作业车间调度模型,并提出改进的遗传算法求解该模型。通过测试标准数据集,并对比其他文献算法,验证了改进的遗传算法的可行性和有效性。     

蚁群系统结合指派规则求解HFS调度问题

以NP-难的最小化时间表长为目标的混合流水车间调度问题为研究对象。把工件在第1阶段开始加工的排序问题转化为旅行商问题,采用蚁群系统求得初始排序;在第1阶段后各阶段采用工件先到先服务规则选择工件、最先空闲机器优先规则选择机器以构建初始工件的机器指派与排序;充分利用已知的机器布局和工件加工时间特点,确定工件加工瓶颈阶段,并以此为基础对工件的机器指派与排序进行改进。用Carlier和Neron设计的Benchmark算例仿真后与著名的NEH算法比较,表明这种算法是有效的。     

Distributed production planning using a graph-based negotiation protocol

A distributed model for allocating a single job to be processed through multiple machines and alternative routings so that the job flow time is experimentally shown to reach its minimum is presented. Issues are addressed pertaining to dynamic and fully distributed decision-making for determining the job flow time in a cooperative manner between system agents (i.e. machines and a job), and for selecting a good routing (i.e. a short flow time) for a job when alternative routings are available. Two cases with confirmed jobs and without confirmed jobs are examined. The proposed protocols can deal with job shop scheduling with multiple product types in a sequential manner. The model is developed on the basis of a distributed shortest path algorithm using asynchronous job-initiated protocols. These protocols are examined using object-oriented simulation models and it is shown how the agents converge to the optimal path in a finite time.     

混合花朵授粉算法在作业车间调度中的应用

对最大完工时间最短的作业车间调度问题进行了研究,总结了当前求解作业车间调度问题的研究现状,提出一种花朵授粉算法与遗传算法的混合算法。混合算法以花朵授粉算法为基础,重新定义其全局搜索和局部搜索迭代公式,在同化操作过程中融入遗传算法的选择、优先交叉和变异操作,进一步增强算法的勘探能力。通过26个经典的基准算例仿真实验,并与近5年的其他算法比较,结果表明所提算法在求解作业车间调度问题具有一定优势。     

基于Backbone的空间收缩与划分算法

搜索空间的规模和复杂程度是决定问题求解难度的重要因素,而解空间的信息往往可以引导搜索找到最优解.在已知JSP空间结构的基础上,提出一种空间收缩与划分算法.算法利用搜索算法获得的较优解,结合组合优化问题解的backbone的概念,将搜索空间收缩并划分为一个或多个优解域,在优解域内再进行小规模问题的优化.该算法不必在求解前或求解过程中进行大量的统计分析工作,可以利用求解信息对解空间的地形进行估计,提高求解速度和解的质量.实验结果也证明了算法的有效性.     

A job shop distributed scheduling based on Lagrangian relaxation to minimise total completion time

This paper considers a distributed job shop scheduling problem where autonomous sub-production systems share common machines with each other. Each sub-production system is responsible for the scheduling of a set of jobs to minimise the total completion time on shared machines. A sub-production system has ultimate responsibility on maintaining private information such as objective function, processing time and routings on shared machines. Also sub-production systems must cooperate each other in order to achieve a global goal while sharing minimum of private information. In this research, we propose a distributed cooperation method in which sub-production systems and shared machines interact with one another to find a compromised solution between a locally optimised solution and a system-wide solution. We tested the proposed method for small, medium and large size of job shop scheduling problems and compared to a global optimal solutions. The proposed method shows promising results in terms of solution qualities and computational times.     

Scheduling manufacturing systems with blocking: a Petri net approach

This paper introduces a Petri net-based approach for scheduling manufacturing systems with blocking. The modelling of the job routings and the resource and blocking constraints is carried out with the Petri net formalism due to their capability of representing dynamic, concurrent discrete-event dynamic systems. In addition Petri nets can detect deadlocks typically found in systems with blocking constraints. The scheduling task is performed with an algorithm that combines the classical A* search with an aggressive node-pruning strategy. Tests were conducted on a variety of manufacturing systems that included classical job shop, flexible job shop and flexible manufacturing scheduling problems. The optimisation criterion was makespan. The experiments show that the algorithm performed well in all types of problems both in terms of solution quality and computing times.     

