To fulfill the requirements for hybrid real-time system scheduling, a long-release-interval-first （LRIF） real-time scheduling algorithm is proposed. The algorithm adopts both the fixed priority and the dynamic prior...To fulfill the requirements for hybrid real-time system scheduling, a long-release-interval-first （LRIF） real-time scheduling algorithm is proposed. The algorithm adopts both the fixed priority and the dynamic priority to assign priorities for tasks. By assigning higher priorities to the aperiodic soft real-time jobs with longer release intervals, it guarantees the executions for periodic hard real-time tasks and further probabilistically guarantees the executions for aperiodic soft real-time tasks. The schedulability test approach for the LRIF algorithm is presented. The implementation issues of the LRIF algorithm are also discussed. Simulation result shows that LRIF obtains better schedulable performance than the maximum urgency first （MUF） algorithm, the earliest deadline first （EDF） algorithm and EDF for hybrid tasks. LRIF has great capability to schedule both periodic hard real-time and aperiodic soft real-time tasks.展开更多
In hard real-time systems, schedulability analysis is not only one of the important means of guaranteeing the timelines of embedded software but also one of the fundamental theories of applying other new techniques, s...In hard real-time systems, schedulability analysis is not only one of the important means of guaranteeing the timelines of embedded software but also one of the fundamental theories of applying other new techniques, such as energy savings and fault tolerance. However, most of the existing schedulability analysis methods assume that schedulers use preemptive scheduling or non-preemptive scheduling. In this paper, we present a schedulability analysis method, i.e., the worst-case hybrid scheduling (WCHS) algorithm, which considers the influence of release jitters of transactions and extends schedulability analysis theory to timing analysis of linear transactions under fixed priority hybrid scheduling. To the best of our knowledge, this method is the first one on timing analysis of linear transactions under hybrid scheduling. An example is employed to demonstrate the use of this method. Experiments show that this method has lower computational complexity while keeping correctness, and that hybrid scheduling has little influence on the average worst-case response time (WCRT), but a negative impact on the schedulability of systems.展开更多
With the rapid development of cloud computing,edge computing,and smart devices,computing power resources indicate a trend of ubiquitous deployment.The traditional network architecture cannot efficiently leverage these...With the rapid development of cloud computing,edge computing,and smart devices,computing power resources indicate a trend of ubiquitous deployment.The traditional network architecture cannot efficiently leverage these distributed computing power resources due to computing power island effect.To overcome these problems and improve network efficiency,a new network computing paradigm is proposed,i.e.,Computing Power Network(CPN).Computing power network can connect ubiquitous and heterogenous computing power resources through networking to realize computing power scheduling flexibly.In this survey,we make an exhaustive review on the state-of-the-art research efforts on computing power network.We first give an overview of computing power network,including definition,architecture,and advantages.Next,a comprehensive elaboration of issues on computing power modeling,information awareness and announcement,resource allocation,network forwarding,computing power transaction platform and resource orchestration platform is presented.The computing power network testbed is built and evaluated.The applications and use cases in computing power network are discussed.Then,the key enabling technologies for computing power network are introduced.Finally,open challenges and future research directions are presented as well.展开更多
Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay ...Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay can hamper the performance of IoT-enabled cloud platforms.However,efficient task scheduling can lower the cloud infrastructure’s energy consumption,thus maximizing the service provider’s revenue by decreasing user job processing times.The proposed Modified Chimp-Whale Optimization Algorithm called Modified Chimp-Whale Optimization Algorithm(MCWOA),combines elements of the Chimp Optimization Algorithm(COA)and the Whale Optimization Algorithm(WOA).To enhance MCWOA’s identification precision,the Sobol sequence is used in the population initialization phase,ensuring an even distribution of the population across the solution space.Moreover,the traditional MCWOA’s local search capabilities are augmented by incorporating the whale optimization algorithm’s bubble-net hunting and random search mechanisms into MCWOA’s position-updating process.This study demonstrates the effectiveness of the proposed approach using a two-story rigid frame and a simply supported beam model.Simulated outcomes reveal that the new method outperforms the original MCWOA,especially in multi-damage detection scenarios.MCWOA excels in avoiding false positives and enhancing computational speed,making it an optimal choice for structural damage detection.The efficiency of the proposed MCWOA is assessed against metrics such as energy usage,computational expense,task duration,and delay.The simulated data indicates that the new MCWOA outpaces other methods across all metrics.The study also references the Whale Optimization Algorithm(WOA),Chimp Algorithm(CA),Ant Lion Optimizer(ALO),Genetic Algorithm(GA)and Grey Wolf Optimizer(GWO).展开更多
