Multi-objective Flexible Job Shop Scheduling Research Articles

Flexible job-shop scheduling with tolerated time interval and limited starting time interval based on hybrid discrete PSO-SA: An application from a casting workshop

In this paper, we addressed two significant characteristics in practical casting production, namely tolerated time interval (TTI) and limited starting time interval (LimSTI). With the consideration of TTI and LimSTI, a multi-objective flexible job-shop scheduling model is constructed to minimize total overtime of TTI, total tardiness and maximum completion time. To solve this model, we present a hybrid discrete particle swarm optimization integrated with simulated annealing (HDPSO-SA) algorithm which is decomposed into global and local search phases. The global search engine based on discrete particle swarm optimization includes two enhancements: a new initialization method to improve the quality of initial population and a novel gBest selection approach based on extreme difference to speed up the convergence of algorithm. The local search engine is based on simulated annealing algorithm, where four neighborhood structures are designed under two different local search strategies to help the proposed algorithm jump over the trap of local optimal solution. Finally, computational results of a real-world case and simulation data expanded from benchmark problems indicate that our proposed algorithm is significant in terms of the quality of non-dominated solutions compared to other algorithms.

An Imperialist Competitive Algorithm With the Diversified Operators for Many-Objective Scheduling in Flexible Job Shop

A number of related works have been done on multi-objective flexible job shop scheduling problem, however, many-objective flexible job shop scheduling problems (MaOFJSP) with at least four objectives are seldom considered. In this paper, an imperialist competitive algorithm with the diversified operators (DOICA) is proposed for MaOFJSP with the minimization of makespan, total tardiness, total workload, and total energy consumption. In DOICA, the diversified assimilation and revolution are used according to the features of empires, a novel imperialist competition is implemented by excluding the strongest empire and doing multiple neighborhood search of a solution in the strongest empire. The extensive experiments are conducted by using a number of benchmark instances to test the impact of strategies of DOICA on its performance and compare DOICA with other algorithms from literature finally. The computational results validate that the new strategies of DOICA are effective and DOICA can provide promising results for the considered MaOFJSP.

Multi-Agent Based Hyper-Heuristics for Multi-Objective Flexible Job Shop Scheduling: A Case Study in an Aero-Engine Blade Manufacturing Plant

In the paper, a case study focusing on multi-objective flexible job shop scheduling problem (MO-FJSP) in an aero-engine blade manufacturing plant is presented. The problem considered in this paper involves many attributes, including working calendar, due dates, and lot size. Moreover, dynamic events occur frequently in the shop-floor, making the problem more challenging and requiring real-time responses. Therefore, the priority-based methods are more suitable than the computationally intensive search-based methods for the online scheduling. However, developing an effective heuristic for online scheduling problem is a tedious work even for domain experts. Furthermore, the domain knowledge of the practical production scheduling needs to be integrated into the algorithm to guide the search direction, accelerate the convergence of the algorithm, and improve the solution quality. To this end, three multi-agent-based hyper-heuristics (MAHH) integrated with the prior knowledge of the shop floor are proposed to evolve scheduling policies (SPs) for the online scheduling problem. To evaluate the performance of evolved SPs, a 5-fold cross-validation method which is frequently used in machine learning is adopted to avoid the overfitting problem. Both the training and test results demonstrate that the bottleneck-agent-based hyper-heuristic method produces the best result among the three MAHH methods. Furthermore, both the effectiveness and the efficiency of the evolved SPs are verified by comparison with the well-known heuristics and two multi-objective particle swarm optimization (MOPSO) algorithms on the practical case. The proposed method has been embedded in the manufacturing execution system that is built on JAVA and successfully applied in several manufacturing plants.

A Hybrid Multi-Objective Evolutionary Algorithm With Heuristic Adjustment Strategies and Variable Neighbor-Hood Search for Flexible Job-Shop Scheduling Problem Considering Flexible Rest Time

With the development of society, people have a higher demand for the work environment. It has aroused extensive attention of enterprises. One of the most important demands for workers is to have enough rest time to regain strength and energy during the working day. In this paper, a comprehensive mathematical model is established for the multi-objective flexible job-shop scheduling problem with flexible rest time (MOFJSP-FRT). Then a hybrid multi-objective evolutionary algorithm (MOEA) with heuristic adjustment strategies and variable neighborhood search (VNS), named HMOEAV, is proposed to solve the MOFJSP-FRT with the objectives to minimize the makespan and the machines loads balancing simultaneously. In the proposed hybrid algorithm, the machine-based encoding scheme is designed to improve search effectiveness by reducing computational complexity. Two heuristic adjustment strategies considering both the problem characteristics and the objective features are employed to initialize a high-quality population. To adequately emphasize the local exploitation ability of MOEA, VNS is incorporated into it. The non-dominated solutions got by MOEA are the initial solutions for VNS, in which three types of neighborhood structures according to problem structures are designed. The practical case in a steel structure enterprise is carried out to demonstrate the effectiveness of the proposed model and hybrid algorithm. The influences of rest time length on the MOFJSP-FRT are analyzed to give enterprises new insights to improve the scheduling efficiency while ensuring that employees have enough time to rest.

