An extended continuous estimation of distribution algorithm for solving the permutation flow-shop scheduling problem

This article proposes an extended continuous estimation of distribution algorithm (ECEDA) to solve the permutation flow-shop scheduling problem (PFSP). In ECEDA, to make a continuous estimation of distribution algorithm (EDA) suitable for the PFSP, the largest order value rule is applied to convert continuous vectors to discrete job permutations. A probabilistic model based on a mixed Gaussian and Cauchy distribution is built to maintain the exploration ability of the EDA. Two effective local search methods, i.e. revolver-based variable neighbourhood search and Hénon chaotic-based local search, are designed and incorporated into the EDA to enhance the local exploitation. The parameters of the proposed ECEDA are calibrated by means of a design of experiments approach. Simulation results and comparisons based on some benchmark instances show the efficiency of the proposed algorithm for solving the PFSP.     

An effective shuffled frog-leaping algorithm for solving the hybrid flow-shop scheduling problem with identical parallel machines

In this article, an effective shuffled frog-leaping algorithm (SFLA) is proposed to solve the hybrid flow-shop scheduling problem with identical parallel machines (HFSP-IPM). First, some novel heuristic decoding rules for both job order decision and machine assignment are proposed. Then, three hybrid decoding schemes are designed to decode job order sequences to schedules. A special bi-level crossover and multiple local search operators are incorporated in the searching framework of the SFLA to enrich the memetic searching behaviour and to balance the exploration and exploitation capabilities. Meanwhile, some theoretical analysis for the local search operators is provided for guiding the local search. The parameter setting of the algorithm is also investigated based on the Taguchi method of design of experiments. Finally, numerical testing based on well-known benchmarks and comparisons with some existing algorithms are carried out to demonstrate the effectiveness of the proposed algorithm.     

A competitive memetic algorithm for the distributed two-stage assembly flow-shop scheduling problem

This article addresses the distributed two-stage assembly flow-shop scheduling problem (DTSAFSP) with makespan minimisation criterion. A mixed integer linear programming model is presented, and a competitive memetic algorithm (CMA) is proposed. When designing the CMA, a simple encoding scheme is proposed to represent the factory assignment and the job processing sequence; and a ring-based neighbourhood structure is designed for competition and information sharing. Moreover, some knowledge-based local search operators are developed to enhance the exploitation ability. The influence of parameter setting on the CMA is investigated using the analysis of variance method. Extensive computational tests and comparisons are carried out, which demonstrate the effectiveness of the proposed CMA in solving the DTSAFSP.     

A bounded-search iterated greedy algorithm for the distributed permutation flowshop scheduling problem

As the interest of practitioners and researchers in scheduling in a multi-factory environment is growing, there is an increasing need to provide efficient algorithms for this type of decision problems, characterised by simultaneously addressing the assignment of jobs to different factories/workshops and their subsequent scheduling. Here we address the so-called distributed permutation flowshop scheduling problem, in which a set of jobs has to be scheduled over a number of identical factories, each one with its machines arranged as a flowshop. Several heuristics have been designed for this problem, although there is no direct comparison among them. In this paper, we propose a new heuristic which exploits the specific structure of the problem. The computational experience carried out on a well-known testbed shows that the proposed heuristic outperforms existing state-of-the-art heuristics, being able to obtain better upper bounds for more than one quarter of the problems in the testbed.     

A hybrid genetic-immune algorithm with improved lifespan and elite antigen for flow-shop scheduling problems

In this paper, a hybrid genetic-immune algorithm (HGIA) is proposed to reduce the premature convergence problem in a genetic algorithm (GA) in solving permutation flow-shop scheduling problems. A co-evolutionary strategy is proposed for efficient combination of GA and an artificial immune system (AIS). First, the GA is adopted to generate antigens with better fitness, and then the population in the last generation is transformed into antibodies in AIS. A new formula for calculating the lifespan of each antibody is employed during the evolution processes. In addition, a new mechanism including T-cell and B-cell generation procedures is applied to produce different types of antibodies which will be merged together. The antibodies with longer lifespan will survive and enter the next generation. This co-evolutionary strategy is very effective since chromosomes and antibodies will be transformed and evolved dynamically. The intensive experimental results show the effectiveness of the HGIA approach. The hybrid algorithm can be further extended to solve different combinatorial problems.     

