This paper studied the problem of wafer probing scheduling in wafer fabrication plants. As the final step in the front-end process of semiconductor manufacturing, wafer probing plays a critical role in wafer production. The wafer probing scheduling problem is modeled as a flexible job shop scheduling problem, considering resource constraints and batch processing. Firstly, a mixed-integer programming model is constructed to minimize the makespan. Then, an improved gray wolf optimizer is proposed to address the wafer probing scheduling problem. This improved gray wolf optimizer incorporates three improvement strategies within the framework of the original gray wolf algorithm: (1) an opposition-based learning approach is utilized to enhance the quality of the initial population; (2) leader agents mutation strategy is developed for local search; (3) a parameter adaptive adjustment is introduced to balance local and global search. In addition, an active decoding framework based on prior knowledge is designed to accelerate the convergence of the improved gray wolf optimizer. Finally, the effectiveness of the proposed improved gray wolf optimizer is verified on 15 instances of varying scales, and the results demonstrate that the proposed improved gray wolf optimizer outperforms other state-of-the-art algorithms.

Iron and steel industry is a significant basic industry of national economy. Steelmaking-Refining-Continuous Casting (SRCC) is one of the bottlenecks of the iron and steel production process. SRCC scheduling problems are world-wide and NP-hard problems. SRCC scheduling problems considering energy saving are named Energy-Efficient SRCC (EESRCC) scheduling problems. Effective EESRCC scheduling algorithms would not only help to enhance the production efficiency, but also help to reduce the energy saving. This paper proposed a Discrete Growth Optimizer (DGO) to solve the EESRCC scheduling problems. Differ from the traditional GO, the proposed DGO is enhanced by incorporating five strategies. More specifically, a population initialization heuristic is designed to generate a relatively ‘good’ initial population. The control based local search is devised to enhance the intensification and diversification abilities of the proposed DGO. The restricted local search is designed to further improve the three best solutions found so far. The enhanced learning phase is devised to learn from the three best solutions found so far and elite solutions in the population. The multi-type reflection phase is developed to further enhance the solutions in the population. The effectiveness of the DGO has been verified by the experiments.

This paper investigated Integrated Hybrid Flowshop Scheduling with Sequence-Dependent Setup Times and Vehicle Routing Problems Considering Customer Priority (IHFSS-VRPC). The IHFSS-VRPC are joint optimization problems, which integrate the Hybrid Flowshop Scheduling with Sequence-Dependent Setup Times (HFSP-SDST) with the Vehicle Routing Problems (VRP) Considering Customer Priority and maximum driving distance constraint. The problems are different from the Integrated Hybrid Flowshop Scheduling Problems (HFSP) and VRP. To deal with the IHFSS-VRPC effectively, this paper proposed a Hybrid Fireworks Algorithm (HFWA). In the proposed HFWA, six key components, i.e., Two stage decoding, Population initialization, Variable Neighbourhood Search (VNS) based local search, Explosion amplitude calculation, Mutation operator and Selection strategy, were elaborately to enhance the search abilities. More specifically, the Two stage decoding was presented to compile effective schedules, the Population initialization, Explosion amplitude calculation and Selection strategy were devised to balance the exploitation and exploration capacities. The VNS based local search was developed to improve the exploitation capacities, while the Mutation operator was devised to enhance the exploration capacities. The performance of the proposed HFWA has been demonstrated by conducting comparison experiments on a set of instances.

This paper proposes an iterative branch-and-bound (IB&B) approach for complex product assembly station scheduling problems (CPASSP) to minimize the total weighted tardiness (TWT). First, an iterative adjusting mechanism for upper bounds is designed to improve the efficiency of the algorithm. The upper bound in the proposed algorithm is set directly without a method to obtain a feasible solution. If no feasible solution is found, the upper bound is adjusted and the branch-and-bound component is executed again. Second, a station-based branching strategy is developed to decompose the CPASSP problem, which is able to avoid the many-to-one situations typically encountered with task-based branching strategies. Moreover, a disjunctive graph for CPASSP is formulated to represent and evaluate a schedule. The proposed IB&B is compared with alternative branch-and-bound approaches and a mixed integer linear programming (MILP) model implemented by CPLEX solver on four test instances of different scales. Experimental results demonstrate that the proposed IB&B is more efficient and obtains optimal solutions with less computation time.

