Motivated by the multi-variety, small-lot intermittent production mode in tin chemical enterprises, this paper addresses the distributed heterogeneous factory lot-sizing and scheduling problem (DHFLSP). To this end, a mixed-integer programming (MIP) model is formulated for the first time to minimize total production and delivery costs. To efficiently solve the DHFLSP with a hybrid continuous–discrete decision space, a dueling double deep Q-network (D3QN)-based scheduling decoder is developed, which learns the mapping between lot-sizing encoding states and high-quality scheduling rules through offline training, enabling adaptive decoding for different encoded individuals and effectively decoupling the two decision spaces. Building upon this, a deep reinforcement learning-driven space decomposition variable neighborhood search (DRL-SDVNS) algorithm is proposed to perform parallel search in the entire solution space. In DRL-SDVNS, a novel space decomposition (SD) method is designed to reasonably decompose the encoding space into multiple differentiated subspaces. Within each subspace, an iterative search consisting of small-neighborhood rapid exploration for encoded individuals and large-neighborhood deep exploitation for the decoupled lot-sizing and production scheduling decision spaces is developed to execute broad and in-depth search. Experimental results demonstrate that DRL-SDVNS outperforms state-of-the-art algorithms in both solution quality and computational efficiency.

The task assignment problem (TAP) is a well-known combinatorial optimization problem with rich applications. Most existing TAPs have minimized cost criteria, and are often unsuitable for complex decision-making. This work focuses on a specific multi-objective TAP considering the reliability of agents (MOTAP/RA). The objective is to optimize the total assignment cost and total agent reliability. To solve the problem, we present a Pareto evolutionary algorithm based on data mining (PEADM). The primary contributions of this work are two-fold: a mathematical model of MOTAP/RA and a novel search model of PEADM. For the mathematical model, we propose for the first time the MOTAP/RA model based on which problem-specific heuristics are introduced. For the PEADM framework, we introduce two populations to capture valuable algorithm knowledge: a main population (MP) and an auxiliary population (AP). We update MP using an improved nondominated sorting method while extracting pertinent frequent patterns from MP through a dedicated data mining approach. Then, we generate new individuals of AP based on the mined frequent patterns and so improve MP based on AP. Results of experiments on 180 instances with up to 310 tasks show that PEADM competes favorably with state-of-the-art solution methods.

Copy number variation (CNV) is a remarkable manifestation of genomic structural variations that affect human health. However, CNV detection in low coverage and low purity data is one of the challenging issues. To fill this gap, a hybrid algorithm combining an improved whale optimization algorithm (IWOA) and backpropagation (BP) neural networks (hereafter called IWOABP) is developed for CNV detection. First, to enhance the precision of detection, the detectable categories for the gain and loss are respectively expanded to two types, where gain is divided into tand_gain and inte_gain, and loss is divided into hemi_loss and homo_loss. Then, IWOA is introduced to tune the weights and bias values of BP neural network, which can improve the BP neural network abilities to jump out of the local optimums. Next, to ensure the population diversity and the uniform distribution of solutions, a pooling mechanism and a migration search strategy are designed. In addition, to balance the exploitation and exploration abilities, three position update strategies based on an adaptive inertia-weight are used. Finally, to evaluate the detection performance of IWOABP, seven state-of-the-art detection methods are chosen to make detailed comparisons with the proposed algorithm. The results show that IWOABP has outstanding performance in sensitivity, precision, and Fl-score using both simulated and real data.

Distributed hybrid flow shop scheduling with deterioration effects (DHFSP-DE) is challenging due to the tight coupling among factory assignment, machine selection, and operation sequencing under deterioration effects. An effective and scalable decision-making framework is therefore developed capable of jointly modeling these interdependent factors and generating high-quality schedules. The DHFSP-DE is formulated as a Markov Decision Process, and a deep reinforcement learning (DRL) framework is proposed by integrating a Heterogeneous Composite Graph Attention Network (HCGAN) with a Proximal Policy Optimization (PPO). Factories, machines, and operations are modeled as distinct node types within a composite heterogeneous graph, encoding technological precedence, machine eligibility, factory allocation constraints, and deterioration evolution. Three-stage attention mechanism is employed to extract high-order dependencies, while a deterioration-aware feature module dynamically adjusts operation priorities, and a structured operation–factory–machine action space ensures feasibility. Computational experiments on 36 benchmark instances demonstrate that HCGAN consistently outperforms classical dispatching rules, representative metaheuristics, and a comparative DRL approach. Specifically, average makespan is reduced by 12–22% relative to dispatching rules, improvements of 5–10% are achieved over metaheuristics, and makespan values remain 3–8% lower than the comparative DRL method across small-, medium-, and large-scale instances. Near-optimal solutions are obtained for small instances where exact methods remain tractable, while inference efficiency is preserved for larger instances. These results indicate that the composite heterogeneous graph representation and multi-stage attention mechanism employed by HCGAN more effectively capture inter-factory precedence relationships and deterioration-induced dynamics than existing DRL models, providing a robust and scalable solution for DHFSP-DE.