Hybrid heuristic algorithm for multi-objective scheduling problem

This research provides academic and practical contributions. From a theoretical standpoint, a hybrid harmony search (HS) algorithm, namely the oppositional global-based HS (OGHS), is proposed for solving the multi-objective flexible job-shop scheduling problems (MOFJSPs) to minimize makespan, total machine workload and critical machine workload. An initialization program embedded in opposition-based learning (OBL) is developed for enabling the individuals to scatter in a well-distributed manner in the initial harmony memory (HM). In addition, the recursive halving technique based on opposite number is employed for shrinking the neighbourhood space in the searching phase of the OGHS. From a practice-related standpoint, a type of dual vector code technique is introduced for allowing the OGHS algorithm to adapt the discrete nature of the MOFJSP. Two practical techniques, namely Pareto optimality and technique for order preference by similarity to an ideal solution (TOPSIS), are implemented for solving the MOFJSP. Furthermore, the algorithm performance is tested by using different strategies, including OBL and recursive halving, and the OGHS is compared with existing algorithms in the latest studies. Experimental results on representative examples validate the performance of the proposed algorithm for solving the MOFJSP.

An improved SFLA for flexible job shop scheduling problem considering energy consumption

In this paper, a multi-objective flexible job shop scheduling problem (MOFJSP) was studied systematically. A novel energy-saving scheduling model was established based on considering makespan and total energy consumption simultaneously. Different from previous studies, four types of energy consumption were considered in this model, including processing energy, idle energy, transport energy, and turn-on/off energy. In addition, a turn-off strategy is adopted for energy-saving. A modified shuffled frog-leaping algorithm (SFLA) was applied to solve this model. Moreover, operators of multi-point crossover and neighborhood search were both employed to obtain optimal solutions. Experiments were conducted to verify the performance of the SFLA compared with a non-dominated sorting genetic algorithm with blood variation (BVNSGA-II). The results show that this algorithm and strategy are very effective.

An improved bacterial foraging optimization for multi-objective flexible job-shop scheduling problem

An improved bacterial foraging optimization for multi-objective flexible job-shop scheduling problem

Extracting priority rules for dynamic multi-objective flexible job shop scheduling problems using gene expression programming

In this paper, two new approaches are proposed for extracting composite priority rules for scheduling problems. The suggested approaches use simulation and gene expression programming and are able to evolve specific priority rules for all dynamic scheduling problems in accordance with their features. The methods are based on the idea that both the proper design of the function and terminal sets and the structure of the gene expression programming approach significantly affect the results. In the first proposed approach, modified and operational features of the scheduling environment are added to the terminal set, and a multigenic system is used, whereas in the second approach, priority rules are used as automatically defined functions, which are combined with the cellular system for gene expression programming. A comparison shows that the second approach generates better results than the first; however, all of the extracted rules yield better results than the rules from the literature, especially for the defined multi-objective function consisting of makespan, mean lateness and mean flow time. The presented methods and the generated priority rules are robust and can be applied to all real and large-scale dynamic scheduling problems.

An effective hybrid algorithm for multi-objective flexible job-shop scheduling problem

Genetic algorithm is one of primary algorithms extensively used to address the multi-objective flexible job-shop scheduling problem. However, genetic algorithm converges at a relatively slow speed. By hybridizing genetic algorithm with particle swarm optimization, this article proposes a teaching-and-learning-based hybrid genetic-particle swarm optimization algorithm to address multi-objective flexible job-shop scheduling problem. The proposed algorithm comprises three modules: genetic algorithm, bi-memory learning, and particle swarm optimization. A learning mechanism is incorporated into genetic algorithm, and therefore, during the process of evolution, the offspring in genetic algorithm can learn the characteristics of elite chromosomes from the bi-memory learning. For solving multi-objective flexible job-shop scheduling problem, this study proposes a discrete particle swarm optimization algorithm. The population is partitioned into two subpopulations for genetic algorithm module and particle swarm optimization module. These two algorithms simultaneously search for solutions in their own subpopulations and exchange the information between these two subpopulations, such that both algorithms can complement each other with advantages. The proposed algorithm is evaluated on some instances, and experimental results demonstrate that the proposed algorithm is an effective method for multi-objective flexible job-shop scheduling problem.