Additive manufacturing has revolutionized the way to design and manufacture products by enabling complex geometries and on-demand production. However, 3D printing without scheduling is time-consuming and space-inefficient. To address these issues, a dense pixel-based genetic algorithm (DPGA) is proposed. To fast characterize 3D parts, a tolerant pixel matrix (TPM) is adopted for abstraction. Based on the TPM, a double-layer encoding scheme is designed to represent the solutions. An active decoding strategy is designed to maximize space utilization, which can improve the quality of schemes decoded with the same encoding. In the section of operator design, an initialization strategy based on load balancing is developed, which can effectively improve the quality of initial population. Additionally, a population rebirth mechanism is designed to efficiently escape from local optima. Computational experiments demonstrate the effectiveness of DPGA in solving additive manufacturing scheduling problems with varying sizes and complexities. The proposed DPGA outperforms traditional genetic algorithm and other state-of-the-art methods in terms of processing time and packing density.

Due to the complexity of production scheduling and increasing demand, various methods, including solvers, are widely applied to the job shop scheduling problem. Among these, using machine learning techniques to enhance solver quality has attracted significant attention. However, beyond the model, the characteristics of problems greatly influence solver performance. This study focuses on the classic job shop scheduling problem and explores methods to improve constraint programming model efficiency through machine learning. An automatic branching strategy selection method based on machine learning is proposed, consisting of two components: the problem features extraction and strategy selection identification. For features extraction, three feature extraction approaches are designed. In the strategy selection phase, a classification method based on the graph neural network is used to incorporate the set of three types of features, and the problem-related loss function is designed. We conducted experiments on the proposed method on 3500 training sets and 70 test sets (benchmark), and compared the experiments with the automatic selection strategy that comes with OR-Tools. The results show that the proposed method can obtain equal or better solutions on 81.42% of the instances.

Human–machine hybrid reconfiguration manufacturing is an emerging paradigm in the field of precision equipment production and can greatly improve the production capability of the workshop. However, numerous complex constraints and a dynamic environment make reasonable scheduling very difficult. To this end, this article studies the dynamic human–machine hybrid reconfiguration manufacturing scheduling problem (DHMRSP) and proposes a novel deep reinforcement learning (DRL) scheduling method. Specifically, a dual-agent Markov decision process (MDP) is established, which can handle seven complex constraints and three disturbance events. Then, a heterogeneous competition graph attention network (HCGAN) is designed, where the meta-path-based subgraph conversion reflects the resource-operation competition, and three modules use node-level attention and semantic-level attention to realize important information embedding. Afterward, a dual proximal policy optimization (PPO) algorithm with HCGAN and mixed action space (HM-DPPO) is proposed, where the allocation agent and reconfiguration agent achieve collaborative learning by taking joint action and sharing graph embeddings and reward. Experimental results prove that the proposed approach outperforms rules, genetic programming (GP), and three DRL methods on different instances and can effectively handle various disturbance events.

Cluster tools (CTs) are extensively utilized in semiconductor manufacturing. To tackle the challenging scheduling problems of CTs that concurrently process two wafer types, studies have been previously conducted based on predetermined robot task sequences, resulting in suboptimality of throughput and low wafer residency time constraint (WRTC)-satisfaction ratio. With both WRTC and chamber cleaning operations taken into account for the first time, this work proposes a deterministic scheduling strategy by drawing on previous studies, as well as a novel and efficient mixed integer programming (MIP) model to determine the optimal release sequence of wafer types and robot task sequence. Compared to the existing deterministic scheduling strategies, computational experiments on large randomly generated instances show that the developed MIP model could improve throughput by 2.63% on average, and enhance the WRTC-satisfaction ratio by at least 108.33% demonstrating its effectiveness and significance.

This paper considers a flexible job shop rescheduling problem under machine breakdowns to minimize the sum of the deviations from the preschedule. A deep reinforcement learning (DRL)-based rescheduling method is proposed for the problem. Total slack transmission graph is proposed as the input of the deep neural network and graph attention network is adopted to extract the features of the graph. Operation selection network and machine selection network are designed to perform a series of actions with the aim of repairing the preschedule that affected by a machine breakdown. Especially, a "done" network is designed to stop the action selections. The numerical results show that the proposed DRL-based rescheduling method is effective with comparisons of reactive recovery rescheduling heuristics.