In recent years,the global surge of High-speed Railway(HSR)revolutionized ground transportation,providing secure,comfortable,and punctual services.The next-gen HSR,fueled by emerging services like video surveillance,e...In recent years,the global surge of High-speed Railway(HSR)revolutionized ground transportation,providing secure,comfortable,and punctual services.The next-gen HSR,fueled by emerging services like video surveillance,emergency communication,and real-time scheduling,demands advanced capabilities in real-time perception,automated driving,and digitized services,which accelerate the integration and application of Artificial Intelligence(AI)in the HSR system.This paper first provides a brief overview of AI,covering its origin,evolution,and breakthrough applications.A comprehensive review is then given regarding the most advanced AI technologies and applications in three macro application domains of the HSR system:mechanical manufacturing and electrical control,communication and signal control,and transportation management.The literature is categorized and compared across nine application directions labeled as intelligent manufacturing of trains and key components,forecast of railroad maintenance,optimization of energy consumption in railroads and trains,communication security,communication dependability,channel modeling and estimation,passenger scheduling,traffic flow forecasting,high-speed railway smart platform.Finally,challenges associated with the application of AI are discussed,offering insights for future research directions.展开更多
With notably few exceptions, the existing satellite mission operations cannot provide the ability of schedulability prediction, including the latest satellite planning service （SPS） standard–Sensor Planning Service...With notably few exceptions, the existing satellite mission operations cannot provide the ability of schedulability prediction, including the latest satellite planning service （SPS） standard–Sensor Planning Service Interface Standard 2.0 Earth Observation Satellite Tasking Extension （EO SPS） approved by Open Geospatial Consortium （OGC）. The requestor can do nothing but waiting for the results of time consuming batch scheduling. It is often too late to adjust the request when receiving scheduling failures. A supervised learning algorithm based on robust decision tree and bagging support vector machine （Bagging SVM） is proposed to solve the problem above. The Bagging SVM is applied to improve the accuracy of classification and robust decision tree is utilized to reduce the error mean and error variation. The simulations and analysis show that a prediction action can be accomplished in near real-time with high accuracy. This means the decision makers can maximize the probability of successful scheduling through changing request parameters or take action to accommodate the scheduling failures in time.展开更多
Safety-critical avionics systems which become more complex and tend to integrate multiple functionalities with different levels of criticality for better cost and power efficiency are subject to certifications at vari...Safety-critical avionics systems which become more complex and tend to integrate multiple functionalities with different levels of criticality for better cost and power efficiency are subject to certifications at various levels of rigorousness. In order to simultaneously guarantee temporal constraints at all different levels of assurance mandated by different criticalities, novel scheduling techniques are in need. In this paper, a mixed-criticality sporadic task model with multiple virtual deadlines is built and a certification-cognizant dynamic scheduling approach referred as earliest virtual-deadline first with mixed-criticality（EVDF-MC） is considered, which exploits different relative deadlines of tasks in different criticality modes. As for the corresponding schedulability analysis problem, a sufficient and efficient schedulability test is proposed on the basis of demand-bound functions derived in the mixed-criticality scenario. In addition, a modified simulated annealing（MSA）-based heuristic approach is established for virtual deadlines assignment. Experiments performing simulations with randomly generated tasks indicate that the proposed approach is computationally efficient and competes well against the existing approaches.展开更多
This paper addresses a multi-agent scheduling problem with uniform parallel machines owned by a resource agent and competing jobs with dynamic arrival times that belong to different consumer agents.All agents are self...This paper addresses a multi-agent scheduling problem with uniform parallel machines owned by a resource agent and competing jobs with dynamic arrival times that belong to different consumer agents.All agents are self-interested and rational with the aim of maximizing their own objectives,resulting in intense resource competition among consumer agents and strategic behaviors of unwillingness to disclose private information.Within the context,a centralized scheduling approach is unfeasible,and a decentralized approach is considered to deal with the targeted problem.This study aims to generate a stable and collaborative solution with high social welfare while simultaneously accommodating consumer agents’preferences under incomplete information.For this purpose,a dynamic iterative auction-based approach based on a decentralized decision-making procedure is developed.In the proposed approach,a dynamic auction procedure is established for dynamic jobs participating in a realtime auction,and a straightforward and easy-to-implement bidding strategy without price is presented to reduce the complexity of bid determination.In addition,an adaptive Hungarian algorithm is applied to solve the winner determination problem efficiently.A theoretical analysis is conducted to prove that the proposed approach is individually rational and that the myopic bidding strategy is a weakly dominant strategy for consumer agents submitting bids.Extensive computational experiments demonstrate that the developed approach achieves high-quality solutions and exhibits considerable stability on largescale problems with numerous consumer agents and jobs.A further multi-agent scheduling problem considering multiple resource agents will be studied in future work.展开更多
