Dynamic flexible job shop scheduling (DFJSS) problem is an important scenario in intelligent manufacturing domain with the requirement of real-time decision-making under complex constraints. Existing approaches struggle to handle dynamic environments and heterogeneous job-resource relationships effectively while keeping optimum scheduling performance simultaneously. To address this challenge, a heterogeneous graph reinforcement learning framework combining question-aware neighborhood aggregation and interoption prompt attention (QIHGRL) is presented to address the DFJSS problem with new job insertions and variable processing times to minimize total tardiness. The optimization objectives are transformed into attention-guided signals by the question-aware neighborhood aggregation module to improve feature representation in the heterogeneous graph encoding stage of the QIHGRL. The competition and collaboration among scheduling actions are explicitly modeled by the interoption prompt attention layer in the policy optimization phase of the QIHGRL via adjusting action selection weights through a multihead attention mechanism to balance exploration and exploitation of the candidates in the population of the QIHGRL. The experimental results testified that the performance and efficiency of the QIHGRL outperforms that of the state of the arts algorithms.

The production process of aluminum profiles is a typical distributed flexible job shop environment. The scheduling problem in distributed systems with worker factors is a complex combinatorial optimization problem. In this article, the multiobjective distributed flexible job shop scheduling with worker factors (MO-DFJSPWF), including proficiency and the learning–forgetting effect, is studied to minimize makespan and total resource load (TRL). A mixed-integer linear programming (MILP) model is established according to the degree of proficiency and the rate of learning–forgetting effect of the workers. A tri-stage cooperative optimization algorithm (TSCOA) is designed for the MO-DFJSPWF. First, a knowledge-based initialization method considering worker proficiency, machine load, and job priority is proposed to generate the initial population of the problem. Second, a bi-population cooperative strategy with a dynamic adaptive search strategy (DASS) is developed to balance the convergence speed and candidate diversity of the algorithm. Eight perturbation operators in the second and third stages are introduced to explore and exploit the solution space of the TSCOA. Third, the perturbation operators are selected dynamically via the Q-learning mechanism by leveraging the historical performance data of local search operators. The effectiveness and efficiency of the TSCOA are tested on a benchmark test suite. The experimental results indicated that the performance of the TSCOA outperforms certain state-of-the-art algorithms in solving MO-DFJSPWF.

Addressing the dynamic flexible job shop scheduling (DFJSS) problem to generate a high-quality rescheduling scheme has gained increasing significance in various applications in recent years, such as the intelligent manufacturing system for aluminum profiles. In the intelligent manufacturing system for aluminum profiles, random events such as machine faults and variable processing times significantly affect production completion times. However, existing methods for solving DFJSS face challenges in generating high-quality rescheduling schemes in real time. To address these issues, a search strategy that combines graph neural networks (GNNs) and neighborhood search features is employed in the Monte Carlo tree search (MCTS) algorithm (GNS-MCTS) for real-time solving of the DFJSS. The search strategy in the GNS-MCTS aims to build a model that analyzes the scheduling disjunctive graph and predicts the searching probability, guiding the MCTS to important locations in the solution space rather than searching unimportant areas and wasting computing time. Specifically, the search strategy of GNS-MCTS incorporates encoders that fuse neighborhood search features and graph embedding vectors (GEVs) to improve the quality of the searching probability and make decisions about optimizing the scheduling disjunctive graph by breaking low-importance node pairs and reallocating low-importance nodes to other machines. Experimental results indicate that GNS-MCTS surpasses baseline algorithms across various problem sizes and real-time constraints, significantly enhancing computational efficiency and solution quality for the DFJSS. Further ablation studies and analysis reveal the impact of neighborhood search features on the enhancement of the learning-based search strategy when combined with neighborhood search for real-time DFJSS solutions.

In the production enterprises, the distributed hybrid flow-shop scheduling problems widely exist in the actual production controlling and decision, especially in the production of steel and aluminum. Considering the uncertain processing time in the actual production environment, the constraint of deteriorated variable processing time is added in some problems. In this paper, the distributed hybrid flow-shop scheduling problem with deterioration effect (DHFSP-DE) is investigated. The framework of evolutionary multitasking memetic algorithm (MTMA) is designed to address the proposed model. In the proposed method, evolutionary transfer learning is utilized to communicate between two independent DHFSP-DE solvers. The implicit knowledge of the scheduling scheme can be transferred into other solvers to guide the evolution of the population. The memetic algorithm combines a strategy of local intensification with a population-based paradigm. These strategies can capture the implicit knowledge of DHFSP-DE. This paper makes the first attempt to work on the framework of evolutionary multitasking learning for DHFSP-DE problems. The experimental results on the different instances show the effectiveness and efficiency of the proposed MTMA algorithm.Note to Practitioners—The distributed hybrid flow-shop scheduling problem with deterioration effect (DHFSP-DE) is modeled based on the production process of aluminum. The DHFSP-DE is also widely used in the production process of various industries. As the processing time of the job is varied with time, the determined scheduling problem is transformed into a scheduling problem with deterioration effect. This transformation makes the problem even more complicated. The problems are more complex than static problems because they require greater computational dimensionality for evolutionary computation, resulting in the use of computational resources. An evolutionary multitasking memetic algorithm is designed to solve DHFSP-DEs cooperatively. The solutions of the solver can be transferred to other solvers through the mapping of DHFSP-DEs. The transferred solution can affect the evolution process. The efficiency and effectiveness of the proposed MTMA are verified by the comparison experiments. In addition, the MTMA framework can be applied to other scheduling problems.

