Multi-objective Scheduling Problem Research Articles

Multi-Objective Fuzzy Green Scheduling Optimization Method of Special Vehicle Body-in-White Prototype Shop Considering Equipment Preventive Maintenance

Based on the advantages of non-contact, flexibility, and small heat-affected zone, laser processing technology is widely used in material removal, addition, modification and other manufacturing fields. However, the emission of large amounts of smoke during laser processing of metal materials will result in environmental pollution in the job shop. Additionally, the processing time of laser equipment becomes uncertain as the power decays with prolonged use. Therefore, this paper is mainly focus on a multi-objective flexible job shop fuzzy green scheduling problem to minimize the fuzzy makespan, fuzzy total energy consumption and fuzzy total smoke emission. To solve it, an improved multi-objective particle swarm optimization algorithm has been designed. Firstly, a preventive maintenance strategy is proposed to reduce the makespan and equipment failure frequency by considering periodic power attenuation of laser equipment. Next, different particle updating strategies are employed to enhance particles’ exploration capabilities. Subsequently, five neighborhood structures are introduced to improve the performance of local search. Finally, comparison experiments are conducted with an expanded common benchmark, and a production case study in a special vehicle body-in-white prototype job shop. The results effectively demonstrate the feasibility and effectiveness of the developed model and improved multi-objective particle swarm optimization algorithm.

Solving multi-objective green flexible job shop scheduling problem by an improved chimp optimization algorithm

As environmental contamination becomes more and more severe, enterprises need to consider optimizing environmental criteria while optimizing production criteria. In this study, a multi-objective green flexible job shop scheduling problem (MO_GFJSP) is established with two objective functions: the makespan and the carbon emission. To effectively solve the MO_GFJSP, an improved chimp optimization algorithm (IChOA) is designed. The proposed IChOA has four main innovative aspects: 1) the fast non-dominated sorting (FDS) method is introduced to compare the individuals with multiple objectives and strengthen the solution accuracy. 2) a dynamic convergence factor (DCF) is introduced to strengthen the capabilities of exploration and exploitation. 3) the position weight (PW) is used in the individual position updating to enhance the search efficiency. 4) the variable neighborhood search (VNS) is developed to strengthen the capacity to escape the local optimum. By executing abundant experiments using 20 benchmark instances, it was demonstrated that the developed IChOA is efficient to solve the MO_GFJSP and effective for reducing carbon emission in the flexible job shop.

Multi-policy deep reinforcement learning for multi-objective multiplicity flexible job shop scheduling

This study considers the simultaneous minimization of makespan and total tardiness for the multi-objective multiplicity flexible job shop scheduling problem (MOMFJSP). A deep reinforcement learning framework employing a multi-policy proximal policy optimization algorithm (MPPPO) is developed to solve MOMFJSP. The MOMFJSP is treated as a Markov decision process, allowing an intelligent agent to make sequential decisions based on the current production status. This framework involves multiple policy networks with different objective weight vectors. Using MPPPO, these networks are optimized simultaneously to obtain a set of high-quality Pareto-optimal policies. Moreover, a fluid model is introduced to extract state features and devise composite dispatching rules as discrete actions. A multi-policy co-evolution mechanism (MPCEM) is proposed to facilitate collaborative evolution among policy networks, supported by a reward mechanism that considers the objective weights. A training algorithm based on MPPPO is designed for learning across multiple policy networks. The effectiveness and superiority of the proposed method are confirmed through comparisons with composite dispatching rules and other scheduling methods.

Scheduling of Continuous Annealing With a Multi-Objective Differential Evolution Algorithm Based on Deep Reinforcement Learning

This paper studies a multi-objective scheduling problem in a continuous annealing operation of the steel industry, which is to simultaneously determine the production batch sizes for coils and their schedules so as to minimize the cost of setup, earliness, and tardiness. A large batch can reduce the setup costs but lead to a cost increase in earliness and tardiness. Thus, the conflict objectives of minimizing setup cost, earliness, and tardiness can be formulated separately. In this paper, we formulate a multi-objective optimization model for the problem and develop an adaptive multi-objective differential evolutionary based on deep reinforcement learning (AMODE-DRL) for effectively obtaining the Pareto solutions. In the proposed AMODE-RDL, DRL is integrated into the MODE algorithm as a controller, which can adaptively select mutation operators and parameters according to different search domains. Computational results on randomly generated instances and the practical problem instances show that DRL can effectively guide MODE to select mutation operators and parameters. The proposed algorithm can obtain better solutions compared to other powerful multi-objective evolutionary and adaptive MODE algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Setup usually leads to a decrease in production capacity and an increase in production costs. Similarly, earliness and tardiness costs are also crucial. These costs correspond to production, customer demand, and inventory, which are common objectives in production systems. However, the three objectives are generally conflicting, and it is very hard for practitioners to make appropriate decisions with manual experience. The multi-objective optimization methods can provide different scheduling for practitioners who may choose the suitable one according to current working conditions. Accordingly, the proposed model and algorithm can extend to other fields with similar characteristic problems.