Considering the uncertainty of the speed of horizontal transportation equipment,a cooperative scheduling model of multiple equipment resources in the automated container terminal was constructed to minimize the comple...Considering the uncertainty of the speed of horizontal transportation equipment,a cooperative scheduling model of multiple equipment resources in the automated container terminal was constructed to minimize the completion time,thus improving the loading and unloading efficiencies of automated container terminals.The proposed model integrated the two loading and unloading processes of“double-trolley quay crane+AGV+ARMG”and“single-trolley quay crane+container truck+ARMG”and then designed the simulated annealing particle swarm algorithm to solve the model.By comparing the results of the particle swarm algorithm and genetic algorithm,the algorithm designed in this paper could effectively improve the global and local space search capability of finding the optimal solution.Furthermore,the results showed that the proposed method of collaborative scheduling of multiple equipment resources in automated terminals considering hybrid processes effectively improved the loading and unloading efficiencies of automated container terminals.The findings of this study provide a reference for the improvement of loading and unloading processes as well as coordinated scheduling in automated terminals.展开更多
Time-Sensitive Network(TSN)with deterministic transmission capability is increasingly used in many emerging fields.It mainly guarantees the Quality of Service(QoS)of applications with strict requirements on time and s...Time-Sensitive Network(TSN)with deterministic transmission capability is increasingly used in many emerging fields.It mainly guarantees the Quality of Service(QoS)of applications with strict requirements on time and security.One of the core features of TSN is traffic scheduling with bounded low delay in the network.However,traffic scheduling schemes in TSN are usually synthesized offline and lack dynamism.To implement incremental scheduling of newly arrived traffic in TSN,we propose a Dynamic Response Incremental Scheduling(DR-IS)method for time-sensitive traffic and deploy it on a software-defined time-sensitive network architecture.Under the premise of meeting the traffic scheduling requirements,we adopt two modes,traffic shift and traffic exchange,to dynamically adjust the time slot injection position of the traffic in the original scheme,and determine the sending offset time of the new timesensitive traffic to minimize the global traffic transmission jitter.The evaluation results show that DRIS method can effectively control the large increase of traffic transmission jitter in incremental scheduling without affecting the transmission delay,thus realizing the dynamic incremental scheduling of time-sensitive traffic in TSN.展开更多
The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worke...The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.展开更多
Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans...Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.展开更多
In current research on task offloading and resource scheduling in vehicular networks,vehicles are commonly assumed to maintain constant speed or relatively stationary states,and the impact of speed variations on task ...In current research on task offloading and resource scheduling in vehicular networks,vehicles are commonly assumed to maintain constant speed or relatively stationary states,and the impact of speed variations on task offloading is often overlooked.It is frequently assumed that vehicles can be accurately modeled during actual motion processes.However,in vehicular dynamic environments,both the tasks generated by the vehicles and the vehicles’surroundings are constantly changing,making it difficult to achieve real-time modeling for actual dynamic vehicular network scenarios.Taking into account the actual dynamic vehicular scenarios,this paper considers the real-time non-uniform movement of vehicles and proposes a vehicular task dynamic offloading and scheduling algorithm for single-task multi-vehicle vehicular network scenarios,attempting to solve the dynamic decision-making problem in task offloading process.The optimization objective is to minimize the average task completion time,which is formulated as a multi-constrained non-linear programming problem.Due to the mobility of vehicles,a constraint model is applied in the decision-making process to dynamically determine whether the communication range is sufficient for task offloading and transmission.Finally,the proposed vehicular task dynamic offloading and scheduling algorithm based on muti-agent deep deterministic policy gradient(MADDPG)is applied to solve the optimal solution of the optimization problem.Simulation results show that the algorithm proposed in this paper is able to achieve lower latency task computation offloading.Meanwhile,the average task completion time of the proposed algorithm in this paper can be improved by 7.6%compared to the performance of the MADDPG scheme and 51.1%compared to the performance of deep deterministic policy gradient(DDPG).展开更多