The Flexible Job Shop Scheduling problem with Automated Guided Vehicles (FJSP-AGVs) is commonly encountered in modern manufacturing systems, with complexity increasing exponentially as the problem scales, making traditional methods inadequate. So far, a limitation of meta-heuristic algorithms incorporating machine learning for solving FJSP-AGVs is that machine learning is primarily used for heuristic selection (e.g., dispatching rules or local search operators) rather than actively guiding solution evolution based on the diverse features of solutions, leading to incomplete exploration and premature convergence. To tackle these issues, this paper first presents a Q-Learning Region Selection Enhanced Quality-Diversity (Q-QD) algorithm, which integrates a pairwise selection scheme to identify potential collaborative solutions within the feature space for two practical Chinese manufacturing scenarios: a coal machinery structural parts production workshop and a machining workshop in Nanjing. Unlike traditional approaches that focus solely on optimizing the objective, Q-QD leverages the customized feature space incorporating behaviors such as job transportation times and machine idle times. By combining Q-learning-based region selection with heuristic rule-based local search for AGV transportation, the proposed method effectively discovers high-performing and diverse solutions. The results obtained from two real-world cases and 21 benchmark instances indicate that the proposed Q-QD algorithm surpasses five advanced counterparts, achieving a makespan reduction of 12.2-30.8% relative to the strongest baseline. These substantial performance gains highlight the robustness and efficiency of QD-based optimization for solving FJSP-AGVs and suggest a valuable avenue for future research in intelligent job shop scheduling.

The hybrid flow shop scheduling problem is used in several industrial processes such as printed circuit board assembly lines. In these realistic manufacturing systems, several key practical constraints such as group setup time and consistent sublots should be considered simultaneously to adapt to the need for heterogeneous configurations. To address these challenges, we developed an adaptive collaborative multi-objective evolutionary algorithm to solve the hybrid flow shop problem with group setup times and consistent sublots, aiming to minimize makespan and energy metrics while guaranteeing sublot consistency across processing phases. First, the proposed algorithm designed high-quality and diverse initial solution sets by integrating heuristic rules and random strategies. Then, a multilevel co-evolutionary mechanism was designed with specific operators developed for each level to explore the potential for interpopulation collaboration, which enhanced global search capability and local exploitation. To further optimize search efficiency, an adaptive evolution mechanism is proposed, which dynamically adjusts weights at different evolutionary stages to balance exploration and exploitation, effectively avoiding local optima. Additionally, a sublot dynamic adjustment energy-saving strategy based on disjunctive graphs was introduced to achieve finer-grained energy optimization. Experimental results demonstrated that the adaptive collaborative multi-objective evolutionary algorithm surpassed existing approaches regarding the rate of convergence, solution efficiency, and overall solution quality, offering an effective approach for solving multi-objective scheduling optimization challenges.

In this study, a special version of the Flexible Job Shop Scheduling Problem with equally and consistently batching constraints (hereafter called ECBFJSP) is considered, which involves multiple aspects of coordination, such as machine selection, process sorting, and batch splitting, which is highly complex and places strict demands on the optimization strategy. To effectively meet this challenge, this study constructs a dual-action deep reinforcement learning algorithm framework based on the Enhanced Heterogeneous Graph Neural Network (EHGNN). First, an enhanced heterogeneous graph and EHGNN model for the ECBFJSP is innovatively proposed. By integrating multi-dimensional node features such as work order priority, machine tool processing capability, and process constraints, dynamic feature aggregation of various types of information is achieved with the help of GATs and GRUs. The model can output context-aware representations containing global resource constraints, greatly improving the joint optimization efficiency of job scheduling and batch partitioning and significantly enhancing the adaptability of the dual-action decision framework to the complexity of the ECBFJSP. At the decision-making mechanism level, this study designed a dual-action decision space of process sequencing-machine selection action and batch partitioning action and used the DAPPO algorithm to collaboratively optimize the dual-action strategy to ensure the stability and efficiency of the decision-making process. The experimental data results show that compared with traditional algorithms, the proposed intelligent decision framework performs better in scheduling quality when solving the ECBFJSP, which fully verifies the significant effectiveness and practicality of the framework in solving the ECBFJSP.