A meta-heuristic approach for solving the no-wait flow-shop problem

No-wait flow-shop scheduling problems refer to the set of problems in which a number of jobs are available for processing on a number of machines in a flow-shop context with the added constraint that there should be no waiting time between consecutive operations of the jobs. The problem is strongly NP-hard. In this paper, the considered performance measure is the makespan. In order to explore the feasible region of the problem, a hybrid algorithm of Tabu Search and Particle Swarm Optimisation (PSO) is proposed. In the proposed approach, PSO algorithm is used in order to move from one solution to a neighbourhood solution. We first employ a new coding and decoding technique to efficiently map the discrete feasible space to the set of integer numbers. The proposed PSO will further use this coding technique to explore the solution space and move from one solution to a neighbourhood solution. Afterwards, the algorithm decodes the solutions to its respective feasible solution in the discrete feasible space and returns the new solutions to the TS. The algorithm is tested by solving a large number of problems available in the literature. Computational results show that the proposed algorithm is able to outperform competitive methods and improves some of the best-known solutions of the considered test problems.     

An improved water wave optimization algorithm with the single wave mechanism for the no-wait flow-shop scheduling problem

In this article, a water wave optimization algorithm with a single wave mechanism, called single water wave optimization (SWWO), is proposed to solve the no-wait flow-shop scheduling problem (NWFSP) with the objective of minimizing the makespan. In the proposed SWWO, an improved Nawaz–Enscore–Ham (NEH) heuristic is applied to construct a high-quality initial candidate. In the propagation operation, a self-adaptive block-shift operation is employed. In the breaking operation, a variable neighbourhood search operation is utilized to explore the local optimal solution. According to the schema theory as presented in genetic algorithms, a crossover operation is adopted as the refraction operation. Finally, the computational results based on several benchmarks and statistical performance comparisons are presented. The experimental results demonstrate the effectiveness and efficiency of the proposed SWWO for solving the NWFSP.     

Minimising makespan in distributed permutation flowshops using a modified iterated greedy algorithm

The distributed permutation flowshop scheduling problem (DPFSP) is a newly proposed topic in the shop scheduling field, which has important application in globalised and multi-plant environments. This study presents a modified iterated greedy (MIG) algorithm for this problem to minimise the maximum completion time among all the factories. Compared with previous approaches, the proposed algorithm is simpler yet more effective, more efficient, and more robust in solving the DPFSP. To validate the performance of the proposed MIG algorithm, computational experiments and comparisons are conducted on an extended benchmark problem set of Taillard. Despite its simplicity, the computational results show that the proposed MIG algorithm outperforms all existing algorithms, and the best-known solutions for almost half of instances are updated. This study can be offered as a contribution to the growing body of work on both theoretically and practically useful approaches to the DPFSP.     

A hybrid Tabu sample-sort simulated annealing approach for solving distributed scheduling problem

The distributed scheduling problem has been considered as the allocation of a task to various machines in such a way that these machines are situated in different factories and these factories are geographically distributed. Therefore distributed scheduling has fulfilled various objectives, such as allocation of task to the factories and machines in such a manner that it can utilise the maximum resources. The objective of this paper is to minimise the makespan in each factory by considering the transportation time between the factories. In this paper, to address such a problem of scheduling in distributed manufacturing environment, a novel algorithm has been developed. The proposed algorithm gleans the ideas both from Tabu search and sample sort simulated annealing. A new algorithm known as hybrid Tabu sample-sort simulated annealing (HTSSA) has been developed and it has been tested on the numerical example. To reveal the supremacy of the proposed algorithm over simple SSA and Tabu search, more computational experiments have also been performed on 10 randomly generated datasets.     