In recent years, target tracking has been considered one of the most important applications of wireless sensornetwork (WSN). Optimizing target tracking performance and prolonging network lifetime are two equally criti...In recent years, target tracking has been considered one of the most important applications of wireless sensornetwork (WSN). Optimizing target tracking performance and prolonging network lifetime are two equally criticalobjectives in this scenario. The existing mechanisms still have weaknesses in balancing the two demands. Theproposed heuristic multi-node collaborative scheduling mechanism (HMNCS) comprises cluster head (CH)election, pre-selection, and task set selectionmechanisms, where the latter two kinds of selections forma two-layerselection mechanism. The CH election innovatively introduces the movement trend of the target and establishesa scoring mechanism to determine the optimal CH, which can delay the CH rotation and thus reduce energyconsumption. The pre-selection mechanism adaptively filters out suitable nodes as the candidate task set to applyfor tracking tasks, which can reduce the application consumption and the overhead of the following task setselection. Finally, the task node selection is mathematically transformed into an optimization problem and thegenetic algorithm is adopted to form a final task set in the task set selection mechanism. Simulation results showthat HMNCS outperforms other compared mechanisms in the tracking accuracy and the network lifetime.展开更多
As the current global environment is deteriorating,distributed renewable energy is gradually becoming an important member of the energy internet.Blockchain,as a decentralized distributed ledger with decentralization,t...As the current global environment is deteriorating,distributed renewable energy is gradually becoming an important member of the energy internet.Blockchain,as a decentralized distributed ledger with decentralization,traceability and tamper-proof features,is an importantway to achieve efficient consumption andmulti-party supply of new energy.In this article,we establish a blockchain-based mathematical model of multiple microgrids and microgrid aggregators’revenue,consider the degree of microgrid users’preference for electricity thus increasing users’reliance on the blockchainmarket,and apply the one-master-multiple-slave Stackelberg game theory to solve the energy dispatching strategy when each market entity pursues the maximum revenue.The simulation results show that the blockchain-based dynamic game of the multi-microgrid market can effectively increase the revenue of both microgrids and aggregators and improve the utilization of renewable energy.展开更多
Cloud service providers generally co-locate online services and batch jobs onto the same computer cluster,where the resources can be pooled in order to maximize data center resource utilization.Due to resource competi...Cloud service providers generally co-locate online services and batch jobs onto the same computer cluster,where the resources can be pooled in order to maximize data center resource utilization.Due to resource competition between batch jobs and online services,co-location frequently impairs the performance of online services.This study presents a quality of service(QoS)prediction-based schedulingmodel(QPSM)for co-locatedworkloads.The performance prediction of QPSM consists of two parts:the prediction of an online service’s QoS anomaly based on XGBoost and the prediction of the completion time of an offline batch job based on randomforest.On-line service QoS anomaly prediction is used to evaluate the influence of batch jobmix on on-line service performance,and batch job completion time prediction is utilized to reduce the total waiting time of batch jobs.When the same number of batch jobs are scheduled in experiments using typical test sets such as CloudSuite,the scheduling time required by QPSM is reduced by about 6 h on average compared with the first-come,first-served strategy and by about 11 h compared with the random scheduling strategy.Compared with the non-co-located situation,QPSM can improve CPU resource utilization by 12.15% and memory resource utilization by 5.7% on average.Experiments show that the QPSM scheduling strategy proposed in this study can effectively guarantee the quality of online services and further improve cluster resource utilization.展开更多
As cloud quantum computing gains broader acceptance,a growing quantity of researchers are directing their focus towards this domain.Nevertheless,the rapid surge in demand for cloud-based quantum computing resources ha...As cloud quantum computing gains broader acceptance,a growing quantity of researchers are directing their focus towards this domain.Nevertheless,the rapid surge in demand for cloud-based quantum computing resources has led to a scarcity,which in turn hampers users from achieving optimal satisfaction.Therefore,cloud quantum computing service providers require a unified analysis and scheduling framework for their quantumresources and user jobs to meet the ever-growing usage demands.This paper introduces a new multi-programming scheduling framework for quantum computing in a cloud environment.The framework addresses the issue of limited quantum computing resources in cloud environments and ensures a satisfactory user experience.It introduces three innovative designs:1)Our framework automatically allocates tasks to different quantum backends while ensuring fairness among users by considering both the cloud-based quantum resources and the user-submitted tasks.2)Multi-programming mechanism is employed across different quantum backends to enhance the overall throughput of the quantum cloud.In comparison to conventional task schedulers,our proposed framework achieves a throughput improvement of more than two-fold in the quantum cloud.3)The framework can balance fidelity and user waiting time by adaptively adjusting scheduling parameters.展开更多
