Multi-objective Job Shop Scheduling Research Articles

Grid-based artificial bee colony algorithm for multi-objective job shop scheduling with manual loading and unloading tasks

This paper investigates a multi-objective job shop scheduling problem with manual loading and unloading tasks (MOJSSPLU) aiming to minimize makespan and total workload simultaneously. Taking human factors into consideration achieves a better balance between production efficiency and resource utilization. To address this problem, we first establish a bi-objective mixed-integer linear programming (MILP) model. Afterward, we combine the artificial bee colony algorithm with the grid technique to develop a grid-based artificial bee colony algorithm (GABC) for solving MOJSSPLU. The algorithm uses a decomposition approach with the earliest-shortest dispatching rule to reduce the complexity of MOJSSPLU. A grid coordinate system is constructed to divide the objective space into cells, facilitating individuals’ location and evaluation in the decision space. Moreover, we focus on improving the cooperation between the employed and onlooker bees and design a mathematical formula based on priority weights to generate onlooker bees to maximize information utilization and improve the exploration and exploitation capabilities of the algorithm. To ensure that the most promising individuals are retained and protected from being eliminated during the evolutionary, we propose an elitist non-dominated solutions reservation strategy for improving the diversity of the population. We further propose a dynamic adjustment of the grid-division method that focuses on improving the exploitation capacity of the algorithm in the objective space to enhance the diversity and convergence of the population. To test the performance of the GABC algorithm, we compare it to the MILP approach and other algorithms using modified benchmark instances. Furthermore, we conduct the Friedman and Wilcoxon nonparametric tests to validate the comparison results among the different algorithms. The computational results demonstrate that the algorithm GABC is efficient.

Automatically evolving preference-based dispatching rules for multi-objective job shop scheduling

Dispatching rules represent a simple heuristic for finding good solutions for job shop scheduling problems. Due to their fast applicability and easy handling, they are often used in manufacturing companies to create appropriate production schedules. It has been shown that dispatching rules that are specifically designed for the requirements of a particular environment improve the performance of schedules. Hyper-heuristics based on genetic programming can be used for the automated generation of such dispatching rules. Evolutionary algorithms search the space of dispatching rule components for the most effective priority function to optimize the performance of the resulting schedule. Various studies have highlighted the advantages in the single-objective case, which made it possible to derive a large number of new dispatching rules that exceeded previous benchmark rules. Because it is usually necessary to consider more than one objective simultaneously to ensure effective creation of schedules, the need for a multi-objective optimization method arises. In this paper, we propose an interactive multi-objective optimization method, namely the reference point method, implemented in a hyper-heuristic genetic programming framework. A decision support system has also been developed and implemented in a web-based application to facilitate interaction with the user. Incorporating preferences into the solution process aims to efficiently evolve a dispatching rule that meets the expectations of a decision-maker. A fictitious experiment was carried out in a benchmark job shop environment. The results show that the final solution selected by the decision-maker can produce schedules achieving a desired compromise between the makespan, total tardiness, and total waiting time. Testing the evolved dispatching rule on an independent set of instances and comparing its performance with other benchmark dispatching rules revealed that the proposed method successfully finds dispatching rules that meet the decision-maker’s expectations and are capable of reproducing similar compromise schedules for unseen problems in the same environment.

Integrating machine layout, transporter allocation and worker assignment into job-shop scheduling solved by an improved non-dominated sorting genetic algorithm

To meet the everchanging production demand and close to the actual scheduling environment, a multi-objective job-shop scheduling problem (MOJSP) with multiple resource constraints is investigated. Specifically, an integrated mathematical model is constructed based on a job-shop scheduling problem (JSP) considering machine layout rearrangement, transporter allocation with capacity limitation, and worker assignment with skill variance to simultaneously minimize the exit time, labor cost, worker workload difference, and transportation time. To tackle the concerned problem, an improved non-dominated sorting genetic algorithm with a hybrid local search (INSGA-HLS) is designed. In the numerical simulation, a test dataset is first constructed according to the literature. Second, an orthogonal experiment is utilized to find the best combination of key parameters for INSGA-HLS. Third, the exploitation competence of the proposed hybrid local search (HLS) is verified. Then, the superiority of the designed INSGA-HLS algorithm is demonstrated by comparing it with the other intelligent algorithms. Thereafter, the influence of three considered factors on the integrated scheduling problem is illustrated: (1) flexible machine layout rearrangement may reduce the handling time, and improve production efficiency to some extent; (2) transporter capacity limitation can prolong the transport time, which extends the exit time; and (3) worker assignment with skill variance can not only improve productivity and reduce the labor cost, but also narrow the workload difference to improve employee satisfaction. Finally, an actual production line application further verifies the practicability and benefit of the model, and the managerial significance is analyzed.

