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As multi-factory production models are more widespread in modern manufacturing systems, a distributed blocking flowshop scheduling problem (DBFSP) is studied in which no buffer between adjacent machines and setup time constraints are considered. To address the above problem, a mixed integer linear programming (MILP) model is first constructed, and its correctness is verified. Then, an iterated greedy-algorithm-blending multi-factory collaboration mechanism (mIG) is presented to optimize the makespan criterion. In the mIG algorithm, a rapid evaluation method is designed to reduce the time complexity, and two different iterative processes are selected by a certain probability. In addition, collaborative interactions between cross-factory and inner-factory are considered to further improve the exploitation and exploration of mIG. Finally, the 270 tests showed that the average makespan and RPI values of mIG are 1.93% and 78.35% better than the five comparison algorithms on average, respectively. Therefore, mIG is more suitable to solve the studied DBFSP_SDST. [ABSTRACT FROM AUTHOR]

Production scheduling, which directly influences the completion time and throughput of workshops, has received extensive research. However, due to the high cost of real-world production verification, most literature did not verify the optimized scheduling scheme in real-world workshops. This paper studied the verification of scheduling schemes and environments, using a discrete event simulation (DES) platform. The aim of this study is to provide an efficient way to verify the correctness of scheduling environments established by programming languages and scheduling results obtained by intelligent algorithms. The system architecture of scheduling verification based on DES is established. The modelling approach via DES is proposed by designing parametric workshop generation, flexible production control, and real-time data processing. The popular distributed permutation flowshop scheduling problem is selected as a case study, where the optimal scheduling scheme obtained by a deep reinforcement learning algorithm is fed into the production simulation model in Plant Simulation software. The experiment results show that the proposed scheduling verification approach can validate the scheduling scheme and environment effectively. The utilization and Gantt charts clearly show the performance of scheduling schemes. This work can help to verify the scheduling schemes and programmed scheduling environment efficiently without costly real-world validation. [ABSTRACT FROM AUTHOR]

With the advancement of the global economy, there is a growing focus on distributed manufacturing. This study addresses the complex challenges posed by the distributed heterogeneous flow shop scheduling problem (DHFSP), wherein multiple machine processing speeds are taken into account. The primary objectives involve the simultaneous minimization of both makespan and total energy consumption. To tackle this intricate problem, we propose an evolutionary computation and reinforcement learning integrated algorithm (ECRLIA) approach. Initially, an optimization framework is meticulously crafted to synergistically integrate both evolutionary computation and reinforcement learning solvers. Subsequently, a multi-rule cooperation initialization is devised to expedite the pre-search process across all solvers. Following this, a competition-based cooperative evolutionary algorithm is introduced to conduct a global search, thereby providing an initial solution to the DHFSP. The interplay of competition and cooperation among individuals enhances convergence. Further, a Q-learning approach employing dual agents is designed to perform a local search, supplementing solutions that evolutionary algorithms may struggle to uncover. This learning method incorporates an auxiliary agent to evaluate the action predictions of the primary agent, ensuring more stable learning. The effectiveness of the proposed algorithm is assessed through numerical experiments, which validate the efficacy of the cooperation framework, initialization cooperation, and the enhanced Q-learning method. Furthermore, ECRLIA is benchmarked against five state-of-the-art algorithms for DHFSP, and the results affirm the significant superiority of the proposed ECRLIA in addressing DHFSP compared to other algorithms. • An evolution and reinforcement cooperation framework is proposed for shop scheduling. • A competition strategy is designed to enhance the convergence of EC. • An auxiliary agent is designed to improve the action prediction of RL. • The proposed approach obtains the superior performance for solving DHFS. [ABSTRACT FROM AUTHOR]

The scheduling problems under distributed production or flexible assembly settings have achieved increasing attention in recent years. This paper considers scheduling the integration of these two environments and proposes an original distributed flowshop scheduling problem with flexible assembly and set-up time. Distributed production stage is deployed several homogeneous flowshop factories that process the jobs to be assembled into final products in the flexible assembly stage. The objective is to find a schedule, including a production subschedule for jobs and an assembly subschedule for products, to minimise the makespan. Such a scheduling problem involves four successive decisions: assigning jobs to production factories, sequencing jobs at every factory, designating an assembly machine for each product and sequencing products on each assembly machine. The computational model is first established, and then a constructive heuristic (TPHS) and two hybrid metaheuristics (HVNS and HPSO) are proposed. Numerical experiments have been carried out and results validate the algorithmic feasibility and effectiveness. TPHS can obtain reasonable solutions in a shorter time, while metaheuristics can report better solutions using more yet acceptable time. HPSO is statistically comparable yet less robust compared with HVNS for small-scale instances. For the large-scale case, HPSO outperforms HVNS on both effectiveness and robustness. [ABSTRACT FROM AUTHOR]