The growing development of the Internet of Things(IoT)is accelerating the emergence and growth of new IoT services and applications,which will result in massive amounts of data being generated,transmitted and pro-cess...The growing development of the Internet of Things(IoT)is accelerating the emergence and growth of new IoT services and applications,which will result in massive amounts of data being generated,transmitted and pro-cessed in wireless communication networks.Mobile Edge Computing(MEC)is a desired paradigm to timely process the data from IoT for value maximization.In MEC,a number of computing-capable devices are deployed at the network edge near data sources to support edge computing,such that the long network transmission delay in cloud computing paradigm could be avoided.Since an edge device might not always have sufficient resources to process the massive amount of data,computation offloading is significantly important considering the coop-eration among edge devices.However,the dynamic traffic characteristics and heterogeneous computing capa-bilities of edge devices challenge the offloading.In addition,different scheduling schemes might provide different computation delays to the offloaded tasks.Thus,offloading in mobile nodes and scheduling in the MEC server are coupled to determine service delay.This paper seeks to guarantee low delay for computation intensive applica-tions by jointly optimizing the offloading and scheduling in such an MEC system.We propose a Delay-Greedy Computation Offloading(DGCO)algorithm to make offloading decisions for new tasks in distributed computing-enabled mobile devices.A Reinforcement Learning-based Parallel Scheduling(RLPS)algorithm is further designed to schedule offloaded tasks in the multi-core MEC server.With an offloading delay broadcast mechanism,the DGCO and RLPS cooperate to achieve the goal of delay-guarantee-ratio maximization.Finally,the simulation results show that our proposal can bound the end-to-end delay of various tasks.Even under slightly heavy task load,the delay-guarantee-ratio given by DGCO-RLPS can still approximate 95%,while that given by benchmarked algorithms is reduced to intolerable value.The simulation results are demonstrated the effective-ness of DGCO-RLPS for delay guarantee in MEC.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
Improving the cooperative scheduling efficiency of equipment is the key for automated container terminals to copewith the development trend of large-scale ships. In order to improve the solution efficiency of the exis...Improving the cooperative scheduling efficiency of equipment is the key for automated container terminals to copewith the development trend of large-scale ships. In order to improve the solution efficiency of the existing spacetimenetwork (STN) model for the cooperative scheduling problem of yard cranes (YCs) and automated guidedvehicles (AGVs) and extend its application scenarios, two improved STN models are proposed. The flow balanceconstraints in the original model are decomposed, and the trajectory constraints of YCs and AGVs are added toacquire the model STN_A. The coupling constraint in STN_A is updated, and buffer constraints are added toSTN_A so that themodel STN_B is built.As the size of the problem increases, the solution speed of CPLEX becomesthe bottleneck. So a heuristic method containing three groups of heuristic rules is designed to obtain a near-optimalsolution quickly. Experimental results showthat the computation time of STN_A is shortened by 49.47% on averageand the gap is reduced by 1.69% on average compared with the original model. The gap between the solution ofthe heuristic rules and the solution of CPLEX is less than 3.50%, and the solution time of the heuristic rules is onaverage 99.85% less than the solution time of CPLEX. Compared with STN_A, the computation time for solvingSTN_B increases by 58.93% on average.展开更多
基金The Natural Science Foundation of Jiangsu Province(NoBK2005408)
文摘To fulfill the requirements for hybrid real-time system scheduling, a long-release-interval-first （LRIF） real-time scheduling algorithm is proposed. The algorithm adopts both the fixed priority and the dynamic priority to assign priorities for tasks. By assigning higher priorities to the aperiodic soft real-time jobs with longer release intervals, it guarantees the executions for periodic hard real-time tasks and further probabilistically guarantees the executions for aperiodic soft real-time tasks. The schedulability test approach for the LRIF algorithm is presented. The implementation issues of the LRIF algorithm are also discussed. Simulation result shows that LRIF obtains better schedulable performance than the maximum urgency first （MUF） algorithm, the earliest deadline first （EDF） algorithm and EDF for hybrid tasks. LRIF has great capability to schedule both periodic hard real-time and aperiodic soft real-time tasks.