A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking

A flow-shop scheduling problem with blocking has important applications in a variety of industrial systems but is underrepresented in the research literature. In this study, a novel discrete artificial bee colony (ABC) algorithm is presented to solve the above scheduling problem with a makespan criterion by incorporating the ABC with differential evolution (DE). The proposed algorithm (DE-ABC) contains three key operators. One is related to the employed bee operator (i.e. adopting mutation and crossover operators of discrete DE to generate solutions with good quality); the second is concerned with the onlooker bee operator, which modifies the selected solutions using insert or swap operators based on the self-adaptive strategy; and the last is for the local search, that is, the insert-neighbourhood-based local search with a small probability is adopted to improve the algorithm's capability in exploitation. The performance of the proposed DE-ABC algorithm is empirically evaluated by applying it to well-known benchmark problems. The experimental results show that the proposed algorithm is superior to the compared algorithms in minimizing the makespan criterion.     

An improved memetic algorithm based on a dynamic neighbourhood for the permutation flowshop scheduling problem

The permutation flowshop scheduling problem (PFSP) has been extensively studied in the scheduling literature. In this paper, we present an improved memetic algorithm (MA) to solve the PFSP to minimise the total flowtime. In the proposed MA, we develop a stochastic local search based on a dynamic neighbourhood derived from the NEH method. During the evolution process, the size of the neighbourhood is dynamically adjusted to change the search focus from exploration to exploitation. In addition, we introduce a new population generation mechanism to guarantee both the quality and diversity of the new populations. We also design a diversity index for the population to monitor the diversity of the current population. If the diversity index is less than a given threshold value, the current population will be replaced by a new one with good diversity so that the proposed MA has good ability to overcome local optima. We conduct computational experiments to test the effectiveness of the proposed algorithm. The computational results on randomly generated problem instances and benchmark problem instances show that the proposed MA is effective and superior or comparable to other algorithms in the literature.     

A particle swarm optimization algorithm for hybrid flow-shop scheduling with multiprocessor tasks

The multistage hybrid flow-shop scheduling problem with multiprocessor tasks has been found in many practical situations. Due to the essential complexity of the problem, many researchers started to apply metaheuristics to solve the problem. In this paper, we address the problem by using particle swarm optimization (PSO), a novel metaheuristic inspired by the flocking behaviour of birds. The proposed PSO algorithm has several features, such as a new encoding scheme, an implementation of the best velocity equation and neighbourhood topology among several different variants, and an effective incorporation of local search. To verify the PSO algorithm, computational experiments are conducted to make a comparison with two existing genetic algorithms (GAs) and an ant colony system (ACS) algorithm based on the same benchmark problems. The results show that the proposed PSO algorithm outperforms all the existing algorithms for the considered problem.     

Modelling and solving algorithm for two-stage scheduling of construction component manufacturing with machining and welding process

This paper focuses on a two-stage machining and welding scheduling problem based on an investigation at a structural metal manufacturing plant, aiming to minimise the total makespan. Several parts processed at Stage one according to classical job-shop scheduling are grouped into a single construction component at the second welding stage. Fabrication of the construction component cannot begin until all comprising parts have been completed at Stage one. This paper establishes a novel mathematic model to minimise the total makespan by mainly considering the dominance relationship between the construction component and the corresponding parts. In order to solve this two-stage problem, we propose an improved harmony search algorithm. A local search method is applied to the best vector at each iteration, so that a more optimal vector can be subsequently realised. The average value, minimum value, relative percentage deviation and standard deviation are discussed in the experimental section, and the proposed local best harmony search algorithm outperforms the genetic algorithm, immune algorithm and harmony search algorithm without local search. Moreover, six optimal solutions are given as Gantt charts, which vividly illustrate that the mathematical model established in this paper can facilitate the development of a better scheduling scheme.     