Deterministic processing time are no longer applicable under realistic circumstances because of the uncertainties involved in manufacturing and production processes. The present study aims to address a multiobjective distributed assembly flexible job shop scheduling problem with type-2 fuzzy time (DAT2FFJSP), focusing on the optimization objectives of minimizing the makespan and total energy consumption. To address this problem, a mixed-integer linear programming model is presented. Then, a population-based iterative greedy algorithm (PBIGA) with a Q-learning mechanism is proposed, which possesses the following characteristics: 1) a hybrid initialization method is used to generate the population; 2) six local search operators, crossover operators, and mutation operators are applied to explore and exploit the solution space; and 3) the Q-learning mechanism intelligently utilizes historical information on the success of local search operator updates to determine the most suitable perturbation operator; and 4) an energy-saving strategy is applied to improve the candidate solutions. Finally, the effectiveness of the proposed components is validated through extensive experiments that are conducted on 30 instances. The PBIGA outperforms the state-of-the-art algorithms on the DAT2FFJSP.

Learning differential evolution (DE) algorithms are widely adopted to address flexible job-shop scheduling problems (FJSPs) because of the optimization ability. However, traditional learning DEs are not sufficient to develop the feature information of the problem. In this article, a feature-based learning DE algorithm (FLDE) is proposed to address FJSP considering worker health. Occupational repetitive actions index (OCRA) is an indicator that describes the degree of worker fatigue. The OCRA is utilized to ensure the feasibility of scheduling solutions generated by FLDE. A feature-based decision model (FDM) is designed to select the appropriate optimization operator for a scheduling solution. A critical operation search method is introduced to extract feature information from the scheduling solution. Experimental results reveal that FDM is critical to improving the local optimization ability of FLDE, and that FLDE outperforms the comparison algorithms on 40 problem instances.

In the face of environmental deterioration and global climate change, the concept of carbon neutrality and carbon peaking has gained prominence as a means to balance development and environmental preservation worldwide. Energy-aware scheduling is becoming the key scenario for environment conservation in manufacturing. This study focuses on addressing the energy-aware distributed no-wait flow-shop scheduling problem in a heterogeneous factory system (EDNWFSP-HFS) to minimize total energy consumption (TEC) and total tardiness (TTDs). A mixed-integer linear programming (MILP) model is formulated and a policy-based meta-heuristic algorithm (MHA-PG) is specifically designed to solve EDNWFSP-HFS. First, the optimal allocation rules based on random sequence (OAR-RS) are designed to initialize the population. Second, a policy-based method is employed to guide the algorithm toward making a better decision. Third, the energy-saving strategy considering specific knowledge of EDNWFSP-HFS is summarized to further optimize the feasible solution. Extensive simulations are conducted, comparing the performance of MHA-PG against several state-of-the-art algorithms. The results demonstrate that the proposed algorithm outperforms the competing approaches in solving EDNWFSP-HFS, indicating its superior performance and effectiveness.

The production process of steelmaking continuous casting (SCC) is a typical heterogeneous distributed manufacturing system. The scheduling problem in heterogeneous distributed manufacturing systems is a complex combinatorial optimization problem. In this article, the energy-aware distributed heterogeneous flexible flow shop scheduling problem (EADHFFSP) with variable speed constraints is studied with objectives, including total tardiness (TTD) and total energy consumption (TEC). A mixed-integer linear programming (MILP) model is constructed for the EADHFFSP. A co-evolution algorithm with dueling reinforcement learning mechanism (DRLCEA) is presented to address EADHFFSP. In DRLCEA, a knowledge-based hybrid initialization operation is proposed to generate the initial population of the problem. A global search based on adversarial generative learning is designed to search the solution space. The dueling double deep Q-network (DDQN) is applied to select the operator for the local search. A speed adjustment strategy and an energy-saving strategy based on knowledge are proposed to reduce TTD and TEC of the EADHFFSP with regard to the properties of EADHFFSP. The results of experiments show that the performance of DRLCEA is superior to certain state-of-the-art comparison algorithms in solving EADHFFSP.