The flexible job scheduling problem with batch processing machines (FJSP-BPM) is an extension of the flexible job shop scheduling problem and batch scheduling problem in some engineering scenarios. It allows an operation to be processed by any usable machines, and multiple jobs can be processed on a batch in batch processing machines simultaneously. In this study, a mixed integer linear programming model is proposed to minimize the makespan. This study first designs a strategy of chromosome slicing based on the marginal cost to generate batches and a hybrid genetic algorithm (HGA) is proposed to solve the FJSP-BPM problem. Neighborhood structures are designed to search for better solutions. Finally, the experimental results demonstrate that the proposed HGA has obtained the best solutions for all instances and has effectively solved the FJSP-BPM problem.

In real-life production systems, arrivals of jobs are usually unpredictable, which makes it necessary to develop solid reactive scheduling policies to meet delivery requirements. Deep reinforcement learning (DRL) based scheduling methods are capable of quickly responding to dynamic events by learning from the training data. However, most of policy networks in DRL algorithms are trained to choose priority dispatching rules (PDR), thus, to some extent, the efficiency of obtained scheduling plans is limited by the performance of PDRs. This paper investigates a dynamic flexible job shop scheduling problem with random job arrivals for the total tardiness minimization. A DRL-based reactive scheduling method, proximal policy optimization with attention-based policy network (PPO-APN), is proposed to make real-time decisions for the dynamic scheduling environment, where the attention-based policy network (APN) is able to directly select pending jobs distinguished from the action space that consists of PDRs. Additionally, a global/local reward function (GLRF) is designed to address the reward sparsity issue during training processes. The proposed PPO-APN is tested on randomly generated instances with different production configurations, and is compared with frequently-used PDRs and DRL-based methods. Numerical experimental results indicate that APN and GLRF components significantly improve the training efficiency, and the PPO-APN shows better overall performance compared with other methods.Note to Practitioners—This work is motivated by a typical production scenario in discrete manufacturing systems, where orders randomly arrive at the shop floor and require to be scheduled in a short time to ensure the on-time delivery. Previous research work tends to apply DRL algorithms to choose suitable dispatching rules for the ease of implementation. Nevertheless, the jobs that can be selected by dispatching rules are rather limited, thus many possible high-quality scheduling plans are ignored. This work first sorts all the unscheduled jobs by a heuristic algorithm, and puts some of top-ranked jobs to a pool. When a machine becomes available, it will directly choose a job from the pool as the next processing task. The job selection policy is represented by a novel attention-based network, and is trained by a powerful DRL algorithm. The aforementioned process is repeatedly executed in a simulation environment to collect the training data. Therefore, after being trained for a certain period of time, the policy will become smarter and can be applied to make right decisions in real-time. The proposed reactive scheduling method has been proved to be more efficient than dispatching rules and DRL-based approaches, and is effective in the production scheduling for a wide variety of discrete manufacturing scenarios, such as automobile and electronics industries. Moreover, the proposed method can be further extended to address dynamic scheduling problems with some production characteristics via adding constraints for the job selection or re-defining calculations for the completion time of operations accordingly.

This paper studies a flexible job shop rescheduling problem with lot-streaming and machine reconfigurations (FJRP-LSMR) to minimize the sum of the instability and total weighted tardiness, where machine reconfigurations are performed by assembling selected auxiliary modules for processing different batches of products. In this case, a rescheduling process is triggered by dynamic events, and requires to determine the lot-sizing plan, machine assignment, and sublot sequencing simultaneously. To address the intractable problem with multiple decision-making processes, a matheuristic integrating the genetic algorithm (GA) and the mixed integer linear programming (MILP) technique is proposed, where an MILP model is developed for optimally solving the lot-sizing sub-problem, and is embedded to the GA as a local search function. The proposed matheuristic is tested on randomly-generated instances to investigate the performance of all the algorithmic components. Experimental results demonstrate that the GA representation is effective in the complicated dynamic scheduling problem, and the lot-sizing sub-problem can be well addressed by the proposed MILP-based local search.

This paper proposes a bi-level Multi-Start Variable Neighborhood Search-Genetic Algorithm (MSVNS-GA) for the heat pipe-constrained component layout optimization (HCLO) problems. The proposed algorithm has won the first place in the CEC’2022 Competition on the Heat Pipe-Constrained Component Layout Optimization. First, the HCLO problem is divided into two sub-problems, heat pipe assignment (HA) and component location (CL). In the HA problem, components are assigned to different heat pipes. The best assignment scheme is taken as the input of the CL problem. In the CL problem, the specific coordinates of components are determined to meet practical engineering constraints. In this way, the complexity of the problem is lowered, and a part of the infeasible solution is cropped. Second, to address the HA problem, a multi-start variable neighborhood search algorithm is proposed and five efficient bottleneck-aware neighborhood structures are designed. And the genetic algorithm is used for CL problem. Finally, 30 independent experiments are carried out on the calculation examples with sizes of 6×4, 15×6, 40×16, and 90×32. The best result obtained by MSVNS-GA is 0.0%, 1.0%, 0.8%, and 1.1% different from the estimated lower bounds.