基金the National Natural Science Foundation of China (No. 60533040)the Hi-Tech Research and Development Program (863) of China (Nos. 2007AA010304 and 2007AA01Z129)the Key Scientific and Technological Project of Hangzhou Tech-nology Bureau, China (No. 20062412B01)
文摘In hard real-time systems, schedulability analysis is not only one of the important means of guaranteeing the timelines of embedded software but also one of the fundamental theories of applying other new techniques, such as energy savings and fault tolerance. However, most of the existing schedulability analysis methods assume that schedulers use preemptive scheduling or non-preemptive scheduling. In this paper, we present a schedulability analysis method, i.e., the worst-case hybrid scheduling (WCHS) algorithm, which considers the influence of release jitters of transactions and extends schedulability analysis theory to timing analysis of linear transactions under fixed priority hybrid scheduling. To the best of our knowledge, this method is the first one on timing analysis of linear transactions under hybrid scheduling. An example is employed to demonstrate the use of this method. Experiments show that this method has lower computational complexity while keeping correctness, and that hybrid scheduling has little influence on the average worst-case response time (WCRT), but a negative impact on the schedulability of systems.
基金supported by the National Science Foundation of China under Grant 62271062 and 62071063by the Zhijiang Laboratory Open Project Fund 2020LCOAB01。
文摘With the rapid development of cloud computing,edge computing,and smart devices,computing power resources indicate a trend of ubiquitous deployment.The traditional network architecture cannot efficiently leverage these distributed computing power resources due to computing power island effect.To overcome these problems and improve network efficiency,a new network computing paradigm is proposed,i.e.,Computing Power Network(CPN).Computing power network can connect ubiquitous and heterogenous computing power resources through networking to realize computing power scheduling flexibly.In this survey,we make an exhaustive review on the state-of-the-art research efforts on computing power network.We first give an overview of computing power network,including definition,architecture,and advantages.Next,a comprehensive elaboration of issues on computing power modeling,information awareness and announcement,resource allocation,network forwarding,computing power transaction platform and resource orchestration platform is presented.The computing power network testbed is built and evaluated.The applications and use cases in computing power network are discussed.Then,the key enabling technologies for computing power network are introduced.Finally,open challenges and future research directions are presented as well.
文摘Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay can hamper the performance of IoT-enabled cloud platforms.However,efficient task scheduling can lower the cloud infrastructure’s energy consumption,thus maximizing the service provider’s revenue by decreasing user job processing times.The proposed Modified Chimp-Whale Optimization Algorithm called Modified Chimp-Whale Optimization Algorithm(MCWOA),combines elements of the Chimp Optimization Algorithm(COA)and the Whale Optimization Algorithm(WOA).To enhance MCWOA’s identification precision,the Sobol sequence is used in the population initialization phase,ensuring an even distribution of the population across the solution space.Moreover,the traditional MCWOA’s local search capabilities are augmented by incorporating the whale optimization algorithm’s bubble-net hunting and random search mechanisms into MCWOA’s position-updating process.This study demonstrates the effectiveness of the proposed approach using a two-story rigid frame and a simply supported beam model.Simulated outcomes reveal that the new method outperforms the original MCWOA,especially in multi-damage detection scenarios.MCWOA excels in avoiding false positives and enhancing computational speed,making it an optimal choice for structural damage detection.The efficiency of the proposed MCWOA is assessed against metrics such as energy usage,computational expense,task duration,and delay.The simulated data indicates that the new MCWOA outpaces other methods across all metrics.The study also references the Whale Optimization Algorithm(WOA),Chimp Algorithm(CA),Ant Lion Optimizer(ALO),Genetic Algorithm(GA)and Grey Wolf Optimizer(GWO).