Surrogate-assisted automatic evolving of dispatching rules for multi-objective dynamic job shop scheduling using genetic programming

Dispatching rules are simple but efficient heuristics to solve multi-objective job shop scheduling problems, particularly useful to face the challenges of dynamic shop environments. A promising method to automatically evolve non-dominated rules represents multi-objective genetic programming based hyper-heuristic (MO-GP-HH). The aim of such methods is to approximate the Pareto front of non-dominated dispatching rules as good as possible in order to provide a sufficient set of efficient solutions from which the decision maker can select the most preferred one. However, one of the main drawbacks of existing approaches is the computational demanding simulation-based fitness evaluation of the evolving rules. To efficiently allocate the computational budget, surrogate models can be employed to approximate the fitness. Two possible ways, that estimate the fitness either based on a simplified problem or based on samples of fully evaluated individuals making use of machine learning techniques are investigated in this paper. Several representatives of both categories are first examined with regard to their selection accuracy and execution time. Furthermore, we developed a surrogate-assisted MO-GP-HH framework, incorporating a pre-selection task in the NSGA-II algorithm. The most promising candidates are consequently implemented in the framework. Using a dynamic job shop scenario, the two proposed algorithms are compared to the original one without using surrogates. With the aim to minimize the mean flowtime and maximum tardiness, experimental results demonstrate that the proposed algorithms outperform the former. Making use of surrogates leads to a reduction in computational costs of up to 70%. Another interesting finding shows that the enhanced ability to identify duplicates based on the phenotypic characterization of individuals is particularly helpful in increasing diversity within a population. This study illustrates the positive effect of this mechanism on the exploration of the entire Pareto front.

Energy-Aware Multi-Objective Job Shop Scheduling Optimization with Metaheuristics in Manufacturing Industries: A Critical Survey, Results, and Perspectives

In recent years, the application of artificial intelligence has been revolutionizing the manufacturing industry, becoming one of the key pillars of what has been called Industry 4.0. In this context, we focus on the job shop scheduling problem (JSP), which aims at productions orders to be carried out, but considering the reduction of energy consumption as a key objective to fulfill. Finding the best combination of machines and jobs to be performed is not a trivial problem and becomes even more involved when several objectives are taken into account. Among them, the improvement of energy savings may conflict with other objectives, such as the minimization of the makespan. In this paper, we provide an in-depth review of the existing literature on multi-objective job shop scheduling optimization with metaheuristics, in which one of the objectives is the minimization of energy consumption. We systematically reviewed and critically analyzed the most relevant features of both problem formulations and algorithms to solve them effectively. The manuscript also informs with empirical results the main findings of our bibliographic critique with a performance comparison among representative multi-objective evolutionary solvers applied to a diversity of synthetic test instances. The ultimate goal of this article is to carry out a critical analysis, finding good practices and opportunities for further improvement that stem from current knowledge in this vibrant research area.

Optimising the job-shop scheduling problem using a multi-objective Jaya algorithm

This paper presents an effective multi-objective Jaya (EMOJaya) algorithm to solve a multi-objective job-shop scheduling problem, aiming to simultaneously minimise the makespan, total flow time and mean tardiness. A strategy based on grey entropy parallel analysis (GEPA) is developed to assess and select solutions during the search process. To obtain a high-quality reference sequence for GEPA, an opposition-based learning (OBL) strategy is used in parallel. Additionally, the OBL strategy is incorporated into Jaya’s search operation and external archive to enhance the search ability and convergence rate of the algorithm. Computational experiments based on 30 benchmark instances with different scales confirm that GEPA and OBL can significantly improve the performance of our proposed EMOJaya. Experimental results also show that EMOJaya is able to outperform three state-of-the-art multi-objective algorithms in solving the problem at hand in terms of convergence, diversity and distribution. Further, EMOJaya can obtain more high-quality scheduling schemes, which provide more and better options for decision makers.

