The flexible job shop scheduling problem with job insertions (FJSP-JI) poses significant challenges in real-time industrial environments, where minimizing the maximum completion time (makespan) is critical. To address this, we propose a novel approach that combines heterogeneous graph neural networks (HGNN) and deep reinforcement learning (DRL). A heterogeneous graph is designed to model the complex relationships between machines and operations, capturing both topological and temporal dependencies. The joint decision of operation selection and machine assignment is formulated as a Markov decision process (MDP) and optimized via proximal policy optimization (PPO). Experiments demonstrate that our method has a smaller makespan in addressing the dynamic challenge compared to the classical prioritized scheduling rule. Furthermore, the algorithm exhibits strong generalization capabilities, achieving comparable efficiency on large-scale instances without additional training.

In the era of economic globalization, the distributed heterogeneous welding shop scheduling problem (DHWSP) has been considered. Meanwhile, in some actual production scenarios, some jobs can only be processed in certain designated factories (i.e., factory eligibility), and the inevitable uncontrollable system disturbances (e.g., machine maintenance and human factors) lead to uncertain processing time for jobs. However, the research considering uncertain processing time in DHWSP with factory eligibility remains unexplored. Considering the advantages of interval type-2 fuzzy number (IT2FN) in representing the high level of uncertainty, the concept of IT2FN is introduced to tackle uncertain processing time. Then, under the context of green manufacturing, this paper investigates an energy-efficient distributed heterogeneous type-2 fuzzy welding shop scheduling problem with factory eligibility (EDHFWSP-FE). A learning-based hybrid artificial bee colony algorithm (LHABC) is designed to minimize both total energy consumption and makespan in EDHFWSP-FE. Within LHABC, a cooperative initialization is presented to create excellent initial solutions. In employed bee phase, a Q-learning based method is developed to help solutions select a superior neighborhood structure. In onlooker bee phase, a variable neighborhood search (VNS) is proposed to excavate promising neighborhood solutions. In scout bee phase, an estimation of distribution algorithm (EDA) based method is devised to generate new excellent solutions. Finally, experimental results on 27 test instances demonstrate that LHABC outperforms five other multi-objective optimization algorithms. Note to Practitioners—This paper aims to extend DHWSP to EDHFWSP-FE according to practical situations. In the actual production procedure, DHWSP poses more significant challenges. Not only operation sequencing, factory allocation and welding machine allocation matters, but also uncertain processing time and production constraint (e.g., factory eligibility) in the environment are important. Thus, this paper formulates an EDHFWSP-FE with the goals of minimizing total energy consumption and makespan. This problem model is applicable across many welding manufacturing enterprises with complex production environments. To solve this problem, we design a LHABC that hybridizes ABC with other effective methods to enhance its performance. Each component of LHABC is meticulously designed based on the specific characteristics of the problem domain, offering efficient schedules that are both energy-efficient and high-performing for practical implementation. Experimental results verify that all improved components of LHABC contribute to its performance, and LHABC outperforms other optimization algorithms in solving the problem.

