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.     

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 variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

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 hybrid immune algorithm for solving the distributed permutation flow-shop scheduling problem

In this article, an effective hybrid immune algorithm (HIA) is presented to solve the distributed permutation flow-shop scheduling problem (DPFSP). First, a decoding method is proposed to transfer a job permutation sequence to a feasible schedule considering both factory dispatching and job sequencing. Secondly, a local search with four search operators is presented based on the characteristics of the problem. Thirdly, a special crossover operator is designed for the DPFSP, and mutation and vaccination operators are also applied within the framework of the HIA to perform an immune search. The influence of parameter setting on the HIA is investigated based on the Taguchi method of design of experiment. Extensive numerical testing results based on 420 small-sized instances and 720 large-sized instances are provided. The effectiveness of the HIA is demonstrated by comparison with some existing heuristic algorithms and the variable neighbourhood descent methods. New best known solutions are obtained by the HIA for 17 out of 420 small-sized instances and 585 out of 720 large-sized instances.     

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.     

Fast local neighborhood search algorithm for the no-wait flow shop scheduling with total flow time minimization

A fast local neighbourhood search (FLNS) algorithm is proposed in this paper to minimise the total flow time in the no-wait flow shop scheduling problem, which is known to be NP-hard for more than two machines. In this work, an unscheduled job sequence is constructed firstly according to the total processing time and standard deviation of jobs on the machines. This job sequence is undergone an initial optimisation using basic neighbourhood search algorithm. Then, an innovative local neighbourhood search scheme is designed to search for the partial neighbourhood in each iterative processing and calculate the neighbourhood solution with an objective increment method. This not only improves the solution quality significantly, but also speeds up the convergence of the solution of the algorithm. Moreover, a probabilistic acceptance criterion is adopted to help our method escape from the local optima. Based on Taillard’s benchmarks, the experimental results show that the proposed FLNS algorithm is superior to major existing algorithms (IHA, IBH_LS, GA-VNS and DHS) in terms of both quality and robustness, and can provide best upper bounds. The in-depth statistical analysis demonstrates that the promising performance of our proposed algorithm is also statistically significant.     

Flexible job-shop scheduling problem with resource recovery constraints

In this work, we introduce a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC). In the FRRC, besides the constraints of the classical Flexible Job-shop Scheduling Problem (FJSP), operations may require resources to be processed. The resources are available in batches and a recovery time is required between each batch. This problem is inspired by a real situation faced by a brewing company where different yeasts are available in a limited quantity and are recovered only once they have been completely used. The objective is to schedule the operations such that the makespan is minimised. A mathematical model and a metaheuristic based on a General Variable Neighborhood Search is proposed for the solution of the FRRC. Computational results over a large set of instances, adapted from the FJSP literature, are presented.     

An artificial bee colony algorithm for the economic lot scheduling problem

In this study, we present an artificial bee colony (ABC) algorithm for the economic lot scheduling problem modelled through the extended basic period (EBP) approach. We allow both power-of-two (PoT) and non-power-of-two multipliers in the solution representation. We develop mutation strategies to generate neighbouring food sources for the ABC algorithm and these strategies are also used to develop two different variable neighbourhood search algorithms to further enhance the solution quality. Our algorithm maintains both feasible and infeasible solutions in the population through the use of some sophisticated constraint handling methods. Experimental results show that the proposed algorithm succeeds to find the all the best-known EBP solutions for the high utilisation 10-item benchmark problems and improves the best known solutions for two of the six low utilisation 10-item benchmark problems. In addition, we develop a new problem instance with 50 items and run it at different utilisation levels ranging from 50 to 99% to see the effectiveness of the proposed algorithm on large instances. We show that the proposed ABC algorithm with mixed solution representation outperforms the ABC that is restricted only to PoT multipliers at almost all utilisation levels of the large instance.     

An improved Intelligent Water Drops algorithm for achieving optimal job-shop scheduling solutions

Job-shop scheduling is a typical NP-hard problem which has drawn continuous attention from researchers. In this paper, the Intelligent Water Drops (IWD) algorithm, which is a new meta-heuristics, is customised for solving job-shop scheduling problems. Five schemes are proposed to improve the original IWD algorithm, and the improved algorithm is named the Enhanced IWD algorithm (EIWD) algorithm. The optimisation objective is the makespan of the schedule. Experimental results show that the EIWD algorithm is able to find better solutions for the standard benchmark instances than the existing algorithms. This paper has made a contribution in two aspects. First, to the best of the authors’ knowledge, this research is the first to apply the IWD algorithm to the job-shop scheduling problem. This work can inspire further studies of applying IWD algorithm to other scheduling problems, such as open-shop scheduling and flow-shop scheduling. Second, this research further improves the original IWD algorithm by employing five schemes to increase the diversity of the solution space as well as the solution quality.     

