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
In the dynamic, complex and unbounded Grid systems, failures of Grid resources caused by malicious attacks and hardware failures are inevitable and have an adverse effect on the execution of tasks. To mitigate this pr...In the dynamic, complex and unbounded Grid systems, failures of Grid resources caused by malicious attacks and hardware failures are inevitable and have an adverse effect on the execution of tasks. To mitigate this problem, a makespan and reliability driven （MRD） sufferage scheduling algorithm is designed and implemented. Different from the traditional Grid scheduling algorithms, the algorithm addresses the makespan as well as reliability of tasks. The simulation experimental results show that the MRD sufferage scheduling algorithm can increase reliability of tasks and can trade off reliability against makespan of tasks by adjusting the weighting parameter in its cost function. So it can be applied to the complex Grid computing environment well.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
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
Cloud computing has rapidly evolved into a critical technology,seamlessly integrating into various aspects of daily life.As user demand for cloud services continues to surge,the need for efficient virtualization and r...Cloud computing has rapidly evolved into a critical technology,seamlessly integrating into various aspects of daily life.As user demand for cloud services continues to surge,the need for efficient virtualization and resource management becomes paramount.At the core of this efficiency lies task scheduling,a complex process that determines how tasks are allocated and executed across cloud resources.While extensive research has been conducted in the area of task scheduling,optimizing multiple objectives simultaneously remains a significant challenge due to the NP(Non-deterministic Polynomial)Complete nature of the problem.This study aims to address these challenges by providing a comprehensive review and experimental analysis of task scheduling approaches,with a particular focus on hybrid techniques that offer promising solutions.Utilizing the CloudSim simulation toolkit,we evaluated the performance of three hybrid algorithms:Estimation of Distribution Algorithm-Genetic Algorithm(EDA-GA),Hybrid Genetic Algorithm-Ant Colony Optimization(HGA-ACO),and Improved Discrete Particle Swarm Optimization(IDPSO).Our experimental results demonstrate that these hybrid methods significantly outperform traditional standalone algorithms in reducing Makespan,which is a critical measure of task completion time.Notably,the IDPSO algorithm exhibited superior performance,achieving a Makespan of just 0.64 milliseconds for a set of 150 tasks.These findings underscore the potential of hybrid algorithms to enhance task scheduling efficiency in cloud computing environments.This paper concludes with a discussion of the implications of our findings and offers recommendations for future research aimed at further improving task scheduling strategies,particularly in the context of increasingly complex and dynamic cloud environments.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
No-wait flow shops with makespan minimization are classified as NP-hard. In this paper, the optimization objective is equivalently transformed to total idle-time minimization. The independence relationship between tas...No-wait flow shops with makespan minimization are classified as NP-hard. In this paper, the optimization objective is equivalently transformed to total idle-time minimization. The independence relationship between tasks is analyzed, and objective increment properties are established for the fundamental operators of the heuristics. The quality of the new schedules generated during a heuristic is judged only by objective increments and not by the traditional method, which computes and compares the objective of a whole schedule. Based on objective increments, the time complexity of the heuristic can be decreased by one order. A seed phase is presented to generate an initial solution according to the transformed objective. Construction and improvement phases are introduced by experimental analysis. The FCH （fast composite heuristic） is proposed and compared with the most effective algorithms currently available for the considered problem. Experimental results show that the effectiveness of the FCH is similar to that of the best methods but requires far less computation time. The FCH can also be efficient in real time scheduling and rescheduling for no-wait flow shops.展开更多
Edge computing nodes undertake an increasing number of tasks with the rise of business density.Therefore,how to efficiently allocate large-scale and dynamic workloads to edge computing resources has become a critical ...Edge computing nodes undertake an increasing number of tasks with the rise of business density.Therefore,how to efficiently allocate large-scale and dynamic workloads to edge computing resources has become a critical challenge.This study proposes an edge task scheduling approach based on an improved Double Deep Q Network(DQN),which is adopted to separate the calculations of target Q values and the selection of the action in two networks.A new reward function is designed,and a control unit is added to the experience replay unit of the agent.The management of experience data are also modified to fully utilize its value and improve learning efficiency.Reinforcement learning agents usually learn from an ignorant state,which is inefficient.As such,this study proposes a novel particle swarm optimization algorithm with an improved fitness function,which can generate optimal solutions for task scheduling.These optimized solutions are provided for the agent to pre-train network parameters to obtain a better cognition level.The proposed algorithm is compared with six other methods in simulation experiments.Results show that the proposed algorithm outperforms other benchmark methods regarding makespan.展开更多
We study an online(over time)scheduling problem on two uniform unbounded parallel-batch machines with processing speed 1 and v(0<≤1),respectively,to minimize the makespan.We first show that no online algorithm can...We study an online(over time)scheduling problem on two uniform unbounded parallel-batch machines with processing speed 1 and v(0<≤1),respectively,to minimize the makespan.We first show that no online algorithm can have a competitive ratio less than 1+αL,whereαL=(√5−1)/2≈0.618 if 0≤1/2,andαL=α2(v)is the positive root ofα^(3)+3α^(2)+(3−1/v)α−1/v=0 if1/2≤1.This lower bound is still valid when all jobs have the same processing times.Then,we provide an online algorithm with a competitive ratio at most min{(√5+1)/2,√2/v}.When the jobs have the same processing times,we present the best possible online algorithm with a competitive ratio 1+αL.展开更多
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In the dynamic, complex and unbounded Grid systems, failures of Grid resources caused by malicious attacks and hardware failures are inevitable and have an adverse effect on the execution of tasks. To mitigate this problem, a makespan and reliability driven （MRD） sufferage scheduling algorithm is designed and implemented. Different from the traditional Grid scheduling algorithms, the algorithm addresses the makespan as well as reliability of tasks. The simulation experimental results show that the MRD sufferage scheduling algorithm can increase reliability of tasks and can trade off reliability against makespan of tasks by adjusting the weighting parameter in its cost function. So it can be applied to the complex Grid computing environment well.