This study presents a deep reinforcement learning method based on an attention-enhanced spliced heterogeneous graph neural network to address the distributed hybrid flow shop scheduling problem with degradation effect (DHFSP-DE). A spliced heterogeneous graph is designed to represent the complex topology of DHFSP-DE, capturing the interactions among operations, jobs, machines, and factories. To enhance the representation of scheduling states, this work constructs a feature extractor using a graph neural network with a heterogeneous composite attention mechanism that captures complex relationships among different node and edge types. Proximal Policy Optimization (PPO) is used to iteratively refine the scheduling policy and improve action selection. Empirical evaluations on multiple benchmarks show that the proposed model outperforms six widely used dispatching rules in terms of convergence speed and generalization capability.

Production scheduling that involves distributed factories, machine maintenance, and resource constraints plays a crucial role in manufacturing. However, these realistic constraints have rarely been considered simultaneously in the hybrid flow shop (HFS). To address this issue, a distributed resource-constrained hybrid flow shop scheduling problem with machine breakdowns (DRCHFSP-MB) is studied. There are two optimization objectives, i.e., makespan and total energy consumption (TEC). To solve the strongly NP-hard problem, a mathematical model is established and a block–neighborhood-based multi-objective evolutionary algorithm (BNMOEA) is developed. In the proposed algorithm, an efficient hybrid initialization method is adopted to obtain high-quality individuals to participate in the evolutionary process of the population. Next, to enhance the search capability of the BNMOEA, three well-designed crossover operators are used in the global search. Then, the convergence of the proposed algorithm is improved by utilizing eight critical factory-based local search operators combined with block–neighborhood. Finally, the BNMOEA is compared with several of the most advanced multi-objective algorithms; the results indicate that the BNMOEA has an outstanding performance in solving DRCHFSP-MB.

Driven by the evolution of smart and sustainable manufacturing paradigms under Industry 5.0, which emphasize adaptability, connectivity, and data-driven decision-making, the dynamic flexible job shop scheduling problem (DFJSSP) has emerged as a critical area of research. The DFJSSP involves scheduling jobs in a highly dynamic and uncertain manufacturing environment where new tasks are continually introduced, further complicating the scheduling process. In this study, the DFJSSP is extended to incorporate single crane transportation and sequence-dependent setup times, reflecting real-world manufacturing constraints. To tackle this multifaceted problem, we introduce a novel approach, i.e., a multipopulation-based evolutionary multitask optimization (EMTO) framework. In addition, the genetic programming algorithm is employed as a generative hyperheuristic to deal with the dynamic uncertainties in the shop floor. Two components are collaborated to optimize two objectives, i.e., minimizing the maximum completion time and the total tardiness. Furthermore, a dynamic transfer ratio is proposed, allowing the proportion of knowledge transfer to adapt throughout the iteration process, balancing convergence speed with population diversity. The results demonstrate that both the EMTO framework and the dynamic transfer ratio significantly enhance the performance of the algorithm. Compared to well-known constructive heuristics and reinforcement learning algorithm, the proposed approach enables parallel resolution of multiple optimization objectives, leading to enhanced scheduling efficiency and adaptability in dynamic manufacturing environments.

Incorporating the concept of delivery time windows into the distributed blocking flowshop group scheduling (DBFGSP) contributes to ensuring the timely delivery of products and enhancing customer satisfaction. Therefore, this paper focuses on the study of DBFGSP with delivery time windows. However, its several unresolved challenges, i.e., establishing the problem model and reducing the algorithmic complexity, persist. Therefore, we first construct a mixed-integer linear programming model for this problem, and verify its correctness by Gurobi solver. Second, we define, for the first time, the concept of the ’critical machine’, and propose the theoretical analysis and methods of a critical machine-based rapid evaluation for the total weighted earliness and tardiness (TWET) criteria. Then, we integrate the proposed strategies, i.e., two rapid evaluation methods, a modified idle time insertion method based on family chunks, and two idle time insertion-driven rapid local search strategies, into iterated greedy (namely RAP_IG_ITI) to coincide better with delivery time windows. Through statistical analysis, it becomes evident that our computational efforts have significantly decreased in computing TWET objective, and the proposed RAP_IG_ITI can effectively solve DBFGSP within an acceptable time.