A decomposition-based approach to flexible flow shop scheduling under machine breakdown

Manufacturing systems in real-world production are generally dynamic and often subject to a wide range of uncertainties. Recently, research on production scheduling under uncertainty has attracted substantial attention. Although some methods have been developed to address this problem, scheduling under uncertainty remains inherently difficult to solve by any single approach. This article considers makespan optimisation of a flexible flow shop (FFS) scheduling problem under machine breakdown. It proposes a novel decomposition-based approach to decompose an FFS scheduling problem into several cluster scheduling problems which can be solved more easily by different approaches. A neighbouring K-means clustering algorithm is developed to first group the machines of an FFS into an appropriate number of machine clusters, based on a proposed machine allocation algorithm and weighted cluster validity indices. Two optimal back propagation networks, corresponding to the scenarios of simultaneous and non-simultaneous job arrivals, are then selectively adopted to assign either the shortest processing time (SPT) or the genetic algorithm (GA) to each machine cluster to solve cluster scheduling problems. If two neighbouring machine clusters are allocated with the same approach, they are subsequently merged. After machine grouping and approach assignment, an overall schedule is generated by integrating the solutions to the sub-problems. Computation results reveal that the proposed approach is superior to SPT and GA alone for FFS scheduling under machine breakdown.     

基于文化基因算法的开放车间调度问题研究

针对开放车间调度问题,运用了文化基因算法进行优化求解。在文化基因算法的框架中,既有种群中的全局搜索,又包含针对问题自身特点的局部搜索,为解决开放车间调度问题提供了一种新的算法。按照文化基因算法的思想和特点,将爬山法作为局部搜索策略加入到全局搜索策略所用到的遗传算法中,通过对开放车间调度问题的邻域结构进行研究,加入爬山搜索法进行优化求解。基于40个标准算例,通过与下界值的比较,验证了所提算法在解决具有较大搜索空间的调度问题时,其拥有更出色的算法性能。     

A scatter search approach to sequence-dependent setup times job shop scheduling

Scheduling jobs on multiple machines is a difficult problem when real-world constraints such as the sequence setup time, setup times for jobs and multiple criteria are used for solution goodness. It is usually sufficient to obtain a near-optimal solution quickly when an optimal solution would require days or weeks of computation. Common scheduling heuristics such as Shortest Processing Time can be used to obtain a feasible schedule quickly, but are not designed for multiple simultaneous objectives. We use a new meta-heuristic known as a scatter search (SS) to solve these types of job shop scheduling problems. The results are compared with solutions obtained by common heuristics, a tabu search, simulated annealing, and a genetic algorithm. We show that by combining the mechanism of diversification and intensification, SS produces excellent results in a very reasonable computation time. The study presents an efficient alternative for companies with a complicated scheduling and production situation.     

Ant colony optimisation with parameterised search space for the job shop scheduling problem

The job-shop scheduling problem (JSSP) is known to be NP-hard. Due to its complexity, many metaheuristic algorithm approaches have arisen. Ant colony metaheuristic algorithm, lately proposed, has successful application to various combinatorial optimisation problems. In this study, an ant colony optimisation algorithm with parameterised search space is developed for JSSP with an objective of minimising makespan. The problem is modelled as a disjunctive graph where arcs connect only pairs of operations related rather than all operations are connected in pairs to mitigate the increase of the spatial complexity. The proposed algorithm is compared with a multiple colony ant algorithm using 20 benchmark problems. The results show that the proposed algorithm is very accurate by generating 12 optimal solutions out of 20 benchmark problems, and mean relative errors of the proposed and the multiple colony ant algorithms to the optimal solutions are 0.93% and 1.24%, respectively.     