Automatic selection of the most appropriate algorithms for complex optimization problems has emerged as a cutting-edge trend in artificial intelligence. This approach circumvents the interpretability challenges posed through trial and error. A hyperheuristic and reinforcement learning-guided meta-heuristic algorithm recommendation (HHRL-MAR) is proposed to facilitate the adaptive selection of a diverse array of meta-heuristic algorithms tailored to the unique characteristics of various problems in this paper. To this end, four meta-heuristics with distinct advantages are integrated to form the action space within the reinforcement learning, serving as the low-level heuristic for hyperheuristic. The incorporated reward mechanism based on the real-time state of the population enhances both the flexibility and accuracy of the algorithm. Three selection strategies in light of simulated annealing and ε–greedy are avoid premature convergence associated with designed to a singular selection approach. The experimental results show the efficacy of HHRL-MAR for large-scale complex continuous optimization in terms of accuracy, stability, and convergence speed.

The distributed no-idle permutation flowshop scheduling problem (DNIPFSP) has widely existed in various manufacturing systems. The makespan and total tardiness are optimized simultaneously considering the variety of scales of the problems with introducing an improved iterative greedy (IIG) algorithm. The variable neighborhood descent (VND) algorithm is applied to the local search method of the iterative greedy algorithm. Two perturbation operators based on the critical factory are proposed as the neighborhood structure of VND. In the destruction phase, the scale of the destruction varies with the size of the problem. An insertion operator-based perturbation strategy sorts the undeleted jobs after the destruction phase. The$Q$-learning mechanism for selecting the weighting coefficients is introduced to obtain a relatively small objective value. Finally, the proposed algorithm is tested on a benchmark suite and compared with other existing algorithms. The experiments show that the IIG algorithm obtained more satisfactory results.

A cooperative two-stage migrating birds optimization (CTMBO) algorithm based on quasi-entropy is proposed to solve complex continuous numerical optimization problems. First, a two-stage cooperative mechanism including different mutation and crossover operators is employed to generate neighborhood solutions. Second, a quasi-entropy index is proposed as the judgment condition to balance exploration and exploitation dynamically. The elitist-guided evolutionary strategy, which is a co-evolution tactic from elite individuals and individuals in the following flock, is applied to strengthen global search capability. Meanwhile, the capability of local search is enhanced by the individual cooperation strategy, which is designed based on a co-evolution tactic among individuals in the following flock. The performance of CTMBO is evaluated on CEC 2017 benchmark suite by comparing it with certain state-of-art algorithms. The experimental results indicate the effectiveness of CTMBO on continuous complex problems.

Selecting appropriate algorithms for specific problems has become a significant challenge with the remarkable growth of heuristics and meta-heuristics. To address this challenge, an iterative greedy selection hyper-heuristic algorithm with linear population size reduction (LIGSHH) was proposed in this paper. Using an iterative greedy strategy to choose the high level of exploration, this heuristic selects the Low-Level Heuristics (LLHs) that best suit the current problem. Nine LLHs are specifically designed for continuous optimization problems. Additionally, the exploration and exploitation capabilities of the LIGSHH are balanced by reducing the population size linearly at different stages of the problem. The proposed LIGSHH algorithm and comparison algorithms are tested on the CEC2017 benchmark test suite, and the experimental results show that the LIGSHH algorithm outperforms other comparison algorithms.

Moth-flame optimization (MFO) algorithm has received a lot of attention recently, due to its simple structure and easy coding. Researchers have demonstrated that the original MFO algorithm suffers from the drawbacks of insufficient variety, slow convergence speed, and readily sliding into local optimum, which are brought about by the imbalance between local and global search. Reinforcement learning driven moth-flame optimization (RLMFO) algorithm is designed to correct these issues. Opposition learning is employed to broaden the variety of the initial population. Reinforcement learning is introduced to direct the local and global search process of the algorithm. A strategy pool containing Gaussian mutation (GM), Cauchy mutation (CM), Lévy mutation (LM), and elite strategy (ES) is created to hold strategies with various functions. RLMFO is verified on the benchmark test suite in CEC 2017. RLMFO performs better than cutting-edge algorithms according to experimental findings.

