Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management fields, is no different. The flowshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the flowshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multi-objective permutation flowshop problem. This algorithm is characterised by an effective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and flowtime. Lastly, we use a novel graphical tool to compare the performances of stochastic Pareto fronts based on Empirical Attainment Functions.     

一种求解双目标job shop问题的混合进化算法

提出一种求解双目标job shop排序问题的混合进化算法．该算法采用改进的精英复制策略,降低了计算复杂性;通过引入递进进化模式,避免了算法的早熟;通过递进过程中的非劣解邻域搜索,增强了算法局部搜索性能．采用该算法和代表性算法NSGA-Ⅱ,MOGLS对82个标准双目标job shop算例进行优化对比,所得结果验证了该算法求解双目标job shop排序问题的有效性．     

Tsp-based scheduling in a batch-wise hybrid flow-shop

In the past few years, flexible production systems have allowed an extensive exploitation of new technologies, but have also led to new difficulties in production planning management science. The model presented in this paper extends the traditional HFS (hybrid flow-shop) scheduling problem to the case in which jobs are due to follow strict precedence constraints and batch assignment constraints and the parallel machines at a stage are served by a bottleneck machine. A variant of the well-known TSP problem is used to develop an efficient heuristic solution for the problem. The effectiveness of the proposed approach is validated through a comparison with different heuristics traditionally used in HFS scheduling problems. Furthermore, a simple insertion heuristic based on the TSP model of the problem is tested. Finally, a MIP-based approach is also explored to provide the optimum solutions within much larger times for comparison.     

Two new meta-heuristics for a bi-objective supply chain scheduling problem in flow-shop environment

In this study, an integrated multi-objective production-distribution flow-shop scheduling problem will be taken into consideration with respect to two objective functions. The first objective function aims to minimize total weighted tardiness and make-span and the second objective function aims to minimize the summation of total weighted earliness, total weighted number of tardy jobs, inventory costs and total delivery costs. Firstly, a mathematical model is proposed for this problem. After that, two new meta-heuristic algorithms are developed in order to solve the problem. The first algorithm (HCMOPSO), is a multi-objective particle swarm optimization combined with a heuristic mutation operator, Gaussian membership function and a chaotic sequence and the second algorithm (HBNSGA-II), is a non-dominated sorting genetic algorithm II with a heuristic criterion for generation of initial population and a heuristic crossover operator. The proposed HCMOPSO and HBNSGA-II are tested and compared with a Non-dominated Sorting Genetic Algorithm II (NSGA-II), a Multi-Objective Particle Swarm Optimization (MOPSO) and two state-of-the-art algorithms from recent researches, by means of several comparing criteria. The computational experiments demonstrate the outperformance of the proposed HCMOPSO and HBNSGA-II.     

Improved cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan

The multistage hybrid flow shop (HFS) scheduling problems are considered in this paper. Hybrid flowshop scheduling problems were proved to be NP-hard. A recently developed cuckoo search (CS) metaheuristic algorithm is presented in this paper to minimize the makespan for the HFS scheduling problems. A constructive heuristic called NEH heuristic is incorporated with the initial solutions to obtain the optimal or near optimal solutions rapidly in the improved cuckoo search (ICS) algorithm. The proposed algorithm is validated with the data from a leading furniture manufacturing company. Computational results show that the ICS algorithm outperforms many other metaheuristics.     

A palmer-based continuous fuzzy flexible flow-shop scheduling algorithm

 Flexible flow shops can be thought of as generalizations of simple flow shops. In the past, the processing time for each job was usually assumed to be known exactly, but in many real-world applications, processing times may vary dynamically due to human factors or operating faults. In the past, we demonstrated how discrete fuzzy concepts could easily be used in the Palmer algorithm for managing uncertain flexible-flow-shop scheduling. In this paper, we generalize it to continuous fuzzy domains. We use triangular membership functions for flexible flow shops with more than two machine centers to examine processing-time uncertainties and to make scheduling more suitable for real applications. We first use the triangular fuzzy LPT algorithm to allocate jobs, and then use the triangular fuzzy Palmer algorithm to deal with sequencing the tasks. The proposed method thus provides a more flexible way of scheduling jobs than conventional scheduling methods.     

