A two-agent scheduling problem on parallel machines is considered in this paper. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. In this paper, we provide ...A two-agent scheduling problem on parallel machines is considered in this paper. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. In this paper, we provide a new approximation algorithm called CLPT. On the one hand, we compare the performance between the CLPT algorithm and the optimal solution and find that the solution obtained by the CLPT algorithm is very close to the optimal solution. On the other hand, we design different experimental frameworks to compare the CLPT algorithm and the A-LS algorithm for a comprehensive performance evaluation. A large number of numerical simulation results show that the CLPT algorithm outperformed the A-LS algorithm.展开更多
It is known that the problem of minimizing total weighted completion time on a series-batching machine is NP-hard. We consider a series-batching bicriteria scheduling problem of minimizing makespan and total weighted ...It is known that the problem of minimizing total weighted completion time on a series-batching machine is NP-hard. We consider a series-batching bicriteria scheduling problem of minimizing makespan and total weighted completion time with equal length job simultaneously. A batching machine can handle up to b jobs in a batch, where b is called the batch capacity of the machine. We study the unbounded model with b ≥ n, where n denotes the number of jobs. A dynamic programming algorithm is proposed to solve the unbounded model, which can find all Pareto optimal schedules in O(n3) time.展开更多
This paper discusses design and comparison of Simulated Annealing Algorithm and Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan in scheduling n single operation independent jobs on m unrel...This paper discusses design and comparison of Simulated Annealing Algorithm and Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan in scheduling n single operation independent jobs on m unrelated parallel machines. This problem of minimizing the makespan in single machine scheduling problem with uniform parallel machines is NP hard. Hence, heuristic development for such problem is highly inevitable. In this paper, two different Meta-heuristics to minimize the makespan of the assumed problem are designed and they are compared in terms of their solutions. In the first phase, the simulated annealing algorithm is presented and then GRASP (Greedy Randomized Adaptive Search procedure) is presented to minimize the makespan in the single machine scheduling problem with unrelated parallel machines. It is found that the simulated annealing algorithm performs better than GRASP.展开更多
This paper proposes a heuristic algorithm, called list-based squeezing branch and bound algorithm, for solving a machine-fixed, machining-assembly flowshop scheduling problem to minimize makespan. The machine-fixed, m...This paper proposes a heuristic algorithm, called list-based squeezing branch and bound algorithm, for solving a machine-fixed, machining-assembly flowshop scheduling problem to minimize makespan. The machine-fixed, machining-assembly flowshop consists of some parallel two-machine flow lines at a machining stage and one robot at an assembly stage. Since an optimal schedule for this problem is not always a permutation schedule, the proposed algorithm first finds a promising permutation schedule, and then searches better non-permutation schedules near the promising permutation schedule in an enumerative manner by elaborating a branching procedure in a branch and bound algorithm. The results of numerical experiments show that the proposed algorithm can efficiently provide an optimal or a near-optimal schedule with high accuracy such as mean relative error being less than 0.2% and the maximum relative error being at most 3%.展开更多
The objective of the research discussed in this paper has been to find an optimal schedule on mixed mass production lines of two and three machines. Johnson's rule on flow shops is generalized to mixed mass produ...The objective of the research discussed in this paper has been to find an optimal schedule on mixed mass production lines of two and three machines. Johnson's rule on flow shops is generalized to mixed mass production lines. Scheduling methods on three-machine lines are proposed for six special kinds of data of processing times of jobs. The scheduling method on two-machine lines is also proposed.展开更多
The problem of scheduling jobs on uniform parallel machines with makespan ( C max ) minimization objective was studied. Due to its non-deterministic polynomial-time ( N ) hard nature,it is difficult to achieve an opti...The problem of scheduling jobs on uniform parallel machines with makespan ( C max ) minimization objective was studied. Due to its non-deterministic polynomial-time ( N ) hard nature,it is difficult to achieve an optimal solution with traditional optimization methods. For this reason,a novel modified differential evolution ( MDE) was proposed to tackle the uniform parallel machine scheduling problem ( UPMSP ) ,taking out the mutation operation and introducing the roulette wheel selection strategy into conventional differential evolution ( DE ) . In MDE, more high quality individuals can be reserved to update the population. And the control parameter F in conventional DE was removed,which could simplify the DE. To verify the proposed MDE,162 randomly generated instances were conducted. The comparison results with DE,genetic algorithm ( GA ) ,simulated annealing ( SA ) , and largest processing time ( LPT) method show that the MDE is an efficient and competitive approach in solving UPMSP.展开更多
This paper considers the scheduling problem observed in chip sorting operation of LED manufacturing, where each lot (job) with release time have four operations to be processed on a set of processing stages without pr...This paper considers the scheduling problem observed in chip sorting operation of LED manufacturing, where each lot (job) with release time have four operations to be processed on a set of processing stages without pre-determined necessary route. Each stage has one and more identical sorting machines. The sorting machines scheduling problem can be treated as a four-stage multiprocessor open shop problem with dynamic job release, and the objective is minimizing the makespan in the paper. This problem is formulated into a mixed integer programming (MIP) model and empirically shows its computational intractability. Due to the computational intractability, a particle swarm optimization (PSO) algorithm is proposed. A series of computational experiments are conducted to evaluate the performance of the proposed PSO in comparison with exact solution on various small-size problem instances. The results show that the PSO algorithm could finds most optimal or better solutions in one second.展开更多