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.
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.
文摘Cloud computing has rapidly evolved into a critical technology,seamlessly integrating into various aspects of daily life.As user demand for cloud services continues to surge,the need for efficient virtualization and resource management becomes paramount.At the core of this efficiency lies task scheduling,a complex process that determines how tasks are allocated and executed across cloud resources.While extensive research has been conducted in the area of task scheduling,optimizing multiple objectives simultaneously remains a significant challenge due to the NP(Non-deterministic Polynomial)Complete nature of the problem.This study aims to address these challenges by providing a comprehensive review and experimental analysis of task scheduling approaches,with a particular focus on hybrid techniques that offer promising solutions.Utilizing the CloudSim simulation toolkit,we evaluated the performance of three hybrid algorithms:Estimation of Distribution Algorithm-Genetic Algorithm(EDA-GA),Hybrid Genetic Algorithm-Ant Colony Optimization(HGA-ACO),and Improved Discrete Particle Swarm Optimization(IDPSO).Our experimental results demonstrate that these hybrid methods significantly outperform traditional standalone algorithms in reducing Makespan,which is a critical measure of task completion time.Notably,the IDPSO algorithm exhibited superior performance,achieving a Makespan of just 0.64 milliseconds for a set of 150 tasks.These findings underscore the potential of hybrid algorithms to enhance task scheduling efficiency in cloud computing environments.This paper concludes with a discussion of the implications of our findings and offers recommendations for future research aimed at further improving task scheduling strategies,particularly in the context of increasingly complex and dynamic cloud environments.
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.
基金the National Natural Science Foundation of China (Grant Nos.60504029 and 60672092)the National High Technology Re-search and Development Program of China (863 Program) (Grant No.2008AA04Z103)
文摘No-wait flow shops with makespan minimization are classified as NP-hard. In this paper, the optimization objective is equivalently transformed to total idle-time minimization. The independence relationship between tasks is analyzed, and objective increment properties are established for the fundamental operators of the heuristics. The quality of the new schedules generated during a heuristic is judged only by objective increments and not by the traditional method, which computes and compares the objective of a whole schedule. Based on objective increments, the time complexity of the heuristic can be decreased by one order. A seed phase is presented to generate an initial solution according to the transformed objective. Construction and improvement phases are introduced by experimental analysis. The FCH （fast composite heuristic） is proposed and compared with the most effective algorithms currently available for the considered problem. Experimental results show that the effectiveness of the FCH is similar to that of the best methods but requires far less computation time. The FCH can also be efficient in real time scheduling and rescheduling for no-wait flow shops.
基金supported by the National Key Research and Development Program of China(No.2021YFE0116900)National Natural Science Foundation of China(Nos.42275157,62002276,and 41975142)Major Program of the National Social Science Fund of China(No.17ZDA092).
文摘Edge computing nodes undertake an increasing number of tasks with the rise of business density.Therefore,how to efficiently allocate large-scale and dynamic workloads to edge computing resources has become a critical challenge.This study proposes an edge task scheduling approach based on an improved Double Deep Q Network(DQN),which is adopted to separate the calculations of target Q values and the selection of the action in two networks.A new reward function is designed,and a control unit is added to the experience replay unit of the agent.The management of experience data are also modified to fully utilize its value and improve learning efficiency.Reinforcement learning agents usually learn from an ignorant state,which is inefficient.As such,this study proposes a novel particle swarm optimization algorithm with an improved fitness function,which can generate optimal solutions for task scheduling.These optimized solutions are provided for the agent to pre-train network parameters to obtain a better cognition level.The proposed algorithm is compared with six other methods in simulation experiments.Results show that the proposed algorithm outperforms other benchmark methods regarding makespan.
基金The first author was supported by the National Natural Science Foundation of China(No.11671368)Natural Science Foundation of Henan Province(No.15IRTSTHN006)+1 种基金Tian was also supported by Natural Science Foundation of Jiangsu Province(No.BK20130169)the National Natural Science Foundation of China(No.61573362).
文摘We study an online(over time)scheduling problem on two uniform unbounded parallel-batch machines with processing speed 1 and v(0<≤1),respectively,to minimize the makespan.We first show that no online algorithm can have a competitive ratio less than 1+αL,whereαL=(√5−1)/2≈0.618 if 0≤1/2,andαL=α2(v)is the positive root ofα^(3)+3α^(2)+(3−1/v)α−1/v=0 if1/2≤1.This lower bound is still valid when all jobs have the same processing times.Then,we provide an online algorithm with a competitive ratio at most min{(√5+1)/2,√2/v}.When the jobs have the same processing times,we present the best possible online algorithm with a competitive ratio 1+αL.
