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
With the development of economic globalization,distributedmanufacturing is becomingmore andmore prevalent.Recently,integrated scheduling of distributed production and assembly has captured much concern.This research s...With the development of economic globalization,distributedmanufacturing is becomingmore andmore prevalent.Recently,integrated scheduling of distributed production and assembly has captured much concern.This research studies a distributed flexible job shop scheduling problem with assembly operations.Firstly,a mixed integer programming model is formulated to minimize the maximum completion time.Secondly,a Q-learning-assisted coevolutionary algorithmis presented to solve themodel:(1)Multiple populations are developed to seek required decisions simultaneously;(2)An encoding and decoding method based on problem features is applied to represent individuals;(3)A hybrid approach of heuristic rules and random methods is employed to acquire a high-quality population;(4)Three evolutionary strategies having crossover and mutation methods are adopted to enhance exploration capabilities;(5)Three neighborhood structures based on problem features are constructed,and a Q-learning-based iterative local search method is devised to improve exploitation abilities.The Q-learning approach is applied to intelligently select better neighborhood structures.Finally,a group of instances is constructed to perform comparison experiments.The effectiveness of the Q-learning approach is verified by comparing the developed algorithm with its variant without the Q-learning method.Three renowned meta-heuristic algorithms are used in comparison with the developed algorithm.The comparison results demonstrate that the designed method exhibits better performance in coping with the formulated problem.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
The flow shop scheduling problem is important for the manufacturing industry.Effective flow shop scheduling can bring great benefits to the industry.However,there are few types of research on Distributed Hybrid Flow S...The flow shop scheduling problem is important for the manufacturing industry.Effective flow shop scheduling can bring great benefits to the industry.However,there are few types of research on Distributed Hybrid Flow Shop Problems(DHFSP)by learning assisted meta-heuristics.This work addresses a DHFSP with minimizing the maximum completion time(Makespan).First,a mathematical model is developed for the concerned DHFSP.Second,four Q-learning-assisted meta-heuristics,e.g.,genetic algorithm(GA),artificial bee colony algorithm(ABC),particle swarm optimization(PSO),and differential evolution(DE),are proposed.According to the nature of DHFSP,six local search operations are designed for finding high-quality solutions in local space.Instead of randomselection,Q-learning assists meta-heuristics in choosing the appropriate local search operations during iterations.Finally,based on 60 cases,comprehensive numerical experiments are conducted to assess the effectiveness of the proposed algorithms.The experimental results and discussions prove that using Q-learning to select appropriate local search operations is more effective than the random strategy.To verify the competitiveness of the Q-learning assistedmeta-heuristics,they are compared with the improved iterated greedy algorithm(IIG),which is also for solving DHFSP.The Friedman test is executed on the results by five algorithms.It is concluded that the performance of four Q-learning-assisted meta-heuristics are better than IIG,and the Q-learning-assisted PSO shows the best competitiveness.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
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 paper addresses the Energy-Aware Distributed Hybrid Flow Shop Scheduling Problem with Multiprocessor Tasks(EADHFSPMT)by considering two objectives simultaneously,i.e.,makespan and total energy consumption.It cons...This paper addresses the Energy-Aware Distributed Hybrid Flow Shop Scheduling Problem with Multiprocessor Tasks(EADHFSPMT)by considering two objectives simultaneously,i.e.,makespan and total energy consumption.It consists of three sub-problems,i.e.,job assignment between factories,job sequence in each factory,and machine allocation for each job.We present a mixed inter linear programming model and propose a Novel MultiObjective Evolutionary Algorithm based on Decomposition(NMOEA/D).We specially design a decoding scheme according to the characteristics of the EADHFSPMT.To initialize a population with certain diversity,four different rules are utilized.Moreover,a cooperative