A hybrid intelligent algorithm for a fuzzy multi-objective job shop scheduling problem with reentrant workflows and parallel machines

This paper presents a multi-objective mathematical model for a flexible job shop scheduling problem (FJSSP) with fuzzy processing times, which is solved by a hybrid intelligent algorithm (HIA). This problem contains a combination of a classical job shop problem with parallel machines (JSPM) to provide flexibility in the production route. Despite the previous studies, the number of parallel machines is not pre-specified in this paper. This constraint with other ones (e.g., sequence-dependent setup times, reentrant workflows, and fuzzy variables) makes the given problem more complex. To solve such a multi-objective JSPM, Pareto-based optimization algorithms based on multi-objective meta-heuristics and multi-criteria decision making (MCDM) methods are utilized. Then, different comparison metrics (e.g., quality, mean ideal distance, and rate of achievement simultaneously) are used. Also, this paper includes two major phases to provide a new model of the FJSSP and introduce a new proposed HIA for solving the presented model, respectively. This algorithm is a hybrid genetic algorithm with the SAW/TOPSIS method, namely HGASAW/HGATOPSIS. The comparative results indicate that HGASAW and HGATOPSIS outperform the non-dominated sorting genetic algorithm (NSGA-II) to tackle the fuzzy multi-objective JSPM.

Metaheuristic for Solving Multi-Objective Job Shop Scheduling Problem in a Robotic Cell

This paper deals with the multi-objective job shop scheduling problem in a robotic cell (MOJRCSP). All the jobs are processed according to their operations order on workstations. Different from classical job shop scheduling problem, the studied problem considers that jobs' transportation is handled by a robot. Also, the jobs are expected to be finished in a time window, instead of a constant due date. A mixed Integer Programming (MIP) model is proposed to formulate this problem. Due to the special characteristics of the studied problem and its NP-hard computational complexity, a metaheuristic based on Teaching Learning Based Optimization (TLBO) algorithm has been proposed. The proposed algorithm determines simultaneously the operations' assignments on workstations, the robot assignments for transportation operations, and the robot moving sequence. The objective is to minimize the makespan and the total earliness and tardiness. Computational results further validated the effectiveness and robustness of our proposed algorithm.

An effective memetic algorithm for multi-objective job-shop scheduling

This paper presents an effective memetic algorithm (EMA) to solve the multi-objective job shop scheduling problem. A new hybrid crossover operator is designed to enhance the search ability of the proposed EMA and avoid premature convergence. In addition, a new effective local search approach is proposed and integrated into the EMA to improve the speed of the algorithm and fully exploit the solution space. Experimental results show that our improved EMA is able to easily obtain better solutions than the best-known solutions for about 95% of the tested difficult problem instances that are widely used in the literature, demonstrating its superior performance both in terms of solution quality and computational efficiency.

Optimization of Multi-objective Job-shop Scheduling under Uncertain Environment

Optimization of Multi-objective Job-shop Scheduling under Uncertain Environment

A Meta-Model-Based Multi-Objective Evolutionary Approach to Robust Job Shop Scheduling

In the real-world manufacturing system, various uncertain events can occur and disrupt the normal production activities. This paper addresses the multi-objective job shop scheduling problem with random machine breakdowns. As the key of our approach, the robustness of a schedule is considered jointly with the makespan and is defined as expected makespan delay, for which a meta-model is designed by using a data-driven response surface method. Correspondingly, a multi-objective evolutionary algorithm (MOEA) is proposed based on the meta-model to solve the multi-objective optimization problem. Extensive experiments based on the job shop benchmark problems are conducted. The results demonstrate that the Pareto solution sets of the MOEA are much better in both convergence and diversity than those of the algorithms based on the existing slack-based surrogate measures. The MOEA is also compared with the algorithm based on Monte Carlo approximation, showing that their Pareto solution sets are close to each other while the MOEA is much more computationally efficient.