An improved memetic algorithm for multi-objective resource-constrained flexible job shop inverse scheduling problem: An application for machining workshop

Resource-constrained flexible job shop scheduling problems are commonly encountered in some manufacturing industries, and have been widely studied in recent years. However, traditional resource constrained flexible job shop scheduling problem rarely consider the uncertainties in actual manufacturing systems, which may make the original schedule become suboptimal or even unfeasible. Therefore, a resource constrained flexible job shop inverse scheduling problem (RCFJISP) is proposed in this paper, which aims to cope with uncertain events by simultaneously adjusting the machine, worker and process parameters of the original schedule. A multi-objective optimization model is constructed to minimize the makespan, worker cost, machine energy consumption and deviation index. Furthermore, an improved memetic algorithm (IMA) is developed for solving the proposed problem. In IMA, a novel double-layer encoding mechanism is designed to enhance the capacity in exploring new solution’s domains. Three initialization strategies utilizing original scheduling information are designed to improve the quality of initial solutions. An adaptive mutation strategy and a local search mechanism are designed to enhance exploration and exploitation ability of the algorithm. And a crowding operator is proposed to reflect the diversity of the population effectively. In computational experiments, 28 extended benchmarks are constructed, and the effectiveness of the proposed strategy and algorithm is verified by comparing IMA with its 4 variants and other 4 widely used algorithms. Finally, two inverse scheduling problems of a real-world hydraulic cylinder machining workshop under two uncertain situations are studied. The results demonstrate that IMA can effectively solve the actual inverse scheduling problem. With a slight adjustment to the original scheduling, it can reduce the makespan by 11.5%, the worker cost by 8.1% and the machine energy consumption by 27.9% on average.

Enhancing multi-objective evolutionary algorithms with machine learning for scheduling problems: recent advances and survey

Multi-objective scheduling problems in workshops are commonly encountered challenges in the increasingly competitive market economy. These scheduling problems require a trade-off among multiple objectives such as time, energy consumption, and product quality. The importance of each optimization objective typically varies in different time periods or contexts, necessitating decision-makers to devise optimal scheduling plans accordingly. In actual production, decision-makers confront intricate multi-objective scheduling problems that demand balancing clients’ requirements and corporate interests while concurrently striving to reduce production cycles and costs. In solving various problems, multi-objective evolutionary algorithms have attracted the attention of researchers and gradually become one of the mainstream methods to solve these problems. In recent years, research combining multi-objective evolutionary algorithms with machine learning technology has shown great potential, opening up new prospects for improving the performance of multi-objective evolutionary methods. This article comprehensively reviews the latest application progress of machine learning in multi-objective evolutionary algorithms for scheduling problems. We review various machine learning techniques employed for enhancing multi-objective evolutionary algorithms, particularly focusing on different types of reinforcement learning methods. Different categories of scheduling problems addressed using these methods were also discussed, including flow-shop scheduling issues, job-shop scheduling challenges, and more. Finally, we highlighted the challenges faced by the field and outlined future research directions.

Approximation schemes for scheduling jobs on identical parallel machines to minimize the maximum lateness and makespan

We consider a multiobjective scheduling problem, with the aim of minimizing the maximum lateness and the makespan on identical machines, when the number of machines is fixed. This paper proposes an exact algorithm (based on a dynamic programming) to generate the complete Pareto Frontier in a pseudo-polynomial time. Moreover, four heuristics have been proposed in order to optimize our algorithm. Then, we present a Polynomial Time Approximation Scheme (PTAS) to generate an approximate Pareto Frontier. In this scheme, we use a simplification technique based on the merging of jobs. Furthermore, we present a Fully Polynomial Time Approximation Scheme (FPTAS) to generate an approximate Pareto Frontier, based on the conversion of the dynamic programming algorithm. The proposed FPTAS is strongly polynomial. Finally, some numerical experiments are provided in order to compare the proposed approaches.