Due to the impact of economic globalization, distributed welding shop has become prevalent in real-world manufacturing systems. Moreover, focusing on human-centric, sustainable and resilient industry, Industry 5.0 puts more emphasis on human-robot collaboration (HRC) for its merit in promoting system flexibility and adaptability. However, owing to the instability of human performance, it becomes necessary to employ fuzzy processing time to simulate practical human production. In the context of Industry 5.0, HRC scheduling in distributed mixed fuzzy welding shop is worth exploring, but no related research on this problem is reported. Thus, to address this research gap, this paper investigates a human-robot collaboration energy-efficient distributed mixed fuzzy welding shop scheduling problem (EDMFWSP-HRC), aiming to minimize makespan and total energy consumption (TEC). To solve this issue, a self-learning memetic algorithm (SLMA) is proposed. In SLMA, a hybrid initialization is designed to yield a high-quality initial population. A genetic operator is proposed to improve the exploration capability. A self-learning variable neighborhood search (SLVNS), which hybridizes Q-learning and VNS, is developed to enhance the exploitation capability. A resource adjustment strategy is presented to further optimize TEC. Additionally, to validate the effectiveness of the proposed SLMA, extensive experimental comparisons with 5 other optimization algorithms are conducted. Experimental results illustrate that SLMA outperforms its competitors. Note to Practitioners—Owing to the widespread presence in manufacturing systems, distributed welding shop has attracted considerable attention in both industry and academia. In the context of Industry 5.0, the incorporation of human-robot collaboration (HRC) scheduling in distributed welding shop can promote system productivity and flexibility. Meanwhile, due to the instability of human performance, employing fuzzy processing time to simulate human production more aligns with the practical manufacturing scenario. Thus, this paper investigates a human-robot collaboration energy-efficient distributed mixed fuzzy welding shop scheduling problem (EDMFWSP-HRC). This problem model can be utilized in many welding manufacturing enterprises with HRC production mode. To solve this problem, we design a self-learning memetic algorithm (SLMA) to minimize both makespan and total energy consumption (TEC). The design of all components in SLMA is based on the characteristics of problem. The SLMA can offer the low-energy and high-efficiency schedules for practitioners. Experimental results verify the effectiveness of the proposed SLMA.

Nowadays, application providers often prefer to execute their workflows on heterogeneous distributed computing resources deployed on cloud infrastructure to achieve a high level of resilience and cost saving. Optimally scheduling workflow on computing resources is a well-known combinatorial optimization problem, where a trend of using evolutionary algorithm (EA) is emerging rapidly. However, conventional EA optimizes only one problem in a single run and suffers from a high computational burden. In practical scenario, cloud platform needs to handle massive amounts of scheduling requests from users, scheduling different workflows simultaneously is highly challenging. Bearing this in mind, we put forward a novel knowledge transfer enabled EA to schedule diverse workflows in tandem, where domain knowledge of scheduling one workflow is extracted to enhance the scheduling efficiency of other related workflows. In our design, the knowledge source selection and the intensity of performing knowledge transfer are adapted in a synergistic way. Furthermore, search operator is enhanced by exploiting both historical experience and heuristic information. Experimental results on real-life workflows and extensive synthetic applications demonstrate the competitiveness of our approach, in comparison to state-of-the-art contenders. Note to Practitioners—Workflow scheduling is an important requirement for users in cloud computing, whose intractability increases exponentially when the size of problem grows, posing stiff challenges to heuristic methods. Using EAs to tackle workflow scheduling has received increasing attention recently. Suppose workflow scheduling is treated as a optimization task, cloud platform typically needs to handle versatile tasks from numerous users. However, traditional EA optimizes only one task in a single run and unable to handle multiple tasks at the same time. To address this issue, we introduce a novel multi-task solver to resolve different tasks jointly via online learning and exploitation of problem-solving experiences across tasks. The results demonstrate that our proposal significantly outperforms the state-of-the-art peers. It is expected to facilitate the practical efficacy of industrial cloud system which faces multiple workflow scheduling tasks submitted from enormous users.

The growing trend toward decentralization within factories has brought attention to distributed welding shop scheduling problem (DWSP) among both practitioners and researchers. However, despite the prevalence of job-to-product assembly process in industrial fields, the investigation of distributed assembly welding shop scheduling problem (DAWSP) remains unexplored. Meanwhile, given the energy-intensive characteristic of welding operations, addressing energy consumption in welding shop is crucial for achieving environmental sustainability. Thus, this study investigates the energy-efficient DAWSP (EDAWSP), focusing on minimizing total energy consumption (TEC) and makespan. The proposed approaches include a mixed integer linear programming (MILP) model and a knowledge-guided co-evolutionary algorithm (KCEA). In KCEA, a knowledge coefficient is defined to build a bridge that connects the welding part and assembly part. By incorporating knowledge coefficient and weight-sum approach, an effective initialization strategy is proposed for producing a superior initial population. To effectively complete evolutionary process, a co-evolutionary operator is devised based on bi-population strategy. To improve KCEA’s exploitation capability, a local search is developed within the variable neighborhood search (VNS) framework, utilizing six critical-path-based neighborhood structures. Besides, an energy-saving strategy is presented to further minimize TEC without increasing makespan. Finally, a series of comparison experiments are executed. The experimental results illustrate that all improved components of KCEA contribute to its performance, and KCEA outperforms other six optimization algorithms in solving EDAWSP.