求解混合流水车间调度问题的改进型PSO算法

针对粒子群优化算法易陷入局部最优以及求解生产调度问题时容易重复搜索的情况,结合混合车间调度问题的优化模型,提出一种改进的粒子群优化算法。在算法设计中,引入基于位置相似度的禁忌策略,避免对刚刚搜索过的区域重复搜索和过早陷入局部最优;同时采用线性微分递减方式更新惯性权重,既保证了算法前期有较高的全局搜索能力,又能保证后期有较高的开发能力。最后通过仿真实验,验证算法的有效性。     

Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects

In this paper we introduce a new scheduling model with learning effects in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the job’s scheduled position. We show that the single-machine problems to minimize makespan and total completion time are polynomially solvable. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. Finally, we present polynomial-time optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time.     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

Intelligent controllers for bi-objective dynamic scheduling on a single machine with sequence-dependent setups

This article addresses the problem of dynamic job scheduling on a single machine with Poisson arrivals, stochastic processing times and due dates, in the presence of sequence-dependent setups. The objectives of minimizing mean earliness and mean tardiness are considered. Two approaches for dynamic scheduling are proposed, a Reinforcement Learning-based and one based on Fuzzy Logic and multi-objective evolutionary optimization. The performance of the two scheduling approaches is tested against the performance of 15 dispatching rules in four simulation scenarios with different workload and due date pressure conditions. The scheduling methods are compared in terms of Pareto optimal-oriented metrics, as well as in terms of minimizing mean earliness and mean tardiness independently. The experimental results demonstrate the merits of the proposed methods.     

Some single-machine and flowshop scheduling problems with a non-linear deterioration function

The deteriorating job scheduling problems have received increasing attention recently. However, most researchers assume that the actual job processing time is a linear function of its starting time. In fact, in some situations, the deterioration rate might increase or decrease as time passes. For example, the temperature of the ingot in the rolling machine might drop at a slower pace as the surface cools down. Thus, the drop of the ingot temperature might have a decreasing rate. On the other hand, the time to control a fire might go dramatically as time passes, and the time to cease a fire might have an increasing rate. In this paper, we propose a new deteriorating model where the deterioration rate might be increasing or decreasing as time passes. Under the proposed model, we provide the optimal solutions for some single-machine problems and some flowshop problems.     

求解PFSP的双种群协同学习算法

在人工蜜蜂群算法的基础上, 提出一种双种群协同学习算法.该算法根据个体适应度高低把蜜蜂群划分为 两个子群, 并重新定义子群的学习交流机制.在10个常用的基准测试函数上与其他4个常用的群体智 能算法进行比较, 比较结果表明, 所提出算法的性能有明显改进.采用双种群协同学习算法求解置换流水车间调度问题, 在一 些著名的中大规模测试问题包括21个Reeves实例和40个Taillard实例上进行 测试, 结果表明, 所提出的算法优于其他算法, 能有效解决置换流水车间调度问题.     

A bi-objective model for robust berth allocation scheduling

Berth allocation is an important port operation problem for container terminals. This paper studies how to develop a robust schedule for berth allocation that incorporates a degree of anticipation of uncertainty (e.g., vessels’ arrival time and operation time) during the schedule’s execution. This study proposes a bi-objective optimization model for minimizing cost and maximizing robustness of schedules. A heuristic is also developed for solving the bi-objective model in large-scale problem cases. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed model and method. Managerial implications are also discussed.     

Some single-machine and m-machine flowshop scheduling problems with learning considerations

Scheduling with learning effect has drawn many researchers’ attention since Biskup [D. Biskup, Single-machine scheduling with learning considerations, European Journal of Opterational Research 115 (1999) 173-178] introduced the concept of learning into the scheduling field. Biskup [D. Biskup, A state-of-the-art review on scheduling with learning effect, European Journal of Opterational Research 188 (2008) 315-329] classified the learning approaches in the literature into two main streams. He claimed that the position-based learning seems to be a realistic model for machine learning, while the sum-of-processing-time-based learning is a model for human learning. In some realistic situations, both the machine and human learning might exist simultaneously. For example, robots with neural networks are used in computers, motor vehicles, and many assembly lines. The actions of a robot are constantly modified through self-learning in processing the jobs. On the other hand, the operators in the control center learn how to give the commands efficiently through working experience. In this paper, we propose a new learning model that unifies the two main approaches. We show that some single-machine problems and some specified flowshop problems are polynomially solvable.     