The distributed no-wait flow-shop scheduling problem (DNWFSP) is a frontier and important research topic. In this paper, a population-based iterated greedy algorithm (PBIGA) is presented to settle the DNWFSP with the makespan criterion. In PBIGA, an improved FRB2 algorithm is proposed to Initialize a high-quality population. Four local search methods based on the framework of variable neighborhood descent (VND) and optimal block knowledge are presented to improve the quality of the individual. Destruction-Construction operator is proposed according to the characteristics of PBIGA. A selection mechanism is proposed to determine which individuals perform the local search. An acceptance criterion determines is presented, which decides whether the offspring are received. Ultimately, the PBIGA and other algorithms for DNWFSP are tested on the benchmark presented by Naderi and Ruiz.

The distributed heterogeneous factory system is a typical scenario in the manufacturing industry. A distributed heterogeneous no-wait flowshop scheduling problem with sequence-dependent setup times (DHNWFSP-SDST) is studied in this paper. The differences in factory configuration and transportation time are considered in DHNWFSP-SDST. A mixed-integer linear programming (MILP) model is constructed and an artificial bee colony algorithm (ABC) with Q-learning (QABC) is proposed to address the DHNWFSP-SDST. Heuristic methods named NEH_H and DHHS are designed to construct potential initial candidates for the population. The neighborhood structures based on the job blocks are introduced in QABC to explore the solution space during the evolution processes. The Q-learning mechanism is employed to select neighborhood structures via empirical knowledge in the operation processes. The speed-up methods to accelerate the evaluation of the obtained neighborhood are designed to reduce the computation time of the QABC. The experimental results show that the QABC is a potential algorithm to address the DHNWFSP-SDST. Note to Practitioners—Distributed manufacturing under the heterogeneous environment generally exists in real manufacturing systems. The scheduling problem refers to the reasonable arrangement of production orders to optimize certain indicators under limited time, resources, and computing costs. Distributed heterogeneous no-wait flowshop scheduling problem with setup times is an important industrial scheduling problem in distributed heterogeneous manufacturing systems. The problem takes into account the differences in factory configuration and transportation time in distributed regions. The problem is a kind of NP-hard problem as the solution space is huge. A reinforcement learning driven artificial bee colony algorithm is designed to address the problem. Heuristic methods are utilized to construct potential initial solutions. Neighborhood structures are designed to further optimize the initial solution. The effective empirical guidance is provided by Q-learning for the selection of the neighborhood structure of the algorithm to avoid invalid search. The experimental results show that the QABC obtains a high-quality scheduling scheme in a reasonable time.

Carbon peaking and carbon neutrality, which are the significant national strategy for sustainable development, have attracted considerable attention from production enterprises. In this study, the energy consumption is considered in the distributed blocking flow shop scheduling problem (DBFSP). A hyperheuristic with Q -learning (HHQL) is presented to address the energy-efficient DBFSP (EEDBFSP). Q -learning is employed to select an appropriate low-level heuristic (LLH) from a predesigned LLH set according to historical information fed back by LLH. An initialization method, which considers both total tardiness (TTD) and total energy consumption (TEC), is proposed to construct the initial population. The ε -greedy strategy is introduced to utilize the learned knowledge while retaining a certain degree of exploration in the process of selecting LLH. The acceleration operation of the job on the critical path is designed to optimize TTD. The deceleration operation of the job on the noncritical path is designed to optimize TEC. The statistical and computational experimentation in an extensive benchmark testified that the HHQL outperforms the other comparison algorithm regarding efficiency and significance in solving EEDBFSP.

Green manufacturing has attracted increasing attention under the background of carbon peaking and carbon neutrality. Distributed production has widely existed in various manufacturing industries with the development of globalization. This article investigates an energy-efficient distributed no-wait flow-shop scheduling problem with sequence-dependent setup time (DNWFSP-SDST) to minimization of makespan and total energy consumption (TEC). A mixed-integer linear programming model of energy-efficient DNWFSP-SDST is constructed and a cooperative meta-heuristic algorithm based on Q-learning (CMAQ) is proposed to address energy-efficient DNWFSP-SDST in this article. In CMAQ, a heuristic named RNRa is proposed to generate initial solutions. A bipopulation cooperative framework based on double Q-learning is designed to further optimize the solutions. According to the properties of energy-efficient DNWFSP-SDST, an energy-saving strategy based on knowledge is proposed to improve makespan and TEC. The results of experiments show that the performance of CMAQ is superior to certain state-of-the-art comparison algorithms in solving energy-efficient DNWFSP-SDST.