Research on Multi-objective Job Shop Scheduling with Dual Particle Swarm Algorithm Based on Greedy Strategy

In order to solve the multi-objective job shop scheduling problem effectively, this paper proposes a greedy strategy to establish the mathematical model of minimizing the maximum completion time, the average flow time and the machine idle time. The algorithm sets up a dual-population structure: leading-population and searching-population. Firstly, the algorithm calculates the fitness values of every particle for each population for the three objectives, and the optimize solutions will be incorporated in the individual optimal value set and the global optimal value set accordingly. Then the algorithm performs a crossover operation which includes two types: one is the leading-cross to lead the searching-population to convergence to the optimal solution quickly, and the other is intro-population crossover of each population in order to increase the diversity of individuals. The mutation operation of each population is followed to further enhance the diversity of individuals. And the simulated annealing algorithm is employed to avoid the algorithm falling into the local optimum effectively. The simulation experiments of various scale instances are carried out and compared with the simulation results of the other two popular algorithms to verify the effectiveness of the algorithm. The simulation results show that the proposed algorithm is superior to the other two algorithms in both the quality of the solution and the time-consuming.

Dynamic Priority Rule Selection for Solving Multi-objective Job Shop Scheduling Problems

In this paper, a new approach has been suggested for solving the multi-objective job shop scheduling problem, in which, simple priority rules are used dynamically, according to the varied state of the scheduling environment. The rules assign priority to the jobs that waiting in queues based on their features and/or the scheduling environment. Since the real scheduling environments are generally dynamic, it is better to use different rules during the scheduling according to the state of the shop floor at each decision time. Based on this approach, a new algorithm is designed, which uses different rules over the scheduling time. This approach can be easily applied to solve the real scheduling problems of the manufacturing systems. The algorithm has been compared with some classic rules from the literature. The results show that the proposed approach is more effective than using a fixed priority rule.

Reduction of carbon emission and total late work criterion in job shop scheduling by applying a multi-objective imperialist competitive algorithm

New environmental regulations have driven companies to adopt low-carbon manufacturing. This research is aimed at considering carbon dioxide in the operational decision level where limited studies can be found, especially in the scheduling area. In particular, the purpose of this research is to simultaneously minimize carbon emission and total late work criterion as sustainability-based and classical-based objective functions, respectively, in the multiobjective job shop scheduling environment. In order to solve the presented problem more effectively, a new multiobjective imperialist competitive algorithm imitating the behavior of imperialistic competition is proposed to obtain a set of non-dominated schedules. In this work, a three-fold scientific contribution can be observed in the problem and solution method, that are: (1) integrating carbon dioxide into the operational decision level of job shop scheduling, (2) considering total late work criterion in multi-objective job shop scheduling, and (3) proposing a new multi-objective imperialist competitive algorithm for solving the extended multi-objective optimization problem. The elements of the proposed algorithm are elucidated and forty three small and large sized extended benchmarked data sets are solved by the algorithm. Numerical results are compared with two well-known and most representative metaheuristic approaches, which are multi-objective particle swarm optimization and non-dominated sorting genetic algorithm II, in order to evaluate the performance of the proposed algorithm. The obtained results reveal the effectiveness and efficiency of the proposed multi-objective imperialist competitive algorithm in finding high quality non-dominated schedules as compared to the other metaheuristic approaches

An improved island model memetic algorithm with a new cooperation phase for multi-objective job shop scheduling problem

This work proposes an improved island model memetic algorithm with a new naturally inspired cooperation phase (IIMMA) for multi-objective job shop scheduling problem. Three objective functions: makespan, total weighted tardiness, and total weighted earliness are considered using the weighting approach. The new cooperation phase is mainly used to improve the exploitation capabilities of an island model memetic algorithm. It is based on the following novel idea. Individuals who have recently performed self-adaptation phases (local search) do not exchange their knowledge about the search space just randomly; instead, they firstly divide their current knowledge into two parts: already existed knowledge and recently acquired knowledge, and secondly exchange their knowledge in favor of the recently acquired one. This is simulated by means of an improved version of the well-known uniform crossover, which uses the history of parents’ evolution to identify the new traits among the old ones, and then to construct the mask vectors that determine the exchanged genetic materials accordingly. Additionally, several straightforward but effective techniques are applied to improve the exploration capabilities as well, such as a diversity-based population creation method, an incest prevention-based tournament selection method, and a similarity-and-quality based replacement method. The presented algorithm is evaluated on 72 benchmarks, with the new components, and without them using the traditional alternatives, and also against similar works found in the literature. The computational results validate the improvements accomplished by the new components, and show its effectiveness and robustness.

