The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because o...The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.展开更多
The shop scheduling problem with limited buffers has broad applications in real-world production scenarios,so this research direction is of great practical significance.However,there is currently little research on th...The shop scheduling problem with limited buffers has broad applications in real-world production scenarios,so this research direction is of great practical significance.However,there is currently little research on the hybrid flow shop scheduling problem with limited buffers(LBHFSP).This paper deeply investigates the LBHFSP to optimize the goal of the total completion time.To better solve the LBHFSP,a multi-level subpopulation-based particle swarm optimization algorithm(MLPSO)is proposed,which is founded on the attributes of the LBHFSP and the shortcomings of the basic PSO(particle swarm optimization)algorithm.In MLPSO,firstly,considering the impact of the limited buffers on the process of subsequent operations,a specific circular decoding strategy is developed to accommodate the characteristics of limited buffers.Secondly,an initialization strategy based on blocking time is designed to enhance the quality and diversity of the initial population.Afterward,a multi-level subpopulation collaborative search is developed to prevent being trapped in a local optimum and improve the global exploration capability.Additionally,a local search strategy based on the first blocked job is designed to enhance the MLPSO algorithm’s exploitation capability.Lastly,numerous experiments are carried out to test the performance of the proposed MLPSO by comparing it with classical intelligent optimization and popular algorithms in recent years.The results confirm that the proposed MLPSO has an outstanding performance when compared to other algorithms when solving LBHFSP.展开更多
A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Se...A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion.展开更多
An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effecti...An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effective combination of the insertion and swap operator is applied to producing neighborhood individual at the employed bee phase. The tournament selection is adopted to avoid falling into local optima, while, the optimized insert operator embeds in onlooker bee phase for further searching the neighborhood solution to enhance the local search ability of algorithm. The tournament selection with size 2 is again applied and a better selected solution will be performed destruction and construction of iterated greedy(IG) algorithm, and then the result replaces the worse one. Simulation results show that our algorithm has a better performance compared with the HDDE and CHS which were proposed recently. It provides the better known solutions for the makespan criterion to flow shop scheduling problem with limited buffers for the Car benchmark by Carlier and Rec benchmark by Reeves. The convergence curves show that the algorithm not only has faster convergence speed but also has better convergence value.展开更多
Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid ...Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.展开更多
This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a com...This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.展开更多
In this paper,we consider the distributed permutation flow shop scheduling problem(DPFSSP)with transportation and eligibility constrains.Three objectives are taken into account,i.e.,makespan,maximum lateness and total...In this paper,we consider the distributed permutation flow shop scheduling problem(DPFSSP)with transportation and eligibility constrains.Three objectives are taken into account,i.e.,makespan,maximum lateness and total costs(transportation costs and setup costs).To the best of our knowledge,there is no published work on multi-objective optimization of the DPFSSP with transportation and eligibility constraints.First,we present the mathematics model and constructive heuristics for single objective;then,we propose an improved The Nondominated Sorting Genetic Algorithm II(NSGA-II)for the multi-objective DPFSSP to find Pareto optimal solutions,in which a novel solution representation,a new population re-/initialization,effective crossover and mutation operators,as well as local search methods are developed.Based on extensive computational and statistical experiments,the proposed algorithm performs better than the well-known NSGA-II and the Strength Pareto Evolutionary Algorithm 2(SPEA2).展开更多
Two-stage hybrid flow shop scheduling has been extensively considered in single-factory settings.However,the distributed two-stage hybrid flow shop scheduling problem(DTHFSP)with fuzzy processing time is seldom invest...Two-stage hybrid flow shop scheduling has been extensively considered in single-factory settings.However,the distributed two-stage hybrid flow shop scheduling problem(DTHFSP)with fuzzy processing time is seldom investigated in multiple factories.Furthermore,the integration of reinforcement learning and metaheuristic is seldom applied to solve DTHFSP.In the current study,DTHFSP with fuzzy processing time was investigated,and a novel Q-learning-based teaching-learning based optimization(QTLBO)was constructed to minimize makespan.Several teachers were recruited for this study.The teacher phase,learner phase,teacher’s self-learning phase,and learner’s self-learning phase were designed.The Q-learning algorithm was implemented by 9 states,4 actions defined as combinations of the above phases,a reward,and an adaptive action selection,which were applied to dynamically adjust the algorithm structure.A number of experiments were conducted.The computational results demonstrate that the new strategies of QTLBO are effective;furthermore,it presents promising results on the considered DTHFSP.展开更多