This article investigates a distributed assembly no-wait flow-shop scheduling problem (DANWFSP), which has important applications in manufacturing systems. The objective is to minimize the total flowtime. A mixed-integer linear programming model of DANWFSP with total flowtime criterion is proposed. A population-based iterated greedy algorithm (PBIGA) is presented to address the problem. A new constructive heuristic is presented to generate an initial population with high quality. For DANWFSP, an accelerated NR3 algorithm is proposed to assign jobs to the factories, which improves the efficiency of the algorithm and saves CPU time. To enhance the effectiveness of the PBIGA, the local search method and the destruction-construction mechanisms are designed for the product sequence and job sequence, respectively. A selection mechanism is presented to determine, which individuals execute the local search method. An acceptance criterion is proposed to determine whether the offspring are adopted by the population. Finally, the PBIGA and seven state-of-the-art algorithms are tested on 810 large-scale benchmark instances. The experimental results show that the presented PBIGA is an effective algorithm to address the problem and performs better than recently state-of-the-art algorithms compared in this article.

Carbon peaking and carbon neutrality, which are significant strategies for national sustainable development, have attracted enormous attention from researchers in the manufacturing domain. A Pareto-based discrete Jaya algorithm (PDJaya) is proposed to solve the carbon-efficient distributed blocking flow shop scheduling problem (CEDBFSP) with the criteria of total tardiness and total carbon emission in this article. The mixed-integer linear programming model is presented for the CEDBFSP. An effective constructive heuristic is produced to generate the initial population. The new individual is generated by the update mechanism of PDJaya. The self-adaptive operator local search strategy is designed to enhance the exploitation capability of PDJaya. A critical-path-based carbon saving strategy is introduced to further reduce carbon emissions. The effectiveness of each strategy in the PDJaya is verified and compared with the state-of-the-art algorithms in the benchmark suite. The numerical results demonstrate that the PDJaya is the efficient optimizer for solving the CEDBFSP.

The integration of reinforcement learning technology into meta-heuristic algorithms to address complex combinatorial optimization problems has attracted much attention in recent years. A cooperative scatter search with$Q$-learning mechanism (QCSS) is proposed for solving the DPFSP-SDST. In the diversification generation method, two effective heuristic algorithms are designed to construct an initial population with high quality and diversity. In the improved method, eight domain knowledge-guided perturbation operators are combined with$Q$-learning to balance the exploration and exploitation capabilities of the QCSS algorithm. The reference set (RefSet) is divided into two subpopulations, and adaptive competition is adopted between the subpopulations to enhance search efficiency. In addition, a restart mechanism is proposed in the RefSet update phase to ensure the diversity of solutions. The performance of the QCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the QCSS algorithm.

The distributed assembly mixed no-idle permutation flowshop scheduling problem (DAMNIPFSP), a common occurrence in modern industries like integrated circuit production, ceramic frit production, fiberglass processing, and steel-making, is a new model that considers mixed machines with no-idle restrictions as well as conventional machines. This article introduces an estimation of distribution algorithm-based hyper-heuristic (EDA-HH) to solve the DAMNIPFSP. Ten simple heuristic rules as low-level operations are utilized to search the solution space. The estimation of distribution algorithm is integrated into the framework of hyper-heuristic as the high-level strategy to control the low-level heuristics sequence in the solution space. The destruction and construction procedures are conducted on products and jobs in order to enhance the exploitation competence of EDA-HH. The computational simulation is carried out and the experimental results show that the proposed EDA-HH is significantly superior to the competitors in the statistical sense. The results of the 810 large-scale problem instances show the effectiveness of the EDA-HH in solving the DAMNIPFSP. Moreover, the CPLEX solver is utilized to verify the correctness of the model with some small instances.

Credit Default Prediction (CDP) has received increasing attention with the prevalence of financial loaning services. Many research efforts have been dedicated to developing novel soft features (i.e. non-financial features), such that they can complement hard features (i.e. financial features) and assist to learn a better default predicting model. But most works combine those features from various sources by just concating them together, and ignore that inappropriate feature fusion methods would compromise model performances. Therefore, in this paper, we propose an Attentive Feature Fusion (AFF) framework for credit default prediction using deep neural networks (DNNs). According to distinct characteristics of the data features, we divide features into multiple groups, and learn their latent representations with separate DNNs, respectively. Then the attention mechanism is applied to integrate those representations together, which allows the important features to be always emphasized and contribute more to the final decision. Experiments on the Lending Club dataset demonstrate that the proposed method can effectively improve the default predicting performances.

The blocking flow-shop scheduling problem (BFSP) with sequence-dependent setup times (SDST), which has important ramifications in the modern industry, is investigated in this paper. The SDST/BFSP is extended from the BFSP, which included the setup times in processing times. However, the setup times in actual processing depend on the preceding and successive jobs in the processing order. Hence, the setup times are considered independently of processing times in this paper. The mixed-integer linear programming (MILP) model of SDST/BFSP is designed. Furthermore, a discrete whale optimization algorithm (DWOA) based on problem-specific knowledge is proposed to solve certain SDST/BFSP. Firstly, a construction heuristic that depends on the properties of the problem is designed to reduce the blocking time and idle times created by SDSTs. Secondly, the leading whales in DWOA are replaced by the critical factories in SDST/BFSP. Further, three different search strategies including the searching for prey, encircling prey, and bubble-net attacking prey are designed to improve the exploitation and exploration capability of the DWOA. The statistical and computational experimentation in an extensive benchmark testified that the DWOA outperforms the state-of-the-art algorithms regarding efficiency and significance in solving SDST/BFSP.