Distributed manufacturing involving heterogeneous factories presents significant challenges to enterprises. Furthermore, the need to prioritize various jobs based on order urgency and customer importance further complicates the scheduling process. Consequently, this study addresses the practical issue by tackling the distributed heterogeneous hybrid flow shop scheduling problem with multiple priorities of jobs (DHHFSP-MPJ). The primary objective is to simultaneously minimize the total weighted tardiness and total energy consumption. To solve DHHFSP-MPJ, a double deep Q-network-based co-evolution (D2QCE) is developed with four features: i) The global and local searches are allocated into two populations to balance computational resources; ii) A hybrid heuristic strategy is proposed to obtain an initialized population with great convergence and diversity; iii) Four knowledge-based neighborhood structures are proposed to accelerate converging. Next, the double deep Q-Network is applied to learn operator selection; and iv) An energy-efficient strategy is presented to save energy. To verify the effectiveness of D2QCE, five state-of-the-art algorithms are compared on 20 instances and a real-world case. The results of numerical experiments indicate that: i) The D2QN can learn fast by only consuming a few computation resources and can select the best operator. ii) Combining D2QN and co-evolution can vastly improve the performance of evolutionary algorithms for solving distributed shop scheduling. iii) The proposed D2QCE has better performance than state-of-the-arts for DHHFSP-MPJNote to Practitioners—This paper is inspired by a real-world problem encountered in blanking workshop systems within the manufacturing of large engineering equipment. In this practical scenario, jobs come with varying priorities and distinct due dates. Balancing these priority and due date constraints while efficiently scheduling a considerable volume of jobs to enhance enterprise profitability poses a significant challenge. Thus, this scheduling problem is abstracted to the distributed heterogeneous hybrid flow shop scheduling problem with multiple priorities of jobs. The objectives are minimizing weighted due date delay and total energy consumption. Notably, this model has never been studied before. To address this, we’ve formulated a mixed-integer linear programming model and developed a novel co-evolutionary algorithm based on double deep Q-networks (DQN). Our approach introduces several key components. First, we present a co-evolutionary framework to strike a balance between global and local search aspects. Additionally, we’ve devised three problem-specific enhancement strategies to expedite convergence, which include hybrid initialization, local search techniques, and energy-saving measures. To accelerate the learning process of selecting the optimal operator with minimal computational resources, we employ the double DQN. Experimental results demonstrate the superior performance of our approach, outperforming state-of-the-art algorithms when applied to a real-world case. In summary, this work proposes an extended DHHFSP and provides a case of designing the deep learning-assisted evolutionary algorithm. However, online deep reinforcement learning (DRL) consumes additional time, and the generalization of online DRL needs to be improved. In future research, we will consider the dynamic events such as new jobs insert and due date change for the blanking workshop. Moreover, the end-to-end model will be considered to save energy and realize sustainable DRL.