search is designed to produce new solutions based on different types of relationship between any solution and its neighbors.To enhance the quality of solutions,two local intensification operators are implemented according to the problem characteristics.In addition,a dynamic adjustment strategy for weight vectors is designed to balance the diversity and convergence,which can adaptively modify weight vectors according to the distribution of the non-dominated front.Extensive computational experiments are carried out by using a number of benchmark instances,which demonstrate the effectiveness of the above special designs.The statistical comparisons to the existing algorithms also verify the superior performances of the NMOEA/D.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
The distributed hybrid flow shop scheduling problem(DHFSP),which integrates distributed manufacturing models with parallel machines,has gained significant attention.However,in actual scheduling,some adjacent machines ...The distributed hybrid flow shop scheduling problem(DHFSP),which integrates distributed manufacturing models with parallel machines,has gained significant attention.However,in actual scheduling,some adjacent machines do not have buffers between them,resulting in blocking.This paper focuses on addressing the DHFSP with blocking constraints(DBHFSP)based on the actual production conditions.To solve DBHFSP,we construct a mixed integer linear programming(MILP)model for DBHFSP and validate its correctness using the Gurobi solver.Then,an advanced iterated greedy(AIG)algorithm is designed to minimize the makespan,in which we modify the Nawaz,Enscore,and Ham(NEH)heuristic to solve blocking constraints.To balance the global and local search capabilities of AIG,two effective inter-factory neighborhood search strategies and a swap-based local search strategy are designed.Additionally,each factory is mutually independent,and the movement within one factory does not affect the others.In view of this,we specifically designed a memory-based decoding method for insertion operations to reduce the computation time of the objective.Finally,two shaking strategies are incorporated into the algorithm to mitigate premature convergence.Five advanced algorithms are used to conduct comparative experiments with AIG on 80 test instances,and experimental results illustrate that the makespan and the relative percentage increase(RPI)obtained by AIG are 1.0%and 86.1%,respectively,better than the comparative algorithms.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.
文摘With the development of economic globalization,distributedmanufacturing is becomingmore andmore prevalent.Recently,integrated scheduling of distributed production and assembly has captured much concern.This research studies a distributed flexible job shop scheduling problem with assembly operations.Firstly,a mixed integer programming model is formulated to minimize the maximum completion time.Secondly,a Q-learning-assisted coevolutionary algorithmis presented to solve themodel:(1)Multiple populations are developed to seek required decisions simultaneously;(2)An encoding and decoding method based on problem features is applied to represent individuals;(3)A hybrid approach of heuristic rules and random methods is employed to acquire a high-quality population;(4)Three evolutionary strategies having crossover and mutation methods are adopted to enhance exploration capabilities;(5)Three neighborhood structures based on problem features are constructed,and a Q-learning-based iterative local search method is devised to improve exploitation abilities.The Q-learning approach is applied to intelligently select better neighborhood structures.Finally,a group of instances is constructed to perform comparison experiments.The effectiveness of the Q-learning approach is verified by comparing the developed algorithm with its variant without the Q-learning method.Three renowned meta-heuristic algorithms are used in comparison with the developed algorithm.The comparison results demonstrate that the designed method exhibits better performance in coping with the formulated problem.
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partially supported by the Guangdong Basic and Applied Basic Research Foundation(2023A1515011531)the National Natural Science Foundation of China under Grant 62173356+2 种基金the Science and Technology Development Fund(FDCT),Macao SAR,under Grant 0019/2021/AZhuhai Industry-University-Research Project with Hongkong and Macao under Grant ZH22017002210014PWCthe Key Technologies for Scheduling and Optimization of Complex Distributed Manufacturing Systems(22JR10KA007).