This paper discusses an efficient heuristic to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. The problem of scheduling the jobs on the unrelated parallel machines is combinat...This paper discusses an efficient heuristic to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. The problem of scheduling the jobs on the unrelated parallel machines is combinatorial in nature. Hence, the heuristic approach is inevitable for quicker solution. In this paper, a simple and efficient heuristic is designed to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. A mathematical model is also presented for this problem. A factorial experiment is used to compare the results of the proposed heuristic with that of a mathematical model by taking “Method” (Heuristic and Model) as the first factor and “Problem Size” (No. of machines X No. of Jobs: 2X5, 2X6, ……, 2X9, 3X5, 3X6, ……, 3X9, ……., 5X5, 5X6, …5X9) as the second factor. It is found that there is no significant difference between the results of the proposed heuristic and that of the mathematical model. Further, the mean percent error of the results obtained by the heuristic from the optimal results obtained by the model is 2.336 %. The heuristic gives optimal solution for 76.67 % of the problems.展开更多
Flexible job shop scheduling problem(FJSP)is the core decision-making problem of intelligent manufacturing production management.The Harris hawk optimization(HHO)algorithm,as a typical metaheuristic algorithm,has been...Flexible job shop scheduling problem(FJSP)is the core decision-making problem of intelligent manufacturing production management.The Harris hawk optimization(HHO)algorithm,as a typical metaheuristic algorithm,has been widely employed to solve scheduling problems.However,HHO suffers from premature convergence when solving NP-hard problems.Therefore,this paper proposes an improved HHO algorithm(GNHHO)to solve the FJSP.GNHHO introduces an elitism strategy,a chaotic mechanism,a nonlinear escaping energy update strategy,and a Gaussian random walk strategy to prevent premature convergence.A flexible job shop scheduling model is constructed,and the static and dynamic FJSP is investigated to minimize the makespan.This paper chooses a two-segment encoding mode based on the job and the machine of the FJSP.To verify the effectiveness of GNHHO,this study tests it in 23 benchmark functions,10 standard job shop scheduling problems(JSPs),and 5 standard FJSPs.Besides,this study collects data from an agricultural company and uses the GNHHO algorithm to optimize the company’s FJSP.The optimized scheduling scheme demonstrates significant improvements in makespan,with an advancement of 28.16%for static scheduling and 35.63%for dynamic scheduling.Moreover,it achieves an average increase of 21.50%in the on-time order delivery rate.The results demonstrate that the performance of the GNHHO algorithm in solving FJSP is superior to some existing algorithms.展开更多
In this paper,we consider a multi-crane scheduling problem in rail stations because their operations directly influence the throughput of the rail stations.In particular,the job is not only assigned to cranes but also...In this paper,we consider a multi-crane scheduling problem in rail stations because their operations directly influence the throughput of the rail stations.In particular,the job is not only assigned to cranes but also the job sequencing is implemented for each crane to minimize the makespan of cranes.A dual cycle of cranes is used to minimize the number of working cycles of cranes.The rail crane scheduling problems in this study are based on the movement of containers.We consider not only the gantry moves,but also the trolley moves as well as the rehandle cases are also included.A mathematical model of multi-crane scheduling is developed.The traditional and parallel simulated annealing(SA)are adapted to determine the optimal scheduling solutions.Numerical examples are conducted to evaluate the applicability of the proposed algorithms.Verification of the proposed parallel SA is done by comparing it to existing previous works.Results of numerical computation highlighted that the parallel SA algorithm outperformed the SA and gave better solutions than other considered algorithms.展开更多
This work proposes a hybrid approach for solving traditional flowshop scheduling problems to reduce the makespan （total completion time）. To solve scheduling problems, a combination of Decision Tree （DT） and Scatt...This work proposes a hybrid approach for solving traditional flowshop scheduling problems to reduce the makespan （total completion time）. To solve scheduling problems, a combination of Decision Tree （DT） and Scatter Search （SS） algorithms are used. Initially, the DT is used to generate a seed solution which is then given input to the SS to obtain optimal / near optimal solutions of makespan. The DT used the entropy function to convert the given problem into a tree structured format / set of rules. The SS provides an extensive investigation of the search space through diversification. The advantages of both DT and SS are used to form a hybrid approach. The proposed algorithm is tested with various benchmark datasets available for flowshop scheduling. The statistical results prove that the proposed method is competent and efficient for solving flowshop problems.展开更多
文摘A two-agent scheduling problem on parallel machines is considered in this paper. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. In this paper, we provide a new approximation algorithm called CLPT. On the one hand, we compare the performance between the CLPT algorithm and the optimal solution and find that the solution obtained by the CLPT algorithm is very close to the optimal solution. On the other hand, we design different experimental frameworks to compare the CLPT algorithm and the A-LS algorithm for a comprehensive performance evaluation. A large number of numerical simulation results show that the CLPT algorithm outperformed the A-LS algorithm.