Knowledge-transfer based genetic programming algorithm for multi-objective dynamic agile earth observation satellite scheduling problem

The multi-objective dynamic agile earth observation satellite scheduling problem (MO-DAEOSSP) aims to schedule a set of real-time arrival requests and form a reasonable observation plan to satisfy various criteria. According to the requirements in practical applications, the total profit and the average image quality of scheduled requests are taken as optimization goals in this study. Compared to manually designed heuristics and iterative-based methods used in previous research, genetic programming based hyper heuristics (GPHH) can automatically evolve high-quality heuristic rules (HRs) for real-time scheduling without being highly dependent on expert knowledge. In this paper, a knowledge-transfer based multi-objective GPHH framework (KT-MOGP) is proposed, equipped with a heuristic-based simulation considering the idle monitoring, to evolve non-dominated HRs for solving MO-DAEOSSP. The heuristic-based simulation generates feasible schedules and returns fitness values for given HRs, which are the individuals evolved by KT-MOGP. KT-MOGP applies a knowledge transfer mechanism to accelerate convergence. Once a source problem is trained, its non-dominated solutions are extracted and their feature importance is transferred to guide the initialization of another target problem, by which the knowledge generated during the training process can be fully utilized. Experimental results on three sets of instances show that KT-MOGP outperforms the existing GPHH-based method and that the evolved HRs are competitive compared to several classical constructive heuristics and multi-objective evolutionary algorithms. The results also show the effectiveness of the proposed knowledge transfer-based initialization. To the best of our knowledge, this study is the first attempt to consider both multi-objective scenarios and real-time arrival requests.

A multi-objective fuzzy flexible job shop scheduling problem considering the maximization of processing quality

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.

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.

Research on multi-objective flow shop scheduling optimization in supply chain environment based on Fuzzy Relevance Entropy Method

For the multi-objective flow shop scheduling problem in the supply chain environment, this paper proposes the Fuzzy Relevance Entropy method (FREM) to solve the adaptive value assignment problem in the multi-objective optimization process of the supply chain environment by combining Fuzzy Information Entropy Theory (FIET) and Degree of Membership Function (DMF). Firstly, the uncertainty of each sub-objective of the ideal solution and Pareto solution of the objective is extracted using the Degree of Membership Function. Secondly, each solution is mapped into an affiliation degree fuzzy set and the information contained in the fuzzy set is reprocessed using Fuzzy Information Entropy Theory. Finally, the amount of information contained in the ideal solution solved by the Pareto method is used to guide the evolution of the Particle Swarm Optimization (PSO) algorithm, thus avoiding the traditional multi-objective optimization process of assigning weights to solve the fitness link. This paper combines both the Fuzzy Relevance Entropy method and the Stochastic Weight method with Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms to address the five-objective flow shop scheduling problem in the supply chain environment. Experimental results demonstrate that the proposed Fuzzy Relevance Entropy method effectively solves the multi-objective flow shop scheduling problem in the supply chain environment and achieves better optimization results compared to the Stochastic Weight method.

Multi-Objective Flexible Flow Shop Production Scheduling Problem Based on the Double Deep Q-Network Algorithm

In this paper, motivated by the production process of electronic control modules in the digital electronic detonators industry, we study a multi-objective flexible flow shop scheduling problem. The objective is to find a feasible schedule that minimizes both the makespan and the total tardiness. Considering the constraints imposed by the jobs and the machines throughout the manufacturing process, a mixed integer programming model is formulated. By transforming the scheduling problem into a Markov decision process, the agent state features and the actions are designed based on the processing status of the machines and the jobs, along with heuristic rules. Furthermore, a reward function based on the optimization objectives is designed. Based on the deep reinforcement learning algorithm, the Dueling Double Deep Q-Network (D3QN) algorithm is designed to solve the scheduling problem by incorporating the target network, the dueling network, and the experience replay buffer. The D3QN algorithm is compared with heuristic rules, the genetic algorithm (GA), and the optimal solutions generated by Gurobi. The ablation experiments are designed. The experimental results demonstrate the high performance of the D3QN algorithm with the target network and the dueling network proposed in this paper. The scheduling model and the algorithm proposed in this paper can provide theoretical support to make the production plan of electronic control modules reasonable and improve production efficiency.