The distributed blocking flow-shop scheduling problem (DBFSP), which has been proven to be a strongly NP-hard problem, has important applications in a variety of industrial systems. In this paper, a self-adapting water wave optimization (SAWWO) algorithm is proposed to solve the blocking flow-shop scheduling problem with the criterion of minimizing the makespan. In SAWWO, the candidates are represented as discrete job permutations. Two heuristics are utilized to obtain the desirable initial solution. In the propagation phase, the self-adapting spatial dispersal operator is designed to balance the exploration and exploitation of SAWWO. Four local search methods are introduced to intensify the exploitation ability of the algorithm in the local region. Furthermore, the redesigned path-relinking method is presented as the modified refraction operator to help the algorithm jump out the local optimal. Additionally, the performance of the proposed algorithm is evaluated by comparing with five other state-of-the-art algorithms. The statistical results demonstrate the effectiveness of SAWWO for solving the DBFSP.

The moth-flame optimization (MFO) algorithm is extensively employed to attain the global optimization of a problem. The original MFO algorithm has drawbacks of low population diversity, slow convergence speed, and falling into local optimum easily. An improved moth-flame optimization algorithm (CLMFOLDS) based on comprehensive learning (CL) mechanism and low discrepancy sequence (LDS) is presented in this paper to solve the problem. A random population with uniform distribution is generated in the search space by using LDS. The information of the entire population is learned to gain the position of the new moth, which is called the CL strategy. External storage is designed to save the suboptimal solution throughout the iteration. The elimination mechanism is employed to strike out the poor solution in the population to enhance the global search capability of the algorithm. The CLMFOLDS is assessed in the CEC 2017 benchmark problem. Experimental results illustrate that the CLMFOLDS algorithm is superior to state-of-the-art algorithms.

In this study, a self-learning discrete Jaya algorithm (SD-Jaya) is proposed to address the energy-efficient distributed no-idle flow-shop scheduling problem (FSP) in a heterogeneous factory system (HFS-EEDNIFSP) with the criteria of minimizing the total tardiness (TTD), total energy consumption (TEC), and factory load balancing (FLB). First, the mixed-integer programming model of HFS-EEDNIFSP is presented. An evaluation criterion of FLB combining the energy consumption and the completion time is introduced. Second, a self-learning operators selection strategy, in which the success rate of each operator is summarized as knowledge, is designed for guiding the selection of operators. Third, the energy-saving strategy is proposed for reducing the TEC. The energy-efficient no-idle FSP is transformed to be an energy-efficient permutation FSP to search the idle times. The speed of operations which adjacent are idle times is reduced. The effectiveness of SD-Jaya is tested on 60 benchmark instances. On the quality of the solution, the experimental results reveal that the efficacy of the SD-Jaya algorithm outperforms the other algorithms for addressing HFS-EEDNIFSP.

In this paper, an orthogonal learning (OL) design whale optimization algorithm (WOA) with clustering mechanism, named OLWOA, is proposed to solve the complex continuous problems. In the proposed algorithm, the OL, as an effective strategy to utilize prior search information (experience), is utilized to overcome the disadvantages of the basic WOA, which converges slowly and falls into local optimum easily. The clustering-based mechanism guides the humpback whales to search toward an interesting area by propagating the information of good solutions from one cluster to another cluster. The experimental results reveal the effectiveness and significance of the OL and the clustering-based learning mechanism in the proposed algorithm.

The fruit fly optimization algorithm has drawn various attention to researchers and engineers, due to the simple theory and flexible frame. For solving the complex continuous optimization problems, an improved fruit fly algorithm based on vision scanning search and extensive learning mechanism is proposed in this paper. The vision scanning search strategy is used to scan the potential area by changing the search angle of swarm center. This strategy is utilized to guide the population to jump out the local trap. The extensive learning is using the knowledge of neighboring structure to increase the diversity of population for solving the non-separable issues. Furthermore, a new mutation strategy based on difference vector is proposed to improve the search efficiency of VLFOA. Testified in CEC 2017 benchmark problems, the results show that the VLFOA has a superior performance compared with the original FOA and the state of art variants of the FOA.