A cloud based improved method for multi-objective flexible job-shop scheduling problem

A cloud based improved method for multi-objective flexible job-shop scheduling problem

A Comparison between Two Modified NSGA-II Algorithms for Solving the Multi-objective Flexible Job Shop Scheduling Problem

Many evolutionary algorithms have been used to solve multi-objective scheduling problems. NSGA-II is one of them that is based on the Pareto optimality concept and generally obtains good results. However, it is possible to improve its performance with some modifications. In this paper, two modified NSGA-II algorithms have been suggested for solving the multi-objective flexible job shop scheduling problem. The neighborhood structures defined for the problem are integrated into the algorithms to create better generations during the iterations. Also, their initial populations are created with an effective heuristic. In the first modified NSGA-II, after the creation of the offspring population, a neighbor of each individual in the parent population is constructed, and then one of them is selected according to the domination state of the solutions. Then the populations are merged to create a new population. In the second modified NSGA-II, only the solutions on the first and second fronts of the parent population and also their neighbors are merged with the offspring population. Other operators of the algorithms like the non-dominated sorting and calculating the crowding distances are as the classic NSGA-II. A comparison is done with a classic NSGA-II based on two metrics. The results show that as it is in the first modified NSGA-II, including neighbors of more individuals of the population provides better results because it increases diversity and intensity of the search. The performance of the second modified NSGA-II is almost similar to the NSGA-II. So, it can be concluded that although integrating the neighborhood structures can improve the performance of search, it is better to define that the structures should be applied to how many and which solutions, in otherwise the quality of search may not increase.

Multi-objective Flexible Job Shop Scheduling based on Improved NSGA2 Algorithm

Multi-objective Flexible Job Shop Scheduling based on Improved NSGA2 Algorithm

Flexible Job-Shop Scheduling for Reduced Manufacturing Carbon Footprint

In order to help manufacturing companies quantify and reduce product carbon footprints in a mixed model manufacturing system, a product carbon footprint-oriented multi-objective flexible job-shop scheduling optimization model is proposed. The production portion of the product carbon footprint, based on the mapping relations between products and the carbon emissions within the manufacturing system, is proposed to calculate the product carbon footprint in the mixed model manufacturing system. Nondominated sorting genetic algorithm-II (NSGA-II) is adopted to solve the proposed model. In order to help decision makers to choose the most suitable solution from the Pareto set as its execution solution, a method based on grades of product carbon footprints is proposed. Finally, the efficacy of the proposed model and algorithm are examined via a case study.

A Two-Phase Meta-Heuristic for Multiobjective Flexible Job Shop Scheduling Problem With Total Energy Consumption Threshold

Flexible job shop scheduling problem (FJSP) has been extensively considered; however, multiobjective FJSP with energy consumption threshold is seldom investigated, the goal of which is to minimize makespan and total tardiness under the constraint that total energy consumption does not exceed a given threshold. Energy constraint is not always met and the threshold is difficult to be decided in advance. These features make it more difficult to solve the problem. In this paper, a two-phase meta-heuristic (TPM) based on imperialist competitive algorithm (ICA) and variable neighborhood search (VNS) is proposed. In the first phase, the problem is converted into FJSP with makespan, total tardiness and total energy consumption and the new FJSP is solved by an ICA, which uses some new methods to build initial empires and do imperialist competition. In the second phase, new strategies are provided for comparing solutions and updating the nondominated set of the first phase and a VNS is used for the original problem. The current solution of VNS is periodically replaced with member of the set Ω to improve solution quality. An energy consumption threshold is obtained by optimization. Extensive experiments are conducted to test the performance of TPM finally. The computational results show that TPM is a very competitive algorithm for the considered FJSP.

A memetic algorithm for multi-objective flexible job-shop problem with worker flexibility

In existing scheduling models, the flexible job-shop scheduling problem mainly considers machine flexibility. However, human factor is also an important element existing in real production that is often neglected theoretically. In this paper, we originally probe into a multi-objective flexible job-shop scheduling problem with worker flexibility (MO-FJSPW). A non-linear integer programming model is presented for the problem. Correspondingly, a memetic algorithm (MA) is designed to solve the proposed MO-FJSPW whose objective is to minimise the maximum completion time, the maximum workload of machines and the total workload of all machines. A well-designed chromosome encoding/decoding method is proposed and the adaptive genetic operators are selected by experimental studies. An elimination process is executed to eliminate the repeated individuals in population. Moreover, a local search is incorporated into the non-dominated sorting genetic algorithm II. In experimental phase, the crossover operator and elimination operator in MA are examined firstly. Afterwards, some extensive comparisons are carried out between MA and some other multi-objective algorithms. The simulation results show that the MA performs better for the proposed MO-FJSPW than other algorithms.