A multi-objective co-evolutionary algorithm for energy-efficient scheduling on a green data center

Nowadays, the environment protection and the energy crisis prompt more computing centers and data centers to use the green renewable energy in their power supply. To improve the efficiency of the renewable energy utilization and the task implementation, the computational tasks of data center should match the renewable energy supply. This paper considers a multi-objective energy-efficient task scheduling problem on a green data center partially powered by the renewable energy, where the computing nodes of the data center are DVFS-enabled. An enhanced multi-objective co-evolutionary algorithm, called OL-PICEA-g, is proposed for solving the problem, where the PICEA-g algorithm with the generalized opposition based learning is applied to search the suitable computing node, supply voltage and clock frequency for the task computation, and the smart time scheduling strategy is employed to determine the start and finish time of the task on the chosen node. In the experiments, the proposed OL-PICEA-g algorithm is compared with the PICEA-g algorithm, the smart time scheduling strategy is compared with two other scheduling strategies, i.e., Green-Oriented Scheduling Strategy and Time-Oriented Scheduling Strategy, different parameters are also tested on the randomly generated instances. Experimental results confirm the superiority and effectiveness of the proposed algorithm.     

柔性Job shop集成化计划调度模型及其求解算法

考虑不同加工工艺路径的成本因素，从集成化的角度研究了柔性Job shop计划和调度问题，针对问题的结构特点，建立了两层混合整数规划模型，提出门槛接受，遗传算法与启发式规则相结合的混合求解算法，综合考虑各层次决策问题进行求解，实例计算表明，该算法可迅速求得问题的近优解，表现出良好的求解性能。     

Application of game theory based hybrid algorithm for multi-objective integrated process planning and scheduling

Process planning and scheduling are two key sub-functions in the manufacturing system. Traditionally, process planning and scheduling were regarded as the separate tasks to perform sequentially. Recently, a significant trend is to integrate process planning and scheduling more tightly to achieve greater performance and higher productivity of the manufacturing system. Because of the complementarity of process planning and scheduling, and the multiple objectives requirement from the real-world production, this research focuses on the multi-objective integrated process planning and scheduling (IPPS) problem. In this research, the Nash equilibrium in game theory based approach has been used to deal with the multiple objectives. And a hybrid algorithm has been developed to optimize the IPPS problem. Experimental studies have been used to test the performance of the proposed approach. The results show that the developed approach is a promising and very effective method on the research of the multi-objective IPPS problem.     

Some scheduling problems with deteriorating jobs and learning effects

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper, we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. For the single-machine case, we derive polynomial-time optimal solutions for the problems to minimize makespan and total completion time. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. For the case of an m-machine permutation flowshop, we present polynomial-time optimal solutions for some special cases of the problems to minimize makespan and total completion time.     

An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems

This paper proposes an effective hybrid tabu search algorithm (HTSA) to solve the flexible job-shop scheduling problem. Three minimization objectives – the maximum completion time (makespan), the total workload of machines and the workload of the critical machine are considered simultaneously. In this study, a tabu search (TS) algorithm with an effective neighborhood structure combining two adaptive rules is developed, which constructs improved local search in the machine assignment module. Then, a well-designed left-shift decoding function is defined to transform a solution to an active schedule. In addition, a variable neighborhood search (VNS) algorithm integrating three insert and swap neighborhood structures based on public critical block theory is presented to perform local search in the operation scheduling component. The proposed HTSA is tested on sets of the well-known benchmark instances. The statistical analysis of performance comparisons shows that the proposed HTSA is superior to four existing algorithms including the AL + CGA algorithm by Kacem, Hammadi, and Borne (2002b), the PSO + SA algorithm by Xia and Wu (2005), the PSO + TS algorithm by Zhang, Shao, Li, and Gao (2009), and the Xing’s algorithm by Xing, Chen, and Yang (2009a) in terms of both solution quality and efficiency.     

A new encoding scheme-based hybrid algorithm for minimising two-machine flow-shop group scheduling problem

This article investigates the two-machine flow-shop group scheduling problem (GSP) with sequence-dependent setup and removal times, and job transportation times between machines. The objective is to minimise the total completion time. As known, this problem is an NP-hard problem and generalises the typical two-machine GSPs. In this article, a new encoding scheme based on permutation representation is proposed to transform a random job permutation to a feasible permutation for GSPs. The proposed encoding scheme simultaneously determines both the sequence of jobs in each group and the sequence of groups. By reasonably combining particle swarm optimisation (PSO) and genetic algorithm (GA), we develop a fast and easily implemented hybrid algorithm (HA) for solving the considered problems. The effectiveness and efficiency of the proposed HA are demonstrated and compared with those of standard PSO and GA by numerical results of various tested instances with group numbers up to 20. In addition, three different lower bounds are developed to evaluate the solution quality of the HA. Limited numerical results indicate that the proposed HA is a viable and effective approach for the studied two-machine flow-shop group scheduling problem.