In the past decades, various attention has been paid to the global optimization problems. The Monarch Butterfly Optimization (MBO) algorithm is an effective meta-heuristic algorithm for the global optimization problems. However, in the MBO, the diversity of the population is lost in the late iteration. The MBO is easy to trap into the local optima. In this study, an algorithm based on MBO with learning mechanism and topological structure, named LTMBO, is proposed to enhance the ability of exploration and exploitation on the global optimization problems. The learning mechanism is present for the migration operator to increase the speed of the iteration. The topological structure is proposed for the butterfly adjusting operator to improve the diversity of the population. The experimental results demonstrated that the efficiency and significance of the proposed LTMBO algorithm.

With the increasing complexity of continuous optimization problems, the requirement of solving algorithms is higher and higher. To improve the performance of brain storm optimization algorithm, an elitist guided parameter adaptive BSO (EGBSO) is proposed in this paper. The population is sorted in the objective space based on the fitness. The top M individuals are regarded as elitists to guide the ordinary individuals to cluster, which accelerates the convergence speed of the algorithm. The updating mechanism of elite guidance is introduced, which utilizes the cooperation between global optimal individual and elitists to guide the population to a better direction. An adaptive selection parameter is set to make the algorithm more inclined to global search in the early stage and local search in the later stage, balancing the exploration and exploitation capabilities. The proposed EGBSO algorithm and three comparison algorithms are tested on the CEC2017 benchmark test suit, and the experimental results show that the EGBSO has good performance in solving complex optimization problems.

A new metaheuristic algorithm, named surrogate-guided algorithm(S-Jaya), is proposed to solve the single objective continuous optimization problems in this paper. A novel mutation strategy for the non-separable single objective continuous optimization problems is introduced to alter the search engine of the Jaya algorithm. The surrogate is embedded to accelerate the convergence of the population and avoid the proposed algorithm falling into the local optimal during the evolutionary process. The suggested S-Jaya algorithm to address the CEC 2017 benchmark problems is effective and validated. On the quality of solution and execution time, the experimental results reveal that the effectiveness of the S-Jaya algorithm is superior compare with the Jaya algorithm and its variants.

Backtracking search algorithm (BSA) has been applied to solve the various optimization problems in recent years. However, BSA is difficult to solve non-separable problems due to its single search mechanism. In this paper, backtracking search algorithm based on knowledge of different populations, named DKBSA, is proposed to solve continuous optimization problems. In DKBSA, sub-population partitioning method is used to enhance the local search ability and alleviate the loss rate of the diversity of population. Afterwards, a mutation strategy with knowledge guidance and rotation invariance, which is based on the current sub-population information and historical information, is designed to improve the convergence speed of the DKBSA. Furthermore, a control parameter of adaptive search factor is embedded in the mutation strategy to balance the exploitation and exploration of the proposed algorithm. Finally, a probabilistic model-based strategy is proposed to generate dominant individuals to further improve the search ability of the proposed algorithm. The experimental results of the state-of-the-art algorithms in the CEC2017 benchmark test suit reveal that the DKBSA is effective for solving non-separable problems.

The invasive weed algorithm (IWO) is a meta-heuristic algorithm, which is an effective and promising optimiser to address the optimisation problems. In this study, a hybrid algorithm based on the self-adaptive invasive weed algorithm (IWO) and differential evolution algorithm (DE), named SIWODE, is proposed to address the continuous optimisation problems. In the proposed SIWODE, first, the two parameters are adaptively proposed to improve the convergence speed of the algorithm. Second, the crossover and mutation operations are introduced in SIWODE to improve the population diversity and increase the exploration capability during the iterative process. Furthermore, a local perturbation strategy is presented to improve exploitation ability during the late process. The exploration and exploitation ability of the algorithm is effectively balanced by cooperative mechanisms. The experiment results of SIWODE show that the SIWODE has the superior searching quality and stability than other mentioned approaches.

Green scheduling in the manufacturing industry has attracted increasing attention in academic research and industrial applications with a focus on energy saving. As a typical scheduling problem, the no-wait flow-shop scheduling has been extensively studied due to its wide industrial applications. However, energy consumption is usually ignored in the study of typical scheduling problems. In this article, a two-stage cooperative evolutionary algorithm with problem-specific knowledge called TS-CEA is proposed to address energy-efficient scheduling of the no-wait flow-shop problem (EENWFSP) with the criteria of minimizing both makespan and total energy consumption. In TS-CEA, two constructive heuristics are designed to generate a desirable initial solution after analyzing the properties of the problem. In the first stage of TS-CEA, an iterative local search strategy (ILS) is employed to explore potential extreme solutions. Moreover, a hybrid neighborhood structure is designed to improve the quality of the solution. In the second stage of TS-CEA, a mutation strategy based on critical path knowledge is proposed to extend the extreme solutions to the Pareto front. Moreover, a co-evolutionary closed-loop system is generated with ILS and mutation strategies in the iteration process. Numerical results demonstrate the effectiveness and efficiency of TS-CEA in solving the EENWFSP.