Smart manufacturing in the“Industry 4.0”strategy promotes the deep integration of manufacturing and information technologies,which makes the manufacturing system a ubiquitous environment.However,the real-time schedu...Smart manufacturing in the“Industry 4.0”strategy promotes the deep integration of manufacturing and information technologies,which makes the manufacturing system a ubiquitous environment.However,the real-time scheduling of such a manufacturing system is a challenge faced by many decision makers.To deal with this challenge,this study focuses on the real-time hybrid flow shop scheduling problem(HFSP).First,the characteristic of the hybrid flow shop in a smart manufacturing environment is analyzed,and its scheduling problem is described.Second,a real-time scheduling approach for the HFSP is proposed.The core module is to employ gene expression programming to construct a new and efficient scheduling rule according to the real-time status in the hybrid flow shop.With the scheduling rule,the priorities of the waiting job are calculated,and the job with the highest priority will be scheduled at this decision time point.A group of experiments are performed to prove the performance of the proposed approach.The numerical experiments show that the real-time scheduling approach outperforms other single-scheduling rules and the back-propagation neural network method in optimizing most objectives for different size instances.Therefore,the contribution of this study is the proposal of a real-time scheduling approach,which is an effective approach for real-time hybrid flow shop scheduling in a smart manufacturing environment.展开更多
The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this wor...The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.展开更多
This work addresses bi-objective hybrid flow shop scheduling problems considering consistent sublots(Bi-HFSP_CS).The objectives are to minimize the makespan and total energy consumption.First,the Bi-HFSP_CS is formali...This work addresses bi-objective hybrid flow shop scheduling problems considering consistent sublots(Bi-HFSP_CS).The objectives are to minimize the makespan and total energy consumption.First,the Bi-HFSP_CS is formalized,followed by the establishment of a mathematical model.Second,enhanced version of the artificial bee colony(ABC)algorithms is proposed for tackling the Bi-HFSP_CS.Then,fourteen local search operators are employed to search for better solutions.Two different Q-learning tactics are developed to embed into the ABC algorithm to guide the selection of operators throughout the iteration process.Finally,the proposed tactics are assessed for their efficacy through a comparison of the ABC algorithm,its three variants,and three effective algorithms in resolving 95 instances of 35 different problems.The experimental results and analysis showcase that the enhanced ABC algorithm combined with Q-learning(QABC1)demonstrates as the top performer for solving concerned problems.This study introduces a novel approach to solve the Bi-HFSP_CS and illustrates its efficacy and superior competitive strength,offering beneficial perspectives for exploration and research in relevant domains.展开更多
基金supported in part by the National Key Research and Development Program of China under Grant No.2021YFF0901300in part by the National Natural Science Foundation of China under Grant Nos.62173076 and 72271048.
文摘The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.
基金supported in part by the National Natural Science Foundation of China under Grant No.52175490.
文摘The shop scheduling problem with limited buffers has broad applications in real-world production scenarios,so this research direction is of great practical significance.However,there is currently little research on the hybrid flow shop scheduling problem with limited buffers(LBHFSP).This paper deeply investigates the LBHFSP to optimize the goal of the total completion time.To better solve the LBHFSP,a multi-level subpopulation-based particle swarm optimization algorithm(MLPSO)is proposed,which is founded on the attributes of the LBHFSP and the shortcomings of the basic PSO(particle swarm optimization)algorithm.In MLPSO,firstly,considering the impact of the limited buffers on the process of subsequent operations,a specific circular decoding strategy is developed to accommodate the characteristics of limited buffers.Secondly,an initialization strategy based on blocking time is designed to enhance the quality and diversity of the initial population.Afterward,a multi-level subpopulation collaborative search is developed to prevent being trapped in a local optimum and improve the global exploration capability.Additionally,a local search strategy based on the first blocked job is designed to enhance the MLPSO algorithm’s exploitation capability.Lastly,numerous experiments are carried out to test the performance of the proposed MLPSO by comparing it with classical intelligent optimization and popular algorithms in recent years.The results confirm that the proposed MLPSO has an outstanding performance when compared to other algorithms when solving LBHFSP.
基金Supported by the National Natural Science Foundation of China (61174040, 61104178)the Fundamental Research Funds for the Central Universities
文摘A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion.
基金Projects(61174040,61104178,61374136) supported by the National Natural Science Foundation of ChinaProject(12JC1403400) supported by Shanghai Commission of Science and Technology,ChinaProject supported by the Fundamental Research Funds for the Central Universities,China
文摘An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effective combination of the insertion and swap operator is applied to producing neighborhood individual at the employed bee phase. The tournament selection is adopted to avoid falling into local optima, while, the optimized insert operator embeds in onlooker bee phase for further searching the neighborhood solution to enhance the local search ability of algorithm. The tournament selection with size 2 is again applied and a better selected solution will be performed destruction and construction of iterated greedy(IG) algorithm, and then the result replaces the worse one. Simulation results show that our algorithm has a better performance compared with the HDDE and CHS which were proposed recently. It provides the better known solutions for the makespan criterion to flow shop scheduling problem with limited buffers for the Car benchmark by Carlier and Rec benchmark by Reeves. The convergence curves show that the algorithm not only has faster convergence speed but also has better convergence value.
基金the National Natural Science Foundation of China(Grant Number 61573264).
文摘Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.