The rapid development of the manufacturing industry lead to complex production scheduling processes, in which reentrant operation is an aspect that needs special consideration. Reentrant is rarely considered in the literature, even if it has widespread applications in manufacturing industry. This study investigates the reentrant hybrid flow shop scheduling and rescheduling problems (RHFSRSP) minimize the maximum completion time (makespan). First, a mathematical model is established for the RHFSRSP. Considering the reentrant operation, a left-shift strategy is proposed to optimize the makespan in solution decoding section further. Second, the following four meta-heuristics: genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), and artificial bee colony (ABC) are proposed to solve the concerned problems. Furthermore, five local search operations are developed and integrated into the four meta-heuristics to enhance their performance. Third, for selecting high-quality local search operations efficiently, a Q-learning-based local search selection strategy is adopted to replace the random selection strategy. Finally, the relative percentage deviation metric is employed to verify the effectiveness of the proposed enhancement strategies based on a set of benchmark

In recent years, the application of learning-based methods in flow shop scheduling problem has gained considerable attention. However, there are gaps in the quality of their solution due to the difficulty of fully exploring the huge search space faced by learning-based methods and the difficulty of reward function design. In this paper, a hybrid approach of meta-heuristic algorithm and imitation learning (IL) is proposed to solve the permutation flow shop scheduling problem with sequence-dependent setup times (PFSP-SDST). Firstly, jobs are treated as nodes, and the processing time and setup times of PFSP-SDST are considered as features of the nodes, respectively. Secondly, a graph neural network based on an attention feature fusion (AFF) mechanism is designed as an encoder to embed the feature information of the problem. Finally, an iterative greedy algorithm based on critical path is proposed to provide high-quality expert solutions for the IL algorithm. The running results on randomly generated datasets and benchmark datasets demonstrate the effectiveness of the proposed method.

Confronted with increasingly complex industrial scenarios, limited transportation resources and complicated time constraints introduce significant challenges to production efficiency, requiring more robust and adaptive scheduling heuristics. In this study, a flexible job shop scheduling problem with single crane transportation and sequence-dependent setup time is considered. To address the problem, a mixed integer linear programming model is established, where two objectives, including the maximum completion time and total energy consumption, are determined simultaneously. Additionally, a genetic programming (GP) based cooperative evolutionary algorithm is developed to address the problem, in which GP is investigated as a hyper-heuristic to construct a set of problem-specific dispatching rules (DRs). The GP-based hyper-heuristic (GPHH) first evolves a set of DRs during iterations and then applies these DRs to the initialization of the population. Next, four critical path-based neighborhood structures combined with an adaptive local search mechanism are used to enhance the exploitation capability of the algorithm. The simulation results demonstrate that the GPHH used for initialization significantly outperforms other classical heuristics in convergence capability, while the proposed GP-CEA algorithm also surpasses six state-of-the-art algorithms in exploration and exploitation, achieving superior performance on the HV, IGD, and SC metrics in approximately 59.4%, 46.9%, and 50.0% of instances, respectively.

Although an increasing number of studies have focused on the flexible job shop problem, there has been insufficient consideration of realistic constraints, such as the working hours of employees and the noninterruptible nature of certain operations. To address this issue, here an improved deep reinforcement learning (DRL) approach is presented that utilizes end-to-end multidecision-intelligent body proximal policy optimization (m-PPO). In the proposed framework, a heterogeneous graph self-attention neural network (HGAN) model is embedded, which efficiently extracts valuable features from the original state in heterogeneous graphs to capture intricate relationships. Within this framework, agents are divided into five rule-driven job decision agents and data-driven operation-machine ( $\mathcal {O}\text {-}\mathcal {M}$ ) pair decision agents, which incorporate problem-specific knowledge. To optimize the makespan, total costs, and total lateness concurrently, the weight parameters for the objectives are generated by the network and self-updated based on the current state. Numerical experiments demonstrate the effectiveness of the proposed method.

Enterprises have increasingly focused on integrated production and transportation problems, recognizing their potential to enhance cohesion across different decision-making levels. The whale optimization algorithm, with its advantages such as minimal parameter control, has garnered attention. In this study, a hybrid whale optimization algorithm (HWOA) is designed to settle the distributed no-wait flow-shop scheduling problem with batch delivery (DNWFSP-BD). Two objectives are considered concurrently, namely, the minimization of the makespan and total energy consumption. In the proposed algorithm, four vectors are proposed to represent a solution, encompassing job scheduling, factory assignment, batch delivery and speed levels. Subsequently, to generate high-quality candidate solutions, a heuristic leveraging the Largest Processing Time (LPT) rule and the NEH heuristic is introduced. Moreover, a novel path-relinking strategy is proposed for a more meticulous search of the optimal solution neighborhood. Furthermore, an insert-reversed block operator and variable neighborhood descent (VND) are introduced to prevent candidate solutions from converging to local optima. Finally, through comprehensive comparisons with efficient algorithms, the superior performance of the HWOA algorithm in solving the DNWFSP-BD is conclusively demonstrated.