An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t-tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms.

AIS-SFHM APPROACH FOR OPTIMIZATION OF MULTI OBJECTIVE JOB SHOP PROBLEMS

The n-job, m-machine Job shop scheduling (JSP) problem is one of the general production scheduling problems. The JSP problem is a scheduling problem, where a set of ‘n’ jobs must be processed or assembled on a set of ‘m’ dedicated machines. Each job consists of a specific set of operations, which have to be processed according to a given technical precedence order. Job shop scheduling problem is a NP-hard combinatorial optimization problem.  In this paper, optimization of three practical performance measures mean job flow time, mean job tardiness and makespan are considered. The hybrid approach of Sheep Flocks Heredity Model Algorithm (SFHM) is used for finding optimal makespan, mean flow time, mean tardiness. The hybrid SFHM approach is tested with multi objective job shop scheduling problems. Initial sequences are generated with Artificial Immune System (AIS) algorithm and results are refined using SFHM algorithm. The results show that the hybrid SFHM algorithm is an efficient and effective algorithm that gives better results than SFHM Algorithm, Genetic Algorithm (GA). The proposed hybrid SFHM algorithm is a good problem-solving technique for job shop scheduling problem with multi criteria.

Approach of hybrid GA for multi-objective job-shop scheduling

In recent years, scholars have made many research results on job-shop scheduling (JSP) problem, especially in single objective such as the maximum completion time. But most of the actual system scheduling problems are more than one object. Therefore, the research of multi-objective scheduling problem is very important and meaningful. In this paper, we proposed a multi-objective scheduling model which adopts weighted sum method to optimize two important indexes (makespan and total flow time). Genetic algorithm (GA) has diversified global search ability, while simulated annealing (SA) combined with tabu search (TS) have intensified capabilities in local neighborhood search. To overcome the drawback of the GA, we proposed a new hybrid GA (NewHGA) which produces initial solutions by GA firstly, and then take SA operator incorporate TS operator to search in the local space. By adding the novel local search strategy, the diversity of solutions will be improved greatly so that it can ensure the algorithm jump out of the local optimal value. We test this algorithm using the benchmark instances of different sizes taken from the OR-Library, and the results show that the algorithm is efficient than another hybrid algorithm.

An improved MOEA/D for multi-objective job shop scheduling problem

In this article, an improved multi-objective evolutionary algorithm, which is based on decomposition (IMOEA/D) for multi-objective job shop scheduling problem, is proposed to solve multiple objectives job shop scheduling problems. Three minimisation objectives – the maximum completion time (makespan), the total flow time and the tardiness time are considered simultaneously. In the proposed algorithm, several prior rules are presented to construct the initial population with a high level of quality. Meanwhile, according to the contribution of each operator to the external archive, an adaptive mechanism is adopted to select corresponding operators to generate new solutions, which can accelerate convergence speed. Simulation results on the standard test instances show that IMOEA/D has a better convergence performance compared with multi-objective evolutionary algorithms based on Pareto dominance.

An Artificial Bee Colony Approach for Multi-objective Job Shop Scheduling

Scheduling is the proper allocation of resources over a period for performing a set of tasks with the objective of optimizing one or more performance measures. The actual assignment of starting and completion times of operations on jobs, if the manufacturing order is to be completed on time is known as Production scheduling. The Job Shop Scheduling Problem (JSSP) is one of the most difficult scheduling problems. Since JSSP is NP-complete, that is, the selection of the best scheduling solution is not polynomially bounded, heuristic approaches are often considered. This is an important practical problem in the field of production management and combinatorial optimization. Inspired by the decision-making capability of bee swarms in the nature, this paper proposes an efficient scheduling method based on Artificial Bee Colony (ABC) for solving the JSSP. Most of the researchers in production scheduling are concerned with the optimization of a single criterion. However, the performance of a schedule often involves more than one aspect and, therefore requires a multi-objective treatment. Minimization of makespan and total tardiness are the two performance measures considered in this paper. The Artificial Bee Colony algorithm was coded in MATLAB 2009. A parameter analysis was done to fix the control parameters of Artificial Bee Colony algorithm. The performance of the algorithm was analyzed on the benchmark problems provided by E. Taillard.