Job shop scheduling with the option of jobs outsourcing

Incorporating outsourcing in scheduling is addressed by several researchers recently. However, this scope is not investigated thoroughly, particularly in the job shop environment. In this paper, a new job shop scheduling problem is studied with the option of jobs outsourcing. The problem objective is to minimise a weighted sum of makespan and total outsourcing cost. With the aim of solving this problem optimally, two solution approaches of combinatorial optimisation problems, i.e. mathematical programming and constraint programming are examined. Furthermore, two problem relaxation approaches are developed to obtain strong lower bounds for some large scale problems for which the optimality is not proven by the applied solution techniques. Using extensive numerical experiments, the performance of the solution approaches is evaluated. Moreover, the effect the objectives's weights in the objective function on the performance of the solution approaches is also investigated. It is concluded that constraint programming outperforms mathematical programming significantly in proving solution optimality, as it can solve small and medium size problems optimally. Moreover, by solving the relaxed problems, one can obtain good lower bounds for optimal solutions even in some large scale problems.     

Cultural algorithms,an alternative heuristic to solve the job shop scheduling problem

In this work, an approach for solving the job shop scheduling problem using a cultural algorithm is proposed. Cultural algorithms are evolutionary computation methods that extract domain knowledge during the evolutionary process. Additional to this extracted knowledge, the proposed approach also uses domain knowledge given a priori (based on specific domain knowledge available for the job shop scheduling problem). The proposed approach is compared with respect to a Greedy Randomized Adaptive Search Procedure (GRASP), a Parallel GRASP, a Genetic Algorithm, a Hybrid Genetic Algorithm, and a deterministic method called shifting bottleneck. The cultural algorithm proposed in this article is able to produce competitive results with respect to the two approaches previously indicated at a significantly lower computational cost than at least one of them and without using any sort of parallel processing.     

Production sequencing problem with re-entrant work flows and sequence dependent setup times

This paper addresses a shop scheduling problem where a set of n jobs needs to be scheduled on two machines for the side frame press shop in a truck manufacturing company. A most unusual aspect of the problem is that the setup times required for a job in the first machine depend not on the immediately preceding job but on the job which is two steps prior to it. Redefining the job elements, the problem is formulated into a general two machine flow shop problem which can be solved by dynamic programming with the objective of the minimum makespan. An optimal schedule is found utilizing the sequence dominance conditions and the decisiondelay scheme. Since the computational requirements of dynamic programming are impracticably demanding for large-sized problems, a genetic algorithm is developed and its performance is examined through a comparative study.     

Linguistic-based meta-heuristic optimization model for flexible job shop scheduling

In this paper, a linguistic based meta-heuristic modelling and solution approach for solving the Flexible Job Shop Scheduling Problem (FJSSP) is presented. FJSSP is an extension of the classical job-shop scheduling problem. The present problem definition is to assign each operation to a machine out of a set of capable machines ( the routing problem ) and to order the operations on the machines ( the sequencing problem ), such that a predefined performance measure is optimized. The scope of the problem is widened by taking into account the alternative process plans for each part ( process plan selection problem ) in the present study. Moreover, instead of using operations to represent product processing requirements and machine processing capabilities, machine independent capability units, which are known as Resource Elements (RE), are used. Representation of unique and shared capability boundaries of machine tools and part processing requirements is possible via RE. Using REs in scheduling can also reduce the problem size. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls. Using these controls and the Giffler and Thompson (1960) priority rule-based heuristic, a simulated annealing algorithm is developed to solve FJSSP. This novel approach simplifies the modelling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its solution. The results obtained from the computational study have shown that the proposed algorithm can solve this complex problem effectively within reasonable time. The results have also given some insights on the effect of the selection of dispatching rules and the flexibility level on the job shop performance. It is observed that the effect of dispatching rule selection on the job shop performance diminishes by increasing the job shop flexibility.     