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 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.     

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 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 particle swarm optimisation for the no-wait flow shop problem with due date constraints

This paper considers the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, a due date is associated with the completion of each job. The considered objective function is makespan. This problem is proved to be strongly NP-Hard. In this paper, a particle swarm optimisation (PSO) is developed to deal with the problem. Moreover, the effect of some dispatching rules for generating initial solutions are studied. A Taguchi-based design of experience approach has been followed to determine the effect of the different values of the parameters on the performance of the algorithm. To evaluate the performance of the proposed PSO, a large number of benchmark problems are selected from the literature and solved with different due date and penalty settings. Computational results confirm that the proposed PSO is efficient and competitive; the developed framework is able to improve many of the best-known solutions of the test problems available in the literature.     

Bi-objective mathematical model and improved algorithm for optimisation of welding shop scheduling problem

This paper addresses a bi-objective welding shop scheduling problem (BWSSP) aiming to minimise the total tardiness and the machine interaction effect. The BWSSP is a special flow-shop scheduling problem (FSP) which is characterised by the fact that more than one machine can process on one job at a certain stage. This study analyses the operation of a structural metal manufacturing plant, and includes various aspects such as job sequence, machine-number-dependent processing time, lifting up time, lifting down time and different delivery time. A novel mixed-integer programming model (MIPM) is established, which can be used to minimise the delayed delivery time and the total machine interaction effect. One machine interaction effect formula is given in this paper. In order to solve this BWSSP, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII), embedded with a restarted strategy (RNSGAIII), is proposed. The restarted strategy, which can increase the diversity of the solutions, will be triggered with a restart probability. Following the iterative process, an effective strategy is applied to reduce the interaction effect penalty, on the premise that the makespan will remain unchanged. Total five algorithms, namely NSGAII, NSGAIII, harmony search algorithm (HSA), strength Pareto evolutionary algorithm (SPEA2), and RNSGAIII are utilised to solve this engineering problem. Numerical simulations show that the improved RNSGAIII outperforms the other methods, and the Pareto solution distribution and diversity, in particular, are significantly improved.     

A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.     

基于MPSO的有限缓冲区多产品厂间歇调度问题的研究

研究了以最小化最大完工时间为目标的有限缓冲区多产品厂间歇调度问题,提出了一种基于多种群粒子群优化(MPSO)的间歇调度算法.该算法采用多种群,增加了种群初始粒子的多样性,在每一代子种群并行进化的过程中引入移民粒子,使子种群之间相互影响和促进,避免算法过早地陷入局部最优,提高了算法的全局搜索能力;每代进化后选出子种群中的优秀粒子作为精华种群,并对其进行变邻域搜索(VNS),进一步提高了算法的收敛精度.通过对不同规模调度问题的仿真,以及与其它算法的对比,证明了该算法解决有限缓冲区多产品厂间歇调度问题的有效性和优越性.     

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.     

An adaptive multi-population genetic algorithm for job-shop scheduling problem

Job-shop scheduling problem (JSP) is a typical NP-hard combinatorial optimization problem and has a broad background for engineering application. Nowadays, the effective approach for JSP is a hot topic in related research area of manufacturing system. However, some JSPs, even for moderate size instances, are very difficult to find an optimal solution within a reasonable time because of the process constraints and the complex large solution space. In this paper, an adaptive multi-population genetic algorithm (AMGA) has been proposed to solve this problem. Firstly, using multi-populations and adaptive crossover probability can enlarge search scope and improve search performance. Secondly, using adaptive mutation probability and elite replacing mechanism can accelerate convergence speed. The approach is tested for some classical benchmark JSPs taken from the literature and compared with some other approaches. The computational results show that the proposed AMGA can produce optimal or near-optimal values on almost all tested benchmark instances. Therefore, we can believe that AMGA can be considered as an effective method for solving JSP.