A memetic NSGA-II for the multi-objective flexible job shop scheduling problem with real-time energy tariffs

AbstractRising costs for energy are increasingly becoming a vital factor for the production planning of manufacturing companies. Manufacturers face the challenge to react to dynamic energy prices and design energy cost efficient schedules in their production planning. In the literature, the energy cost-aware Flexible Job Shop Scheduling Problem addresses minimization of both makespan and energy costs. Recent studies provide multi-objective approaches to model the trade-off of minimizing makespan and energy costs. However, the literature is limited to coarse-grained time periods and does not consider dynamic tariffs where costs change at short intervals, so that production schedules may fall short on energy costs. We aim to close this research gap by considering frequently changing real-time energy tariffs. We propose a multi-objective memetic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) with both makespan and energy cost minimization as the objectives. We evaluate our approach by conducting computational experiments using prominent FJSP-benchmark instances from the literature, which we supplement with empiric dynamic energy prices. We show results on method performance and compare the memetic NSGA-II with the results of an exact state-of-the-art solver. To investigate the trade-off between a short makespan and low energy costs, we present solutions on the approximated Pareto front and discuss our results.

An improved spider monkey optimization algorithm for multi-objective planning and scheduling problems of PCB assembly line

In recent years, the demand for printed circuit boards (PCBs) with various electronic components has tremendously increased due to high customization in smart electronic devices. To meet the market competition, efficient and realistic decisions with optimum planning and scheduling are required to enhance the productivity of PCB industries. Processing time of surface mounting technology (SMT) machines defines the pace of PCB production because of time consuming and critical process. In addition, it is observed that various planning and scheduling problems exist in PCB assembly line which are required to emphasize to increase the productivity. Therefore, in this study critical planning and scheduling problems i.e., component allocation problem (CAP) and component placement sequence problem (CPSP) are considered to optimize. Moreover, the periodic maintenance (PM) is also considered to maintain the efficiency of machines and make the problem more realistic. A mathematical model is formulated to minimize the maximum completion time, total energy consumption and the total maintenance time simultaneously. To solve this multi-objective NP-hard problem, an improved spider monkey optimization (ISMO) algorithm is developed. The efficiency and effectiveness of ISMO algorithm is improved by embedding few additional features. a) Two heuristics to ensure better initial solutions; b) evolutionary state judgment based on change in Pareto entropy to ensure the tradeoff between exploration and exploitation; c) an archive-based Q-Learning strategy to ensure the parametric adaptive tuning. Finally, computational experiments and comprehensive performance comparisons with other well-known multi-objective algorithms are performed with several size problem instances. The statistical results and analysis demonstrate that the proposed ISMO algorithm outperforms the other competitors.

Multi-objective scheduling of a steelmaking plant integrated with renewable energy sources and energy storage systems: Balancing costs, emissions and make-span

As an energy-intensive industry, the steel industry grapples with increasing energy costs and decarbonisation pressures. Therefore, multi-objective optimisation is widely applied in the production scheduling of the steelmaking plant. However, the optimal solution prioritising energy savings and emission reductions may lead to impractical or less economically efficient solutions, since the processing time requirement (PTR) of steel production orders in real-world production is neglected. This study fills the research gap by discussing the impact of PTR on the make-span of the steelmaking process and incorporating it into the optimisation model. Considering the variability of PTR, the solving of the multi-objective scheduling problem is transformed into the selection from Pareto solutions with different make-spans. To better leverage the temporal flexibility of the steelmaking process, a what-if-analysis-based strategy coupled with the Normal Boundary Intersection method is proposed to generate a series of evenly distributed Pareto solutions. The energy storage system is integrated to improve the time granularity of the steelmaking plant's flexibility. Our case studies demonstrate that the electricity and emission costs are reduced by 68.5%, indirect emissions are reduced by 83.5%, and the on-site renewable energy self-consumption rate increases by 12.1%. The effectiveness of the proposed method implies that it is of great relevance to the development of a cleaner steel industry in the future.