A novel hybrid meta-heuristic algorithm for a no-wait flexible flow shop scheduling problem with sequence dependent setup times

In this paper, we contemplate the problem of scheduling a set of n jobs in a no-wait flexible flow shop manufacturing system with sequence dependent setup times to minimising the maximum completion time. With respect to NP-hardness of the considered problem, there seems to be no avoiding application of metaheuristic approaches to achieve near-optimal solutions for this problem. For this reason, three novel metaheuristic algorithms, namely population based simulated annealing (PBSA), adapted imperialist competitive algorithm (AICA) and hybridisation of adapted imperialist competitive algorithm and population based simulated annealing (AICA?+?PBSA), are developed to solve the addressed problem. Because of the sensitivity of our proposed algorithm to parameter's values, we employed the Taguchi method as an optimisation technique to extensively tune different parameters of our algorithm to enhance solutions accuracy. These proposed algorithms were coded and tested on randomly generated instances, then to validate the effectiveness of them computational results are examined in terms of relative percentage deviation. Moreover, some sensitive analyses are carried out for appraising the behaviour of algorithms versus different conditions. The computational evaluations manifestly support the high performance of our proposed novel hybrid algorithm against other algorithms which were applied in literature for related production scheduling problems.     

Combined scheduling algorithm for re-entrant batch-processing machines in semiconductor wafer manufacturing

In this paper, a new combined scheduling algorithm is proposed to address the problem of minimising total weighted tardiness on re-entrant batch-processing machines (RBPMs) with incompatible job families in the semiconductor wafer fabrication system (SWFS). The general combined scheduling algorithm forms batches according to parameters from the real-time scheduling simulation platform (ReS²), and then sequences batches through slack-based mixed integer linear programming model (S-MILP), which is defined as batch-oriented combined scheduling algorithm. The new combined scheduling algorithm obtains families’ parameters from ReS² and then sequences these families through modified S-MILP, which is defined as family-oriented combined scheduling algorithm. With rolling horizon control strategy, two combined scheduling algorithms can update RBPMs scheduling continually. The experiments are implemented on ReS² of SWFS and ILOG CPLEX, respectively. The results demonstrate the effectiveness of our proposed methods.     

Integrated process planning and scheduling using an imperialist competitive algorithm

Effective performance of modern manufacturing systems requires integrating process planning and scheduling more tightly, which is consistently challenged by the intrinsic interrelation and intractability of these two problems. Traditionally, these two problems are treated sequentially or separately. Integration of process planning and scheduling (IPPS) provides a valuable approach to improve system performance. However, IPPS is more complex than job shop scheduling or process planning. IPPS is strongly NP-hard in that, compared to an NP-hard job shop scheduling problem with a determined process plan, the process plan for each job in IPPS is also to be optimised. So, an imperialist competitive algorithm (ICA) is proposed to address the IPPS problem with an objective of makespan minimisation. An extended operation-based representation scheme is presented to include information on various flexibilities of process planning with respect to determined job shop scheduling. The main steps of the proposed ICA, including empires construction, assimilation, imperialistic competition, revolution and elimination, are elaborated using an illustrative example. Performance of the proposed ICA was evaluated on four sets of experiments taken from the literature. Computational results of the ICA were compared with that of some existing algorithms developed for IPPS, which validates the efficiency and effectiveness of the ICA in solving the IPPS problem.     

Robust makespan minimisation in identical parallel machine scheduling problem with interval data

Parallel machine scheduling problems are commonly encountered in a wide variety of manufacturing environments and have been extensively studied. This paper addresses a makespan minimisation scheduling problem on identical parallel machines, in which the specific processing time of each job is uncertain, and its probability distribution is unknown because of limited information. In this case, the deterministic or stochastic scheduling model may be unsuitable. We propose a robust (min–max regret) scheduling model for identifying a robust schedule with minimal maximal deviation from the corresponding optimal schedule across all possible job-processing times (called scenarios). These scenarios are specified as closed intervals. To solve the robust scheduling problem, which is NP-hard, we first prove that a regret-maximising scenario for any schedule belongs to a finite set of extreme point scenarios. We then derive two exact algorithms to optimise this problem using a general iterative relaxation procedure. Moreover, a good initial solution (optimal schedule under a mid-point scenario) for the aforementioned algorithms is discussed. Several heuristics are developed to solve large-scale problems. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.