基金supported by the National Natural Science Foundation of China under Grant Nos.62076225 and 62122093the Open Project of Xiangjiang Laboratory under Grant No 22XJ02003.
文摘This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.
基金This research was partially supported by the National Natural Science Foundation of China(Nos.71390334 and 11271356).
文摘In this paper,we consider the distributed permutation flow shop scheduling problem(DPFSSP)with transportation and eligibility constrains.Three objectives are taken into account,i.e.,makespan,maximum lateness and total costs(transportation costs and setup costs).To the best of our knowledge,there is no published work on multi-objective optimization of the DPFSSP with transportation and eligibility constraints.First,we present the mathematics model and constructive heuristics for single objective;then,we propose an improved The Nondominated Sorting Genetic Algorithm II(NSGA-II)for the multi-objective DPFSSP to find Pareto optimal solutions,in which a novel solution representation,a new population re-/initialization,effective crossover and mutation operators,as well as local search methods are developed.Based on extensive computational and statistical experiments,the proposed algorithm performs better than the well-known NSGA-II and the Strength Pareto Evolutionary Algorithm 2(SPEA2).
文摘Two-stage hybrid flow shop scheduling has been extensively considered in single-factory settings.However,the distributed two-stage hybrid flow shop scheduling problem(DTHFSP)with fuzzy processing time is seldom investigated in multiple factories.Furthermore,the integration of reinforcement learning and metaheuristic is seldom applied to solve DTHFSP.In the current study,DTHFSP with fuzzy processing time was investigated,and a novel Q-learning-based teaching-learning based optimization(QTLBO)was constructed to minimize makespan.Several teachers were recruited for this study.The teacher phase,learner phase,teacher’s self-learning phase,and learner’s self-learning phase were designed.The Q-learning algorithm was implemented by 9 states,4 actions defined as combinations of the above phases,a reward,and an adaptive action selection,which were applied to dynamically adjust the algorithm structure.A number of experiments were conducted.The computational results demonstrate that the new strategies of QTLBO are effective;furthermore,it presents promising results on the considered DTHFSP.
基金This paper was supported partly by the National Natural Science Foundation of China(No.52175449)partly by the National Key R&D Plan of China(No.2020YFB1712902).
文摘Smart manufacturing in the“Industry 4.0”strategy promotes the deep integration of manufacturing and information technologies,which makes the manufacturing system a ubiquitous environment.However,the real-time scheduling of such a manufacturing system is a challenge faced by many decision makers.To deal with this challenge,this study focuses on the real-time hybrid flow shop scheduling problem(HFSP).First,the characteristic of the hybrid flow shop in a smart manufacturing environment is analyzed,and its scheduling problem is described.Second,a real-time scheduling approach for the HFSP is proposed.The core module is to employ gene expression programming to construct a new and efficient scheduling rule according to the real-time status in the hybrid flow shop.With the scheduling rule,the priorities of the waiting job are calculated,and the job with the highest priority will be scheduled at this decision time point.A group of experiments are performed to prove the performance of the proposed approach.The numerical experiments show that the real-time scheduling approach outperforms other single-scheduling rules and the back-propagation neural network method in optimizing most objectives for different size instances.Therefore,the contribution of this study is the proposal of a real-time scheduling approach,which is an effective approach for real-time hybrid flow shop scheduling in a smart manufacturing environment.
基金Projects(61573144,61773165,61673175,61174040)supported by the National Natural Science Foundation of ChinaProject(222201717006)supported by the Fundamental Research Funds for the Central Universities,China
文摘The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.
基金supported by the National Natural Science Foundation of China(No.62173356)Science and Technology Development Fund(FDCT),Macao SAR(No.0019/2021/A)+2 种基金Zhuhai Industry-University-Research Project with Hongkong and Macao(No.ZH22017002210014PWC)Guangdong Basic and Applied Basic Research Foundation(No.2023A1515011531)Key Technologies for Scheduling and Optimization of Complex Distributed Manufacturing Systems(No.22JR10KA007).
文摘This work addresses bi-objective hybrid flow shop scheduling problems considering consistent sublots(Bi-HFSP_CS).The objectives are to minimize the makespan and total energy consumption.First,the Bi-HFSP_CS is formalized,followed by the establishment of a mathematical model.Second,enhanced version of the artificial bee colony(ABC)algorithms is proposed for tackling the Bi-HFSP_CS.Then,fourteen local search operators are employed to search for better solutions.Two different Q-learning tactics are developed to embed into the ABC algorithm to guide the selection of operators throughout the iteration process.Finally,the proposed tactics are assessed for their efficacy through a comparison of the ABC algorithm,its three variants,and three effective algorithms in resolving 95 instances of 35 different problems.The experimental results and analysis showcase that the enhanced ABC algorithm combined with Q-learning(QABC1)demonstrates as the top performer for solving concerned problems.This study introduces a novel approach to solve the Bi-HFSP_CS and illustrates its efficacy and superior competitive strength,offering beneficial perspectives for exploration and research in relevant domains.