This paper studies a novel and practical distributed flexible assembly permutation flowshop scheduling problem with makespan criterion, which has attracted wide attention due to important applications in modern manufacturing. The problem integrates two machine environments of distributed production and flexible assembly, which can process and assemble the jobs into customized products. We first present a mixed integer linear programming model to characterize the problem essence and to solve small-size problems. Due to the NP-hard, we further propose an efficient memetic algorithm, which consists of a global exploration optimizer designed based on improved social spider optimization and two local exploitation optimizers designed based on meta-Lamarckian learning and simplex search, respectively. To implement the algorithm, a problem-specific encoding scheme is presented. Algorithmic parameters are calibrated by a design of experiments, and a comprehensive computational campaign is conducted to evaluate the performance of the mathematical model and algorithms. Statistical results show that their problem-solving abilities are effective, and especially the proposed memetic algorithm outperforms the existing algorithms significantly.

As multi-factory production models are more widespread in modern manufacturing systems, a distributed blocking flowshop scheduling problem (DBFSP) is studied in which no buffer between adjacent machines and setup time constraints are considered. To address the above problem, a mixed integer linear programming (MILP) model is first constructed, and its correctness is verified. Then, an iterated greedy-algorithm-blending multi-factory collaboration mechanism (mIG) is presented to optimize the makespan criterion. In the mIG algorithm, a rapid evaluation method is designed to reduce the time complexity, and two different iterative processes are selected by a certain probability. In addition, collaborative interactions between cross-factory and inner-factory are considered to further improve the exploitation and exploration of mIG. Finally, the 270 tests showed that the average makespan and RPI values of mIG are 1.93% and 78.35% better than the five comparison algorithms on average, respectively. Therefore, mIG is more suitable to solve the studied DBFSP_SDST.

• The dynamic distributed reconfigurable flowshop scheduling problem is studied via DRL. • The DRL-based intelligent scheduling and reconfiguration systems are modelled. • An expected deep Q-network algorithm with precise state-action values is proposed. • The DRL-based training and execution processes for the studied problem are proposed. • Our proposed expected deep Q-network outperforms some popular DRL algorithms. Distributed manufacturing has become common in the globalized production environment. Facing the tendency of mass customization, distributed workshops are required to have the reconfiguration capability to produce multiple products. Based on the scheduling demands of distributed workshops, this paper studied the dynamic distributed reconfigurable flowshop scheduling problem (DRFSP) with new job arrivals using deep reinforcement learning (DRL) for the first time. The DRL-based intelligent scheduling and reconfiguration systems are modeled by designing efficient rewards, actions, and state features for both scheduling and reconfiguration agents. A new state feature normalization approach is proposed to address the variability in production configurations and dynamics. A novel expected deep Q-network (EDQN) algorithm is proposed to provide more precise state-action values rather than using estimations. Moreover, the DRL-based training and execution procedures for the dynamic DRFSP are provided by combining decision-making, agent learning, and reconfigurable production. Training curves validate the reasonableness of system modeling and the good learning efficiency of the EDQN algorithm. Extensive comparison experiments show that our EDQN algorithm outperforms three popular DRL algorithms and four well-known priority dispatching rules (PDRs) by around 20 % and 89 % respectively, with good generalization ability and time efficiency. The average decision time under dynamics is only 0.65 ms, which enables real-time scheduling. [ABSTRACT FROM AUTHOR]

• Addressing the reconfigurability and grouped families in the DFSP. • Proposing a MILP model of the addressed problem. • Proposing dynamic solution encoding and decoding strategies. • Integrating a nested search strategy into the VND. • Good performance of the proposed approaches on two sets of instances. Inspired by a real-world cellular manufacturing system for processing printed circuit boards (PCBs), this study addresses a reconfigurable distributed flowshop scheduling problem (RDFGSP), where the flowline is considered as a cell and a complete process includes two flows through the flowlines. The characteristics of the RDFGSP lie in the reconfigurability of the flowlines and the families with grouped jobs. To solve this problem, at the two flows the family assignment part and sequence part (including family sequence and job sequence) are all required to be addressed. To solve the problem, a mixed integer linear programming (MILP) model is first developed, which can solve the small-scaled instances to optimality. Since the NP-hard property of the problem, a nested variable neighborhood descent (NVND) algorithm is developed. Its core ideas lie in the dynamic solution encoding and decoding strategies and the specially designed nested loops, including the external and internal loops. In the external loop, the solution encoding and decoding only consider the sequence part, and the family assignment part is conceived using the machine property in the decoding process. The internal loop is triggered when a decoding process in the external loop is completed, where the family assignment part and sequence part are all considered. In addition, a collaborative process and a restart strategy are employed to guarantee the global search capability. In the experimental study, the iterated F-Race (I/F-Race) is used to help determine the algorithm parameters with minimum user intervention. Comprehensive computational results demonstrate that the proposed algorithm outperforms the math solver CPLEX and other state-of-the-art metaheuristics. [ABSTRACT FROM AUTHOR]