As an extension of the classical flow-shop scheduling problem, the hybrid flow-shop scheduling problem (HFSP) widely exists in large-scale industrial production systems and has been considered to be challenging for its complexity and flexibility. Evolutionary algorithms based on encoding and heuristic decoding approaches are shown effective in solving the HFSP. However, frequently used encoding and decoding strategies can only search a limited area of the solution space, thus leading to unsatisfactory performance during the later period. In this article, a hybrid evolutionary algorithm (HEA) using two solution representations is proposed to solve the HFSP for makespan minimization. First, the proposed HEA searches the solution space by a permutation-based encoding representation and two heuristic decoding methods to find some promising areas. Afterward, a Tabu search (TS) procedure based on a disjunctive graph representation is introduced to expand the searching space for further optimization. Two classical neighborhood structures focusing on critical paths are extended to the problem-specific backward schedules to generate candidate solutions for the TS. The proposed HEA is tested on three public HFSP benchmark sets from the existing literature, including 567 instances in total, and is compared with some state-of-the-art algorithms. Extensive experimental results indicate that the proposed HEA performs much better than the other algorithms. Moreover, the proposed method finds new best solutions for 285 hard instances.

Job shop scheduling problem (JSSP) is a typical scheduling problem in manufacturing. Traditional scheduling methods fail to guarantee both efficiency and quality in complex and changeable production environments. This paper proposes an end-to-end deep reinforcement learning (DRL) method to address the JSSP. In order to improve the quality of solutions, a network model based on transformer and attention mechanism is constructed as the actor to enable a DRL agent to search in its solution space. The Proximal policy optimization (PPO) algorithm is utilized to train the network model to learn optimal scheduling policies. The trained model generates sequential decision actions as the scheduling solution. Numerical experiment results demonstrate the superiority and generality of the proposed method compared with other three classic heuristic rules.

When a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is applied to solve problems with discontinuous Pareto front (PF), a set of evenly distributed weight vectors may lead to many solutions assembling in boundaries of the discontinuous PF. To overcome this limitation, this article proposes a mechanism of resetting weight vectors (RWVs) for MOEA/D. When the RWV mechanism is triggered, a classic data clustering algorithm DBSCAN is used to categorize current solutions into several parts. A classic statistical method called principal component analysis (PCA) is used to determine the ideal number of solutions in each part of PF. Thereafter, PCA is used again for each part of PF separately and virtual targeted solutions are generated by linear interpolation methods. Then, the new weight vectors are reset according to the interrelationship between the optimal solutions and the weight vectors under the Tchebycheff decomposition framework. Finally, taking advantage of the current obtained solutions, the new solutions in the decision space are updated via a linear interpolation method. Numerical experiments show that the proposed MOEA/D-RWV can achieve good results for bi-objective and tri-objective optimization problems with discontinuous PF. In addition, the test on a recently proposed MaF benchmark suite demonstrates that MOEA/D-RWV also works for some problems with other complicated characteristics.

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The${\varepsilon }$-constrained method is a very effective one. In the literature, the${\varepsilon }$value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive${\varepsilon }$control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of${\varepsilon }$through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive${\varepsilon }$-constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive${\varepsilon }$control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method.

With rapid population growth and urbanization, municipal solid waste (MSW) generation rates are rising around the world. Incineration is considered as an effective way to deal with the growing demand for MSW disposal. The prediction of concentrations of pollutants generated from MSW incineration plants is a powerful support for waste incineration process control, which aims to reduce pollutant emissions. This paper proposes a two-stage prediction method based on the long short-term memory (LSTM) network to forecast typical flue gas pollutants of an MSW incineration plant in South China. In the first stage, an LSTM-based classification model is utilized to determine whether the pollutants are at a low level, and over-sampling strategy is applied to deal with the class-imbalance problem. At the second stage, an LSTM-based prediction model is built to further estimate the amounts of pollutants. Besides, the sliding average method is used to process the multi-scale raw data. Experiment results proved the effectiveness of the proposed method and indicated how different inputs affect the forecasting of pollutant emissions.

