Multi-objective Job Shop Scheduling Problem 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.

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.

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.

Chaotic Multi-Objective Simulated Annealing and Threshold Accepting for Job Shop Scheduling Problem

The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best algorithms. However, in Multi-Objective JSSP (MOJSSP), these algorithms have barely been analyzed, and the Threshold Accepting Algorithm has not been published for this problem. It is worth mentioning that the researchers in this area have not reported studies with more than three objectives, and the number of metrics they used to measure their performance is less than two or three. In this paper, we present two MOJSSP metaheuristics based on Simulated Annealing: Chaotic Multi-Objective Simulated Annealing (CMOSA) and Chaotic Multi-Objective Threshold Accepting (CMOTA). We developed these algorithms to minimize three objective functions and compared them using the HV metric with the recently published algorithms, MOMARLA, MOPSO, CMOEA, and SPEA. The best algorithm is CMOSA (HV of 0.76), followed by MOMARLA and CMOTA (with HV of 0.68), and MOPSO (with HV of 0.54). In addition, we show a complexity comparison of these algorithms, showing that CMOSA, CMOTA, and MOMARLA have a similar complexity class, followed by MOPSO.

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.

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.

A multi-strategy integration Pareto based artificial colony algorithm for multi-objective flexible job shop scheduling problem with the earliness & tardiness criterion

A multi-strategy integration Pareto based artificial colony algorithm for multi-objective flexible job shop scheduling problem with the earliness & tardiness criterion

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.

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.

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.

Particle swarm optimization with variable neighborhood search for multiobjective flexible job shop scheduling problem

The simulation on benchmarks is a very simple and efficient method to evaluate the performance of the algorithm for solving flexible job shop scheduling model. Due to the assignment and scheduling decisions, flexible job shop scheduling problem (FJSP) becomes extremely hard to solve for production management. A discrete multi-objective particle swarm optimization (PSO) and simulated annealing (SA) algorithm with variable neighborhood search is developed for FJSP with three criteria: the makespan, the total workload and the critical machine workload. Firstly, a discrete PSO is designed and then SA algorithm performs variable neighborhood search integrating two neighborhoods on public critical block to enhance the search ability. Finally, the selection strategy of the personal-best individual and global-best individual from the external archive is developed in multi-objective optimization. Through the experimental simulation on matlab, the tests on Kacem instances, Brdata instances and BCdata instances show that the modified discrete multi-objective PSO algorithm is a promising and valid method for optimizing FJSP with three criteria.

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.

Two-generation Pareto ant colony algorithm for multi-objective job shop scheduling problem with alternative process plans and unrelated parallel machines

The flexibilities of alternative process plans and unrelated parallel machines are benefit for the optimization of the job shop scheduling problem, but meanwhile increase the complexity of the problem. This paper constructs the mathematical model for the multi-objective job shop scheduling problem with alternative process plans and unrelated parallel machines, splits the problem into two sub-problems, namely flexible processing route decision and task sorting, and proposes a two-generation (father and children) Pareto ant colony algorithm to generate a feasible scheduling solution. The father ant colony system solves the flexible processing route decision problem, which selects the most appropriate process node set from the alternative process node set. The children ant colony system solves the sorting problem of the process task set generated by the father ant colony system. The Pareto ant colony system constructs the applicable pheromone matrixes and heuristic information with respect to the sub-problems and objectives. And NSGAII is used as comparison whose genetic operators are re-defined. The experiment confirms the validation of the proposed algorithm. By comparing the result of the algorithm to NSGAII, we can see the proposed algorithm has a better performance.

Applying an Intelligent Dynamic Genetic Algorithm for Solving a Multi-Objective Flexible Job Shop Scheduling Problem with Maintenance Considerations

In this paper, a multi-objective flexible dynamic job shop scheduling problem (MO-FDJSPM) with maintenance constraint is studied. The objectives of the scheduling are maximizing the completion time, mean job rotation time and mean components' tardiness. Also, in order to adapt with the internal disruptions of the manufacturing system, such as breakdown of existing machines, we consider the machines availability (so called maintenance) as a constraint. The multi-objective mathematical model is formulated and a genetic algorithm (GA) with dynamic bidimensional chromosomes along with a heuristic algorithm to handle maintenance sub-problem is developed as solution approach. In proposed algorithm, since the control parameters change intelligently and dynamically during implementation and optimization process, the early convergence and trapping in local optimum are reduced leading to performance improvement. The performance of the proposed approach is evaluated with respect to convergence speed and solutions quality. The results of computations verify and confirm both two evaluation criteria.

Multi-objective job shop scheduling problem with sequence dependent setup times using a novel metaheuristic

The job shop problem is the most complicated and typical problem of all kinds of production scheduling problems, the allocation of resources over time to perform a collection of tasks. This paper studies multi-objective job shop scheduling problems where the setup times is sequence dependent to minimise two objective functions simultaneously. Since the problem is NP-hard and difficult to find an optimal solution in a reasonable computational time an efficient multi-objective electromagnetism algorithm (MOEA) is presented as the solution procedure. An electromagnetism algorithm is known as a flexible and effective population-based algorithm utilising an attraction/repulsion mechanism to move the particles towards optimality. The algorithm is carefully evaluated for its performance against two available algorithms by means of multi-objective performance measures and statistical tools. All the results demonstrate that our MOEA is very effective for the problem.

Cultural-Based Genetic Tabu Algorithm for Multiobjective Job Shop Scheduling

The job shop scheduling problem, which has been dealt with by various traditional optimization methods over the decades, has proved to be an NP-hard problem and difficult in solving, especially in the multiobjective field. In this paper, we have proposed a novel quadspace cultural genetic tabu algorithm (QSCGTA) to solve such problem. This algorithm provides a different structure from the original cultural algorithm in containing double brief spaces and population spaces. These spaces deal with different levels of populations globally and locally by applying genetic and tabu searches separately and exchange information regularly to make the process more effective towards promising areas, along with modified multiobjective domination and transform functions. Moreover, we have presented a bidirectional shifting for the decoding process of job shop scheduling. The computational results we presented significantly prove the effectiveness and efficiency of the cultural-based genetic tabu algorithm for the multiobjective job shop scheduling problem.