Game theory based real-time multi-objective flexible job shop scheduling considering environmental impact

Production scheduling greatly contributes to optimising the allocation of processes, reducing resource and energy consumption, lowering production costs and alleviating environmental pollution. It is an effective way to progress towards green manufacturing. With the extensive use of the Internet of Things in the manufacturing shop floor, a huge amount of real-time data is created. A typical challenge is how to achieve the real-time data-driven optimisation for the manufacturing shop floor to improve energy efficiency and production efficiency. To address this problem, a dynamic game theory based two-layer scheduling method was developed to reduce makespan, the total workload of machines and energy consumption to achieve real-time multi-objective flexible job shop scheduling. To obtain an optimal solution, a sub-game perfect Nash equilibrium solution was designed. Then, a case study was employed to analyse the performance of the proposed method. The results showed that the makespan, the total workload of machines and energy consumption were reduced by 4.5%, 8.75%, and 9.3% respectively. These improvements can contribute to sustainable development and cleaner production of manufacturing industry.

Multi-objective flexible job shop scheduling problem using variable neighborhood evolutionary algorithm

In this paper, multi-objective flexible job shop scheduling problem (MOFJSP) was studied with the objects to minimize makespan, total workload and critical workload. A variable neighborhood evolutionary algorithm (VNEA) was proposed to obtain a set of Pareto optimal solutions. First, two novel crowded operators in terms of the decision space and object space were proposed, and they were respectively used in mating selection and environmental selection. Then, two well-designed neighborhood structures were used in local search, which consider the problem characteristics and can hold fast convergence. Finally, extensive comparison was carried out with the state-of-the-art methods specially presented for solving MOFJSP on well-known benchmark instances. The results show that the proposed VNEA is more effective than other algorithms in solving MOFJSP.

A Novel Memetic Algorithm Based on Decomposition for Multiobjective Flexible Job Shop Scheduling Problem

A novel multiobjective memetic algorithm based on decomposition (MOMAD) is proposed to solve multiobjective flexible job shop scheduling problem (MOFJSP), which simultaneously minimizes makespan, total workload, and critical workload. Firstly, a population is initialized by employing an integration of different machine assignment and operation sequencing strategies. Secondly, multiobjective memetic algorithm based on decomposition is presented by introducing a local search to MOEA/D. The Tchebycheff approach of MOEA/D converts the three-objective optimization problem to several single-objective optimization subproblems, and the weight vectors are grouped by K-means clustering. Some good individuals corresponding to different weight vectors are selected by the tournament mechanism of a local search. In the experiments, the influence of three different aggregation functions is first studied. Moreover, the effect of the proposed local search is investigated. Finally, MOMAD is compared with eight state-of-the-art algorithms on a series of well-known benchmark instances and the experimental results show that the proposed algorithm outperforms or at least has comparative performance to the other algorithms.

A Bee Evolutionary Guiding Nondominated Sorting Genetic Algorithm II for Multiobjective Flexible Job-Shop Scheduling.

Flexible job-shop scheduling problem (FJSP) is an NP-hard puzzle which inherits the job-shop scheduling problem (JSP) characteristics. This paper presents a bee evolutionary guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) for multiobjective FJSP (MO-FJSP) with the objectives to minimize the maximal completion time, the workload of the most loaded machine, and the total workload of all machines. It adopts a two-stage optimization mechanism during the optimizing process. In the first stage, the NSGA-II algorithm with T iteration times is first used to obtain the initial population N, in which a bee evolutionary guiding scheme is presented to exploit the solution space extensively. In the second stage, the NSGA-II algorithm with GEN iteration times is used again to obtain the Pareto-optimal solutions. In order to enhance the searching ability and avoid the premature convergence, an updating mechanism is employed in this stage. More specifically, its population consists of three parts, and each of them changes with the iteration times. What is more, numerical simulations are carried out which are based on some published benchmark instances. Finally, the effectiveness of the proposed BEG-NSGA-II algorithm is shown by comparing the experimental results and the results of some well-known algorithms already existed.

A hybrid particle swarm optimisation for multi-objective flexible job-shop scheduling problem with dual-resources constrained

In this paper, a hybrid discrete particle swarm algorithm based on maximum fitness function is proposed for a dual-resources constrained flexible job shop scheduling problem with multiple optimisation objectives. An improved position updating mechanism of particles is used to effectively avoid the occurrence of infeasible solution. Additionally, a novel dynamic search strategy is designed to enhance the local exploiting search ability of discrete particle swarms. Finally, simulation results demonstrate that the proposed algorithm effectively decreases both the production time and production cost.