With the tendency of decentralization into factories, production scheduling among heterogeneous factories has become a prominent concern in industrial demand response, spurring research on distributed heterogeneous welding shop scheduling problem (DHWSP). Moreover, owing to the inevitable occurrence of uncontrollable system disturbance in practical production environment, the processing time of jobs is uncertain rather than deterministic. Thus, a L-R fuzzy number (LRFN) is introduced to tackle the uncertainty of processing time. Furthermore, in the pursuit of sustainable development, energy efficiency has been a significant emphasis from countries. An effective production scheduling in distributed heterogeneous L-R fuzzy welding shop can optimize both production and energy efficiency, but no related research is reported. Thus, to address this research gap, this paper investigates an energy-efficient distributed heterogeneous L-R fuzzy welding shop scheduling problem (EDHFWSP) with the objectives of minimizing makespan and total energy consumption (TEC). To solve this issue, a self-learning discrete artificial bee colony (SDABC) algorithm is proposed. First, a collaborative initialization is presented to yield excellent initial solutions. Second, a self-learning selection strategy is developed to help solutions select a superior neighborhood structure in employed bee phase. Third, a self-learning variable neighborhood search (SVNS) is designed to adaptively select a neighborhood structure for execution in onlooker bee phase. Fourth, an energysaving strategy is devised to further optimize TEC without affecting makespan. Additionally, to verify the effectiveness of SDABC, extensive experiments are performed to compare SDABC with other 5 optimization algorithms. Experimental results validate that SDABC outperforms its competitors.

Human–robot collaborative scheduling has been widely applied in modern manufacturing industry. A rational scheduling of human–robot cooperation plays an important role in improving production efficiency. However, human–robot collaborative scheduling problem in welding production has not been studied so far. Thus, this article addresses a human–robot collaborative welding shop scheduling problem (HCWSSP) with minimization objectives of makespan and total energy consumption (TEC). To solve this multiobjective HCWSSP, a Pareto-based memetic algorithm (PMA), which hybridizes a genetic operator and variable neighborhood search (VNS), is presented to obtain a set of tradeoff solutions between makespan and TEC. In PMA, each solution is represented by two parts, i.e., job processing sequence and resource assignment. A novel integrated initialization strategy is proposed to generate one initial population with high quality and good diversity. Furthermore, five kinds of VNS are designed to improve the exploitation capability of PMA. Experimental results on test problems manifest that the proposed PMA performs better than its competitors.

Energy-aware distributed heterogeneous flexible job shop scheduling (DHFJS) problem is an extension of the traditional FJS, which is harder to solve. This work aims to minimize total energy consumption (TEC) and makespan for DHFJS. A deep$Q$-networks-based co-evolution algorithm (DQCE) is proposed to solve this NP-hard problem, which includes four parts: First, a new co-evolutionary framework is proposed, which allocates sufficient computation to global searching and executes local search surrounding elite solutions. Next, nine problem features-based local search operators are designed to accelerate convergence. Moreover, deep$Q$-networks are applied to learn and select the best operator for each solution. Furthermore, an efficient heuristic method is proposed to reduce TEC. Finally, 20 instances and a real-world case are employed to evaluate the effectiveness of DQCE. Experimental results indicate that DQCE outperforms the six state-of-the-art algorithms for DHFJS.

With the development of the economy, distributed manufacturing has gradually become the mainstream production mode. This work aims to solve the energy-efficient distributed flexible job shop scheduling problem (EDFJSP) while simultaneously minimizing makespan and energy consumption. Some gaps are stated following: 1) the previous works usually adopt the memetic algorithm (MA) with variable neighborhood search. However, the local search (LS) operators are inefficient due to strong randomness; 2) the confidence-based adaptive operator selection model follows the experiences of the major crowds, which ignores the efficient operators with low weight, so it can not select the really efficient operator; 3) the previous works lack of efficient strategy to save energy; and 4) the mainstream memetic framework adopts LS to all solutions, which causes the population to converge too quickly and the diversity is extremely reduced. Thus, we propose a surprisingly popular-based adaptive MA (SPAMA) to overcome the above deficiencies. The contributions are as follows: 1) four problem-based LS operators are employed to improve the convergence; 2) a surprisingly popular degree (SPD) feedback-based self-modifying operators selection model is proposed to find the efficient operators with low weight and correct crowd decision making; 3) the full active scheduling decoding is presented to reduce the energy consumption; and 4) an elite strategy is designed to balance the resources between global and LS. In order to evaluate the effectiveness of SPAMA, it is compared with state-of-the-art algorithms on Mk and DP benchmarks. The results demonstrate the superiority of SPAMA to the state-of-art algorithms for solving EDFJSP.