Hybrid multi-objective evolutionary meta-heuristics for a parallel machine scheduling problem with setup times and preferences

Fabric dyeing is a vital production process of textile products. In the dyeing process, orders are scheduled to machines, and the sequence of jobs on a machine is crucial since the machines require washing out that depends on the type of consecutive orders. This washing out process is a significant cost factor of the dyeing process because of the chemicals used, which causes sequence dependent setup times. Also, the order of the products to be processed is important in terms of quality that depends on color and shade of the jobs. In this paper, two metaheuristics, namely a non-dominated sorting genetic algorithm (NSGA-II) and multi-objective evolutionary algorithm based on decomposition (MOEA/D) are presented to solve the multi-objective scheduling problem for the dyeing process with sequence dependent setup times, in which the objectives are makespan, tardiness, total number of setups, color preference, and shade difference. Two different gene designs and corresponding feasible schedule generation methods — one heuristic based and one integer programming based, which are integrated within the metaheuristic framework, are proposed. Finally, proposed algorithms are compared based on single and multiple objective analysis. From the tests conducted, we observed that the use of hybrid-optimal approaches integrated within the meta-heuristic frameworks provide higher quality solutions but suffer from longer computation times.

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

A multi-objective complex product assembly scheduling problem considering transport time and worker competencies

The hybrid flow shop scheduling problem (HFSP) is a research hotspot in the shop scheduling problem. However, few studies have investigated HFSP involving parallel machine scheduling and worker competencies. Therefore, this study investigates a complex product assembly line scheduling problem considering parallel team scheduling, worker competencies, and transport time. The makespan, transport time, imbalance degree of team workload, and imbalance degree of cycle time are taken as optimization objectives. First, a mathematical model considering transport time and worker competencies is developed, and then a mixed encoding and decoding method is proposed. Second, an algorithm that hybridizes the genetic algorithm and simulated annealing algorithm is proposed, involving an improved Nawaz-Enscore-Ham heuristic method and a strengthened elite retention strategy to improve the quality of the solution. Finally, based on nine examples generated from real production statuses, the proposed algorithm is compared with the other four algorithms. The results show that the proposed algorithm is superior in terms of the quality and efficiency of solutions.

Multi-Objective Optimization Flow Shop Scheduling Problem Solving the Makespan and Total Flow Time with Sequence Independent Setup Time

In this paper, a multi-objective permutation flow shop scheduling problem with sequence independent setup time is studied. The bi-objective function that we consider is a linear combination of the makespan and total flow time with a weighted factor for each criterion. We propose a set of exact and approximate methods to minimize the makespan and total flow time in our flow shop optimization problem case. Hence, our main goal is to find the sequence of jobs that minimizes the two criteria of makespan and total flow time. The purpose is to solve this problem, with a mixed integer linear programming model (MILP) and a collection of efficient metaheuristics for different sizes of instances. Moreover, three metaheuristics are used: the Genetic Algorithm (GA), the Iterative Local Search (ILS) algorithm and the Iterated Greedy (IG) algorithm. The three last algorithms GA, ILS and IG are suggested in two ways for exploring the neighborhood. In order to test the efficacy of our resolution approach, different series of instances containing n jobs and m machines are generated randomly ranging from small to relatively large instances. The examination of the suggested simulations allowed us to remark that, for large and medium-scale instances, IG based on the exploration of the neighborhood records the best performances in terms of comparison with the other metaheuristics.

Multi-objective scheduling in dynamic of household paper workshop considering energy consumption in production process

Aim: The uncertainty and complexity of the production process of household paper are growing sharply in modern factories. Due to the influence of rising energy costs and environmental policies, the demand for reducing production costs and energy consumption is also increasing. Therefore, it is studied that the dynamic shop scheduling problem of household paper production considering simultaneously the cost with energy consumption. Methods: A mathematical model of the multi-objective and multi-constraint household paper scheduling problem is established first. The multi-objective scheduling process is transformed into a multi-agent Markov game process by assigning each objective to each agent. Upon which, a multi-agent game model is constructed for the household paper scheduling problem based on deep reinforcement learning; it is a proposed D3QN algorithm and Nash equilibrium strategy, and the state characteristics and action selection space are proposed according to the characteristics of the household paper production. The model performance has been verified by the actual production data. Results: Results show that the proposed method not only achieves better performance than traditional scheduling methods but also persists in its advantages even when the configuration of the manufacturing system changes. Conclusion: Multi-agent deep reinforcement learning in the Markov game has a good prospect in solving multi-objective dynamic scheduling problems for household paper production.