文摘The flow shop scheduling problem is important for the manufacturing industry.Effective flow shop scheduling can bring great benefits to the industry.However,there are few types of research on Distributed Hybrid Flow Shop Problems(DHFSP)by learning assisted meta-heuristics.This work addresses a DHFSP with minimizing the maximum completion time(Makespan).First,a mathematical model is developed for the concerned DHFSP.Second,four Q-learning-assisted meta-heuristics,e.g.,genetic algorithm(GA),artificial bee colony algorithm(ABC),particle swarm optimization(PSO),and differential evolution(DE),are proposed.According to the nature of DHFSP,six local search operations are designed for finding high-quality solutions in local space.Instead of randomselection,Q-learning assists meta-heuristics in choosing the appropriate local search operations during iterations.Finally,based on 60 cases,comprehensive numerical experiments are conducted to assess the effectiveness of the proposed algorithms.The experimental results and discussions prove that using Q-learning to select appropriate local search operations is more effective than the random strategy.To verify the competitiveness of the Q-learning assistedmeta-heuristics,they are compared with the improved iterated greedy algorithm(IIG),which is also for solving DHFSP.The Friedman test is executed on the results by five algorithms.It is concluded that the performance of four Q-learning-assisted meta-heuristics are better than IIG,and the Q-learning-assisted PSO shows the best competitiveness.
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 Fund for Distinguished Young Scholars of China(No.61525304)the National Natural Science Foundation of China(No.61873328)。
文摘This paper addresses the Energy-Aware Distributed Hybrid Flow Shop Scheduling Problem with Multiprocessor Tasks(EADHFSPMT)by considering two objectives simultaneously,i.e.,makespan and total energy consumption.It consists of three sub-problems,i.e.,job assignment between factories,job sequence in each factory,and machine allocation for each job.We present a mixed inter linear programming model and propose a Novel MultiObjective Evolutionary Algorithm based on Decomposition(NMOEA/D).We specially design a decoding scheme according to the characteristics of the EADHFSPMT.To initialize a population with certain diversity,four different rules are utilized.Moreover,a cooperative search is designed to produce new solutions based on different types of relationship between any solution and its neighbors.To enhance the quality of solutions,two local intensification operators are implemented according to the problem characteristics.In addition,a dynamic adjustment strategy for weight vectors is designed to balance the diversity and convergence,which can adaptively modify weight vectors according to the distribution of the non-dominated front.Extensive computational experiments are carried out by using a number of benchmark instances,which demonstrate the effectiveness of the above special designs.The statistical comparisons to the existing algorithms also verify the superior performances of the NMOEA/D.
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).
基金This work was jointly supported by the National Natural Science Foundation of Shandong Province(No.ZR2023MF022)National Natural Science Foundation of China(Nos.61973203,62173216,and 62173356)Guangyue Youth Scholar Innovation Talent Program Support from Liaocheng University(No.LCUGYTD2022-03).
文摘The distributed hybrid flow shop scheduling problem(DHFSP),which integrates distributed manufacturing models with parallel machines,has gained significant attention.However,in actual scheduling,some adjacent machines do not have buffers between them,resulting in blocking.This paper focuses on addressing the DHFSP with blocking constraints(DBHFSP)based on the actual production conditions.To solve DBHFSP,we construct a mixed integer linear programming(MILP)model for DBHFSP and validate its correctness using the Gurobi solver.Then,an advanced iterated greedy(AIG)algorithm is designed to minimize the makespan,in which we modify the Nawaz,Enscore,and Ham(NEH)heuristic to solve blocking constraints.To balance the global and local search capabilities of AIG,two effective inter-factory neighborhood search strategies and a swap-based local search strategy are designed.Additionally,each factory is mutually independent,and the movement within one factory does not affect the others.In view of this,we specifically designed a memory-based decoding method for insertion operations to reduce the computation time of the objective.Finally,two shaking strategies are incorporated into the algorithm to mitigate premature convergence.Five advanced algorithms are used to conduct comparative experiments with AIG on 80 test instances,and experimental results illustrate that the makespan and the relative percentage increase(RPI)obtained by AIG are 1.0%and 86.1%,respectively,better than the comparative algorithms.