基金Foundation item： Supported by the National Natural Science Foundation of China（11201121, 11101383） Supported by the China Scholarship Counci1（201309895008）+1 种基金 Supported bythe 2013GGJS-079 Supported by the 2011B110008
文摘It is known that the problem of minimizing total weighted completion time on a series-batching machine is NP-hard. We consider a series-batching bicriteria scheduling problem of minimizing makespan and total weighted completion time with equal length job simultaneously. A batching machine can handle up to b jobs in a batch, where b is called the batch capacity of the machine. We study the unbounded model with b ≥ n, where n denotes the number of jobs. A dynamic programming algorithm is proposed to solve the unbounded model, which can find all Pareto optimal schedules in O(n3) time.
文摘This paper discusses design and comparison of Simulated Annealing Algorithm and Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan in scheduling n single operation independent jobs on m unrelated parallel machines. This problem of minimizing the makespan in single machine scheduling problem with uniform parallel machines is NP hard. Hence, heuristic development for such problem is highly inevitable. In this paper, two different Meta-heuristics to minimize the makespan of the assumed problem are designed and they are compared in terms of their solutions. In the first phase, the simulated annealing algorithm is presented and then GRASP (Greedy Randomized Adaptive Search procedure) is presented to minimize the makespan in the single machine scheduling problem with unrelated parallel machines. It is found that the simulated annealing algorithm performs better than GRASP.
文摘This paper proposes a heuristic algorithm, called list-based squeezing branch and bound algorithm, for solving a machine-fixed, machining-assembly flowshop scheduling problem to minimize makespan. The machine-fixed, machining-assembly flowshop consists of some parallel two-machine flow lines at a machining stage and one robot at an assembly stage. Since an optimal schedule for this problem is not always a permutation schedule, the proposed algorithm first finds a promising permutation schedule, and then searches better non-permutation schedules near the promising permutation schedule in an enumerative manner by elaborating a branching procedure in a branch and bound algorithm. The results of numerical experiments show that the proposed algorithm can efficiently provide an optimal or a near-optimal schedule with high accuracy such as mean relative error being less than 0.2% and the maximum relative error being at most 3%.
文摘The objective of the research discussed in this paper has been to find an optimal schedule on mixed mass production lines of two and three machines. Johnson's rule on flow shops is generalized to mixed mass production lines. Scheduling methods on three-machine lines are proposed for six special kinds of data of processing times of jobs. The scheduling method on two-machine lines is also proposed.
基金National Natural Science Foundation of China ( No. 60804052 )Chen Guang Project from Shanghai Municipal Education Commission and Shanghai Education Development Foundation,China ( No. 09CG39 )Project of Shanghai Municipal Education Commission,China ( No. 12YZ020)
文摘The problem of scheduling jobs on uniform parallel machines with makespan ( C max ) minimization objective was studied. Due to its non-deterministic polynomial-time ( N ) hard nature,it is difficult to achieve an optimal solution with traditional optimization methods. For this reason,a novel modified differential evolution ( MDE) was proposed to tackle the uniform parallel machine scheduling problem ( UPMSP ) ,taking out the mutation operation and introducing the roulette wheel selection strategy into conventional differential evolution ( DE ) . In MDE, more high quality individuals can be reserved to update the population. And the control parameter F in conventional DE was removed,which could simplify the DE. To verify the proposed MDE,162 randomly generated instances were conducted. The comparison results with DE,genetic algorithm ( GA ) ,simulated annealing ( SA ) , and largest processing time ( LPT) method show that the MDE is an efficient and competitive approach in solving UPMSP.