As the complexity of the real-world engineering problems increases, numerous efficient constraint-handling methods and optimization algorithms have emerged recently. However, the majority of the research consider the constraint-handling method and the optimization algorithm independently. In this paper, we propose a constraint-based mutation operator, in which the constraint violation and objective function are considered simultaneously. We define the pbest individuals as the best in top 5% constraint violators if all the individuals are infeasible. In this way, we could guide the population move towards the feasible region. Two real-world engineering applications are used to test the performance of the IεJADE. Compared with the state-of-the-art algorithms, the experimental results illustrate the effectiveness of the IεJADE algorithm, which also exhibits a fast convergence rate in terms of computation efficiency.

Today, manufacturing enterprises must respond quickly to the ever-changing market environment in order to survive. At the same time, dynamic disturbances in production sites such as machine failures, reworking caused by quality problems, and changes of processing time and personnel will also have negative impacts on the effectiveness of the original plan. In order to ensure the feasibility of scheduling algorithms in highly dynamic environment, this paper presents agent-based rescheduling negotiation mechanisms with five dynamic disturbances, and verifies its feasibility through simulations. A multi-agent system structure with quick responses and simple communication networks is designed according to characteristics of hybrid flow shops, with which the processing of jobs can be easily traced back.

A flexible job shop scheduling problem with lot-streaming (LSFJSP) is studied in this work. Lot-streaming means dividing all jobs in an order into several independent sublots and each sublot contains a certain number of jobs from the order. A discrete grey wolf optimizer (DGWO) is proposed for solving LSFJSP. In the algorithm, an encoding method with two strings including task string and sublot string is designed based on the characteristics of LSFJSP. And a positive decoding method combined with the rules of first come first served (FCFS) and shortest process time (SPT) is developed to reduce the solution space. Several strategies including population guide mechanism, critical task local search, and wolf random walk are adopted in the DGWO to make the algorithm suitable to solve LSFJSP. The results of computational experiments on 120 instances show that the DGWO is an competitive algorithm for LSFJSP.

Economic dispatch problem (EDP) is an important optimization problem in modern power system. When involved with valve-point loading effect, this problem becomes a complex non-convex and non-linear optimization problem. In this case, many researchers adopt evolutionary algorithms to solve it. An equality constraint, the power balance constraint, exists in this problem. This constraint leads some common constraint handling methods, such as feasibility rules and ε constraint method, to failure. In this paper, we propose a new constraint handling method which converts the power balance constraint into two boundary inequality constraints, and apply differential evolution (DE) combined with feasibility rules and ε constraint method to solve this problem. In order to prove its effectiveness, three benchmarks are tested. The numerical results show that with the help of the new transforming method, feasibility rules and ε constraint method perform very well in the three benchmarks. Compared with other algorithms in literatures, the simplest DE combined with ε constraint method also demonstrates competitiveness.

A De-Re-coupling uni-polarity phase-shifted control strategy is proposed in this paper. This waveform control method can achieve zero voltage switching (ZVS) of all the switches in the matrix/cycloconverter and natural commutation of the filter inductance without auxiliary circuits and commutation overlap of the matrix/cycloconverter. For the uni-polarity phase-shifted controlled single-phase high-frequency link matrix inverter (SPHFLMI), a novel optimized waveform method is introduced to solve the problem of low voltage utilization and high harmonic components caused by dead-time through changing the setup of adding dead-time in this paper. The feasibility and effectiveness of the proposed strategy are verified by simulation and experimental results.

The delineation of management zones is an economical and effective measure for the variable-rate application in precision agriculture. The methods of empirical and unsupervised classification have been used by many researchers in the delineation of management zones, but these methods are only built upon the information of attributes in every spatial cell, and the spatial relationships and their spatial interaction between cells are not considered. AS a result, there are many isolated cells or patches in the zoned map, this is not advantageous for the operation of the variable-rate application. Based on the traditional k-means cluster (K-M) and the spatial autocorrelation, a new method, spatial contiguous k-means clustering algorithm (SC-KM), was developed in this study. According to the spatial variability of wheat growth under within-field level extracted from OMIS image of the key growth stage, management zones were delineated by using K-M and SC-KM methods. Two evaluation indices were employed to evaluate the zoned results of the above mentioned two methods .The results showed that the sum of the weighted variance of the corresponding within-zones based on the two methods appeared no significant difference, and that the SC-KM method could remove lots of isolated cells or patches and improved the continuity of the corresponding management zone map, compared with the K-M method. The zoned result based on the SC-KM method can be used as the variable management unit for precision agriculture and can be used to advise the sampling of subsequent soil or crop.