• The dynamic distributed permutation flowshop scheduling problem (DPFSP) is studied. • The training and execution procedures of scheduling agents are provided. • Novel state features, actions, and reward are designed for the scheduling model. • Outperforms state-of-the-art meta-heuristics and priority dispatching rules. • The deep reinforcement learning can provide real-time scheduling after training. Distributed manufacturing plays an important role for large-scale companies to reduce production and transportation costs for globalized orders. However, how to real-timely and properly assign dynamic orders to distributed workshops is a challenging problem. To provide real-time and intelligent decision-making of scheduling for distributed flowshops, we studied the distributed permutation flowshop scheduling problem (DPFSP) with dynamic job arrivals using deep reinforcement learning (DRL). The objective is to minimize the total tardiness cost of all jobs. We provided the training and execution procedures of intelligent scheduling based on DRL for the dynamic DPFSP. In addition, we established a DRL-based scheduling model for distributed flowshops by designing suitable reward function, scheduling actions, and state features. A novel reward function is designed to directly relate to the objective. Various problem-specific dispatching rules are introduced to provide efficient actions for different production states. Furthermore, four efficient DRL algorithms, including deep Q-network (DQN), double DQN (DbDQN), dueling DQN (DlDQN), and advantage actor-critic (A2C), are adapted to train the scheduling agent. The training curves show that the agent learned to generate better solutions effectively and validate that the system design is reasonable. After training, all DRL algorithms outperform traditional meta-heuristics and well-known priority dispatching rules (PDRs) by a large margin in terms of solution quality and computation efficiency. This work shows the effectiveness of DRL for the real-time scheduling of dynamic DPFSP. [ABSTRACT FROM AUTHOR]

• The sequence model of energy-efficient DAPFSP is first established. • A heuristic and a hybrid method are presented to generate initial solutions. • A multidimensional probabilistic model is designed to learn the promising patterns. • A critical path-based local search is used to improve the quality of solutions. • Two speed adjustment strategies are proposed to enhance the performance of MCEDA. In this paper, a matrix-cube-based estimation of distribution algorithm (MCEDA) is proposed to solve the energy-efficient distributed assembly permutation flow-shop scheduling problem (EE_DAPFSP) that minimizes both the maximum completion time (C max) and the total carbon emission (TCE) simultaneously. Firstly, a high-quality and diverse initial population is constructed via a hybrid initialization method. Secondly, a matrix-cube-based probabilistic model and its update mechanism are designed to appropriately accumulate the valuable pattern information from superior solutions. Thirdly, a suitable sampling strategy is developed to sample the probabilistic model to generate a new population per generation, so as to guide the search direction toward promising regions in solution space. Fourthly, a problem-dependent neighborhood search based on critical path is provided to perform an in-depth local search around the promising regions found by the global search. Fifthly, two types of speed adjustment strategies based on problem properties are also embedded to further improve the quality of the obtained solutions. Sixthly, the influence of the parameters is investigated based on the multi-factor analysis of variance of Design-of-Experiments. Finally, extensive experiments and comprehensive comparisons with several recent state-of-the-art multi-objective algorithms are carried out based on the well-known benchmark instances, and the statistical results demonstrate the efficiency and effectiveness of the proposed MCEDA in addressing the EE_DAPFSP. [ABSTRACT FROM AUTHOR]

We solve a distributed permutation flowshop scheduling problem (DPFSP) with non-identical factories, which is also referred to as the distributed heterogeneous permutation flowshop scheduling problem (DHPFSP). Stemming from the practical demands, we introduce the lot-streaming and carryover sequence-dependent setup time into our problem, both of which have not been previously studied under the DPFSP environment. The objective is to minimize the makespan among factories. To address this problem, we first present a mixed integer linear model. Next, we develop five constructive heuristics to find high-quality solutions in a timely manner. Moreover, we propose an enhanced artificial bee colony algorithm (NEABC). In the NEABC, an initialization method with strong intensification is proposed to generate promising swarm. Then, a collaboration mechanism among individuals is presented in the onlooker bee stage to improve the search capability. Besides, a restart strategy is designed in the scout bee stage with the consideration of the special onlooker bee stage of the algorithm. Comprehensive experiments based on instances with a wide range of scales are carried out and the results prove the validity of presented algorithms for the problem under study. [ABSTRACT FROM AUTHOR]