文摘This paper considers the scheduling problem observed in chip sorting operation of LED manufacturing, where each lot (job) with release time have four operations to be processed on a set of processing stages without pre-determined necessary route. Each stage has one and more identical sorting machines. The sorting machines scheduling problem can be treated as a four-stage multiprocessor open shop problem with dynamic job release, and the objective is minimizing the makespan in the paper. This problem is formulated into a mixed integer programming (MIP) model and empirically shows its computational intractability. Due to the computational intractability, a particle swarm optimization (PSO) algorithm is proposed. A series of computational experiments are conducted to evaluate the performance of the proposed PSO in comparison with exact solution on various small-size problem instances. The results show that the PSO algorithm could finds most optimal or better solutions in one second.
文摘This paper discusses an efficient heuristic to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. The problem of scheduling the jobs on the unrelated parallel machines is combinatorial in nature. Hence, the heuristic approach is inevitable for quicker solution. In this paper, a simple and efficient heuristic is designed to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. A mathematical model is also presented for this problem. A factorial experiment is used to compare the results of the proposed heuristic with that of a mathematical model by taking “Method” (Heuristic and Model) as the first factor and “Problem Size” (No. of machines X No. of Jobs: 2X5, 2X6, ……, 2X9, 3X5, 3X6, ……, 3X9, ……., 5X5, 5X6, …5X9) as the second factor. It is found that there is no significant difference between the results of the proposed heuristic and that of the mathematical model. Further, the mean percent error of the results obtained by the heuristic from the optimal results obtained by the model is 2.336 %. The heuristic gives optimal solution for 76.67 % of the problems.
基金Acknowledgements： The authors are grateful for professors LIN Yi-xun and YUAN Jin-jiang for the helpful suggestions. The research in part was supported by NSFC （10671183）, NSFHN（082300410190）, The Nature Science Foundation of the Education Department of Henan （2008AI10004）, Science Foundation （07XJCO02） and Doctor Science Foundation of Henan University of Technology.
文摘Flexible job shop scheduling problem(FJSP)is the core decision-making problem of intelligent manufacturing production management.The Harris hawk optimization(HHO)algorithm,as a typical metaheuristic algorithm,has been widely employed to solve scheduling problems.However,HHO suffers from premature convergence when solving NP-hard problems.Therefore,this paper proposes an improved HHO algorithm(GNHHO)to solve the FJSP.GNHHO introduces an elitism strategy,a chaotic mechanism,a nonlinear escaping energy update strategy,and a Gaussian random walk strategy to prevent premature convergence.A flexible job shop scheduling model is constructed,and the static and dynamic FJSP is investigated to minimize the makespan.This paper chooses a two-segment encoding mode based on the job and the machine of the FJSP.To verify the effectiveness of GNHHO,this study tests it in 23 benchmark functions,10 standard job shop scheduling problems(JSPs),and 5 standard FJSPs.Besides,this study collects data from an agricultural company and uses the GNHHO algorithm to optimize the company’s FJSP.The optimized scheduling scheme demonstrates significant improvements in makespan,with an advancement of 28.16%for static scheduling and 35.63%for dynamic scheduling.Moreover,it achieves an average increase of 21.50%in the on-time order delivery rate.The results demonstrate that the performance of the GNHHO algorithm in solving FJSP is superior to some existing algorithms.
文摘In this paper,we consider a multi-crane scheduling problem in rail stations because their operations directly influence the throughput of the rail stations.In particular,the job is not only assigned to cranes but also the job sequencing is implemented for each crane to minimize the makespan of cranes.A dual cycle of cranes is used to minimize the number of working cycles of cranes.The rail crane scheduling problems in this study are based on the movement of containers.We consider not only the gantry moves,but also the trolley moves as well as the rehandle cases are also included.A mathematical model of multi-crane scheduling is developed.The traditional and parallel simulated annealing(SA)are adapted to determine the optimal scheduling solutions.Numerical examples are conducted to evaluate the applicability of the proposed algorithms.Verification of the proposed parallel SA is done by comparing it to existing previous works.Results of numerical computation highlighted that the parallel SA algorithm outperformed the SA and gave better solutions than other considered algorithms.
文摘This work proposes a hybrid approach for solving traditional flowshop scheduling problems to reduce the makespan （total completion time）. To solve scheduling problems, a combination of Decision Tree （DT） and Scatter Search （SS） algorithms are used. Initially, the DT is used to generate a seed solution which is then given input to the SS to obtain optimal / near optimal solutions of makespan. The DT used the entropy function to convert the given problem into a tree structured format / set of rules. The SS provides an extensive investigation of the search space through diversification. The advantages of both DT and SS are used to form a hybrid approach. The proposed algorithm is tested with various benchmark datasets available for flowshop scheduling. The statistical results prove that the proposed method is competent and efficient for solving flowshop problems.