Deep reinforcement learning approaches for flexible job shop scheduling often overlook critical edge features between operations and processing times on operation-machine edges when leveraging heterogeneous disjunctive graphs for feature extraction and processing. To overcome this challenge, a novel heterogeneous progressive attention network is introduced, incorporating a progressive attention mechanism to process different types of node features independently while integrating weighted edge information. This design allows the model to simultaneously capture both node characteristics and edge relationships, enhancing the accuracy and adaptability of scheduling decisions. The proposed approach is evaluated through comparative experiments using CPLEX and OR-Tools. Experimental results demonstrate superior performance over traditional methods in multi-objective FJSP optimization, achieving a more balanced trade-off among multiple objectives while significantly enhancing scheduling quality and computational efficiency.

In the path of coordinating regional development, if different enterprises cannot coordinate and progress together, it will inevitably lead to the phenomenon of "bad money drives out good money". Therefore, this research addresses a distributed blocking flow shop scheduling problem with sequence-dependent setup time and aims to balance the energy consumption costs among factories while satisfying the makespan upper-bound criterion. This optimization problem is denoted as DFm|block,st(sd)|epsilon(ECC/C-max). We propose an accelerated discrete artificial bee colony (A-DABC) algorithm to address our established mathematical model. In the A-DABC algorithm, various advanced neighborhood operators are integrated to achieve a relative balance in the cost of energy consumption among distributed factories. To address the computational cost associated with the designed operators, we developed three accelerated evaluation mechanisms by integrating the energy cost adjustments resulting from insertions or swaps into the original energy cost, effectively reducing the overall computational complexity. The comprehensive statistical experiments demonstrate that the computational effort of energy consumption costs is significantly decreased, and A-DABC has prominent advantages in addressing DFm|block,st(sd)|epsilon(ECC/C-max) by comparing to four existing algorithms in all test cases.

In practical industrial production, workers are often critical resources in manufacturing systems. However, few studies have considered the level of worker fatigue when assigning resources and arranging tasks, which has a negative impact on productivity. To fill this gap, the distributed hybrid flow shop scheduling problem with dual-resource constraints considering worker fatigue (DHFSPW) is introduced in this study. Due to the complexity and diversity of distributed manufacturing and multi-objective, a Q-learning driven multi-objective evolutionary algorithm (QMOEA) is proposed to optimize both the makespan and total energy consumption of the DHFSPW at the same time. In QMOEA, solutions are represented by a four-dimensional vector, and a decoding heuristic that accounts for real-time worker productivity is proposed. Additionally, three problem-specific initialization heuristics are developed to enhance convergence and diversity capabilities. Moreover, encoding-based crossover, mirror crossover and balanced mutation methods are presented to improve the algorithm’s exploitation capabilities. Furthermore, a Q-learning based local search is employed to explore promising nondominated solutions across different dimensions. Finally, the QMOEA is assessed using a set of randomly generated instances, and a detailed comparison with state-of-the-art algorithms is performed to demonstrate its efficiency and robustness

Incorporating energy consumption into optimization has attracted increasing attention in both academia and industry. Nevertheless, the integration of green, flexible, and dynamic manufacturing in literature remains underexplored. To this end, we focus on a dynamic flexible job shop scheduling problem (dFJSP) relevant to aerospace structural components. The following challenging issues are considered, such as processing route flexibility, limited machine and tool resources, transportation time, setup time, new job arrivals, machine breakdowns, and various machine processing speeds. To address this complex problem, a dual-level multi-objective algorithm based on the nondominated sorting genetic algorithm II (hereafter called DLNSGAII) is developed. The first level incorporates a dynamic diffusion-based strategy (D-DBS), which aims to balance exploration and exploitation effectively. This is achieved by quickly identifying high-quality solutions and discarding inferior ones while also ensuring ample computational resources allocated for exploration to avoid convergence on local optima. At the second level, a static convergence-based search strategy (S-CBS) is conducted to allocate resources according to the potential of solutions to achieve faster convergence. Additionally, to tackle the disruptions, two sets of rescheduling mechanisms have been designed: one includes five strategies for integrating new job arrivals, and another encompasses two strategies for responding to machine breakdowns. Furthermore, to enhance the search capabilities toward different objectives, two critical-path-based neighborhood structures have been incorporated. Utilizing hypervolume (HV) and inverted generational distance (IGD) as evaluation metrics, a comparative analysis of algorithmic performance was conducted. Among the 35 experiments, DLNSGAII exhibited superiority in 88.57