Water Wave Optimisation algorithm (WWO) is a new swarm-based metaheuristic inspired by shallow wave models for global optimisation. In this paper, an enhanced WWO, which combines with multiple assistant strategies (EWWO), is proposed. First, the random opposition-based learning (ROBL) mechanism is introduced to generate the initial population with high quality. Second, a new modified operation is designed and embedded into propagation operation to balance the global exploration and the local exploitation. Third, the covariance matrix self-adaptation evolution strategy (CMA-ES) is employed by the refraction operation to further strengthen the local exploitation. Furthermore, the diversity of the population is maintained in the evolution process by using a crossover operator. The experiment results based on CEC 2017 benchmarks indicate that the EWWO outperforms the state-of-the-art variant algorithms of the WWO and the standard WWO.

Multi-objective evolutionary algorithms usually utilize fixed evolutionary mechanism and the evolutionary operators are static during the process of algorithm evolution. It is easy to cause a simple population structure, unable to exploit the search space fully and trapped in local optimal solution. In this paper, a novel method named Pareto Archive Evolution Strategy (PAES) with adaptive grid strategy (AGS_PAES) which only makes one mutation to create one new solution and use an “archive” which are called Non-Dominated Archive to store the best solution, is introduced. This procedure is completed by a special approach - adaptive grid method, which decides the criterion of the solution to be archived and the place of the grid location the solution would be stored. The Pareto front obtained by the procedure outperforms the classical Multi-objective Genetic Algorithm (MOGA). Simulation results on the standard benchmark problems show that the proposed adaptive scheme has a better convergence and diversity compared with the second generation classical multi-objective evolutionary algorithms.

In the production system, the machine processing ability is unequal, which leads to the low utilization rate of the machine and the long waiting time of the workpiece. Aiming at these problems, the Markov queuing model with unequal processing capability is proposed. A dynamic optimization method of integrated workshop performance indexes based on unequal processing capacities is studied. The M/M/2 and M/M/3 queuing models with Unequal processing abilities are simulated by using the signal simulation module in Matlab. The queuing rules in Markov's queuing model with Unequal processing abilities are optimized aiming at the unequal processing capacities, and a comprehensive priority queuing model is also proposed. Using the same queue rule will reduce the production efficiency of production system under different production intensity, so we propose integrated priority queuing model.

NSGA-II is a well known, fast sorting and elite multi-objective genetic algorithm. The local exploitation ability of NSGA-II is relatively limited by the parameters of crossover and mutation. DE has shown powerful search abilities for continuous optimization. In this paper, an enhanced NSGA-II based on differential evolution and L-near distance (DP-NSGA-II/EDA) is proposed. To improve the diversity and convergence of Pareto optimal solutions by NSGA-II algorithm, DP-NSGA-II/EDA produces two populations by different approaches. One is from NSGA-II itself, the other is from differential evolution (DE). Through the competition between two populations, the superior individuals will be selected to construct new offspring population. Meanwhile, a new distance strategy called L-near distance is introduced to NSGA-II to maintain the diversity of the population. To validate the proposed algorithm, it is compared with the original NSGA-II, SPEA2 and MOEA/D-DE through several numerical benchmark problems. Results show the effectiveness of the proposed approach.

Holonic manufacturing systems (HMS) provide a flexible and decentralized manufacturing environment to accommodate changes dynamically. This paper presents a framework to model and control HMS based on Petri net and MAS theory. A time Petri net (TPN) model was proposed to achieve this goal. A TPN represents a set of established contracts among the agents in HMS to fulfil an order. A scheduling architecture which integrates TPN models and AI techniques is proposed. By introducing dynamic individuals into the reproducing pool randomly according to their fitness, a variable population-size genetic algorithm is presented to enhance the convergence speed of GA. Based on the novel GA and the particle swarm optimization (PSO) algorithms, a hybrid PSO-GA algorithm (HPGA) is also proposed in this paper. Simulation results show that the proposed method is effective for the optimization problems

The dynamic re-organization of holons is a key element of current research on HMS. Dynamic intelligent reconfiguration is important for holonic control. This paper extends the mechanism of virtual clustering to the reorganization of holons and uses contract net-based task allocation protocol to efficiently deal with the communication and coordination problems during task-oriented clustering. The PSO-based virtual clustering optimization algorithm described in this paper can solve the optimization problem of task allocation on the basis of global optimization. The hybrid algorithm combines the high speed of PSO with the powerful ability to avoid being trapped in local minimum of SA. We compare the PSO algorithm to both GA and SA models, the simulation results show that the proposed model and algorithm are effective