Green flexible job-shop scheduling problem (FJSP) aims to improve profit and reduce energy consumption for modern manufacturing. Meanwhile, FJSP with type-2 fuzzy processing time is proposed to predict the uncertainty in timing constraint for better simulating the practical production. This study addresses the multiobjective energy-efficient FJSP with type-2 processing time (ET2FJSP), where the minimization of makespan and total energy consumption are considered simultaneously. The previous studies do not propose the model verification and energy-saving strategy. Moreover, the best parameters required by an algorithm in different stage are different. Therefore, we propose a mixed-integer linear programming model and design a learning-based reference vector memetic algorithm (LRVMA). Its main features are: 1) four problem-specific initial rules that are presented for initialization to generate diverse solutions; 2) four problem-specific local search methods that are incorporated to enhance the exploitation; 3) an effective solution selection method depending on the Tchebycheff decomposition strategy that is utilized to balance the convergence and diversity; 4) a reinforcement learning-based parameter selection strategy that is proposed to improve the diversity of nondominated solutions; and 5) an energy-saving strategy that is designed to reduce energy consumption. To verify the effectiveness of LRVMA, it is compared against other related algorithms. The results demonstrate that LRVMA outperforms the compared algorithms for solving ET2FJSP.

Distributed flow shop scheduling of a camshaft machining is an important optimization problem in the automobile industry. The previous studies on distributed flow shop scheduling problem mainly emphasized homogeneous factories (shop types are identical from factory to factory) and economic criterion (e.g., makespan and tardiness). Nevertheless, heterogeneous factories (shop types are varied in different factories) and environment criterion (e.g., energy consumption and carbon emission) are inevitable because of the requirement of practical production and life. In this article, we address this energy-efficient scheduling of distributed flow shop with heterogeneous factories for the first time, where contains permutation and hybrid flow shops. First, a new mathematical model of this problem with objectives of minimization makespan and total energy consumption is formulated. Then, a hybrid multiobjective optimization algorithm, which integrates the iterated greedy (IG) and an efficient local search, is designed to provide a set of tradeoff solutions for this problem. Furthermore, the parameter setting of the proposed algorithm is calibrated by using a Taguchi approach of design-of-experiment. Finally, to verify the effectiveness of the proposed algorithm, it is compared against other well-known multiobjective optimization algorithms including MOEA/D, NSGA-II, MMOIG, SPEA2, AdaW, and MO-LR in an automobile plant of China. Experimental results demonstrate that the proposed algorithm outperforms these six state-of-the-art multiobjective optimization algorithms in this real-world instance.

This paper presents an industrial application of the analytical target cascading methodology to wellbore trajectory optimal design. Two objective functions are taken into account: minimizing the wellbore trajectory length and to minimize torque on the drill string during the drilling operation. The problem is formulated and solved with the analytical target cascading method. Results shown that ATC would effectively coordinate the objectives to yield reasonable results relative to the existing evolutionary algorithms.

Welding, an irreplaceable process in the modern manufacturing industry, consumes enormous amounts of energy. The schedule in a welding shop greatly impacts both its energy consumption and productivity. Thus, it is of great significance to solve the welding shop scheduling problem (WSSP) considering both energy efficiency and productivity. In this paper, to solve a real-life WSSP, a multiobjective mathematical model is proposed and an effective multiobjective artificial bee colony algorithm (MOABC) is developed. The results of a designed numerical experiment indicate that the proposed MOABC performs better than Strength Pareto Evolutionary Algorithm 2 and Nondominated Sorting Genetic Algorithm II. Finally, the proposed model and MOABC algorithm are applied to solve a real-life girder WSSP of a Chinese crane company. The results also demonstrate that the proposed method can greatly reduce energy consumption and makespan compared to other algorithms.