Collaborative reinforcement learning for a two-robot job transfer flow-shop scheduling problem

A two-robot flow-shop scheduling problem with n identical jobs and m machines is defined and evaluated for four robot collaboration levels corresponding to different levels of information sharing, learning and assessment: Full – robots work together, performing self and joint learning sharing full information; Pull – one robot decides when and if to learn from the other robot; Push – one robot may force the second to learn from it and None – each robot learns independently with no information sharing. Robots operate on parallel tracks, transporting jobs between successive machines, returning empty to a machine to move another job. The objective is to obtain a robot schedule that minimises makespan (C_max) for machines with varying processing times. A new reinforcement learning algorithm is developed, using dual Q-learning functions. A novel feature in the collaborative algorithm is the assignment of different reward functions to robots; minimising robot idle time and minimising job waiting time. Such delays increase makespan. Simulation analyses with fast, medium and slow speed robots indicated that Full collaboration with a fast–fast robot pair was best according to minimum average upper bound error. The new collaborative algorithm provides a tool for finding optimal and near-optimal solutions to difficult collaborative multi-robot scheduling problems.     

Estimation of distribution algorithm with path relinking for the blocking flow-shop scheduling problem

This article presents an effective estimation of distribution algorithm, named P-EDA, to solve the blocking flow-shop scheduling problem (BFSP) with the makespan criterion. In the P-EDA, a Nawaz–Enscore–Ham (NEH)-based heuristic and the random method are combined to generate the initial population. Based on several superior individuals provided by a modified linear rank selection, a probabilistic model is constructed to describe the probabilistic distribution of the promising solution space. The path relinking technique is incorporated into EDA to avoid blindness of the search and improve the convergence property. A modified referenced local search is designed to enhance the local exploitation. Moreover, a diversity-maintaining scheme is introduced into EDA to avoid deterioration of the population. Finally, the parameters of the proposed P-EDA are calibrated using a design of experiments approach. Simulation results and comparisons with some well-performing algorithms demonstrate the effectiveness of the P-EDA for solving BFSP.     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.     

基于阵元接收信号幅度信息的频域盲分离排序算法

排序模糊性问题是影响频域盲源分离算法分离性能的主要原因之一。对于提出了一种新的解决频域盲源分离排序模糊性问题的算法。该算法通过提取阵元接收信号每个频率点上的幅度衰减信息,采用k—means聚类算法将线性分离算法所得分离信号进行归类,来解决排序模糊性问题。该排序算法对阵列阵元排布方式,阵元间距等没有特殊的要求,并且适用于任意数量混合信号的盲分离系统。仿真实验证实了这种开发阵元接收信号幅度衰减信息的排序算法在绝大多数频率点上有效地解决了排序模糊性问题,是一种计算量相对较小而又简单有效的排序算法。     

An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.     

A modified harmony search algorithm for the multi-objective flowshop scheduling problem with due dates

This paper presents a modified harmony search optimisation algorithm (MHSO), specifically designed to solve two- and three-objective permutation flowshop scheduling problems, with due dates. To assess its capability, five sets of scheduling problems have been used to compare the MHSO with a known and highly efficient genetic algorithm (GA) chosen as the benchmark. Obtained results show that the new procedure is successful in exploring large regions of the solution space and in finding a significant number of Pareto non-dominated solutions. For those cases where the exhaustive evaluation of sequences can be applied the algorithm is able to find the whole non-dominated Pareto border, along with a considerable number of solutions that share the same optimal values for the considered optimisation parameters. To validate the algorithm, five sets of scheduling problems are investigated in-depth in comparison with the GA. Results obtained by both methods (exhaustive solutions have been provided as well for small sized problems) are fully described and discussed.     

A Pareto block-based estimation and distribution algorithm for multi-objective permutation flow shop scheduling problem

Multi-objective flow shop scheduling plays a key role in real-life scheduling problem which attract the researcher attention. The primary concern is to find the best sequence for flow shop scheduling problem. Estimation of Distribution Algorithms (EDAs) has gained sufficient attention from the researchers and it provides prominent results as an alternate of traditional evolutionary algorithms. In this paper, we propose the pareto optimal block-based EDA using bivariate model for multi-objective flow shop scheduling problem. We apply a bivariate probabilistic model to generate block which have the better diversity. We employ the non-dominated sorting technique to filter the solutions. To check the performance of proposed approach, we test it on the benchmark problems available in OR-library and then we compare it with non-dominated sorting genetic algorithm-II (NSGA-II). Computational results show that pareto optimal BBEDA provides better result and better convergence than NSGA-II.