基金supported by the National Natural Science Foundation of China(62172033).
文摘In recent years,the global surge of High-speed Railway(HSR)revolutionized ground transportation,providing secure,comfortable,and punctual services.The next-gen HSR,fueled by emerging services like video surveillance,emergency communication,and real-time scheduling,demands advanced capabilities in real-time perception,automated driving,and digitized services,which accelerate the integration and application of Artificial Intelligence(AI)in the HSR system.This paper first provides a brief overview of AI,covering its origin,evolution,and breakthrough applications.A comprehensive review is then given regarding the most advanced AI technologies and applications in three macro application domains of the HSR system:mechanical manufacturing and electrical control,communication and signal control,and transportation management.The literature is categorized and compared across nine application directions labeled as intelligent manufacturing of trains and key components,forecast of railroad maintenance,optimization of energy consumption in railroads and trains,communication security,communication dependability,channel modeling and estimation,passenger scheduling,traffic flow forecasting,high-speed railway smart platform.Finally,challenges associated with the application of AI are discussed,offering insights for future research directions.
基金the National Natural Science Foundation of China(Nos.61174159 and 61101184)
文摘With notably few exceptions, the existing satellite mission operations cannot provide the ability of schedulability prediction, including the latest satellite planning service （SPS） standard–Sensor Planning Service Interface Standard 2.0 Earth Observation Satellite Tasking Extension （EO SPS） approved by Open Geospatial Consortium （OGC）. The requestor can do nothing but waiting for the results of time consuming batch scheduling. It is often too late to adjust the request when receiving scheduling failures. A supervised learning algorithm based on robust decision tree and bagging support vector machine （Bagging SVM） is proposed to solve the problem above. The Bagging SVM is applied to improve the accuracy of classification and robust decision tree is utilized to reduce the error mean and error variation. The simulations and analysis show that a prediction action can be accomplished in near real-time with high accuracy. This means the decision makers can maximize the probability of successful scheduling through changing request parameters or take action to accommodate the scheduling failures in time.
基金co-supported by the National Natural Science Foundation of China(No:61073012)the Aeronautical Science Foundation of China(No:20111951015)the Fundamental Research Funds for the Central Universities of China(No:YWF-14-DZXY018)
文摘Safety-critical avionics systems which become more complex and tend to integrate multiple functionalities with different levels of criticality for better cost and power efficiency are subject to certifications at various levels of rigorousness. In order to simultaneously guarantee temporal constraints at all different levels of assurance mandated by different criticalities, novel scheduling techniques are in need. In this paper, a mixed-criticality sporadic task model with multiple virtual deadlines is built and a certification-cognizant dynamic scheduling approach referred as earliest virtual-deadline first with mixed-criticality（EVDF-MC） is considered, which exploits different relative deadlines of tasks in different criticality modes. As for the corresponding schedulability analysis problem, a sufficient and efficient schedulability test is proposed on the basis of demand-bound functions derived in the mixed-criticality scenario. In addition, a modified simulated annealing（MSA）-based heuristic approach is established for virtual deadlines assignment. Experiments performing simulations with randomly generated tasks indicate that the proposed approach is computationally efficient and competes well against the existing approaches.
基金supported by the National Natural Science Foundation of China(51975482)the China Scholarship Council.
文摘This paper addresses a multi-agent scheduling problem with uniform parallel machines owned by a resource agent and competing jobs with dynamic arrival times that belong to different consumer agents.All agents are self-interested and rational with the aim of maximizing their own objectives,resulting in intense resource competition among consumer agents and strategic behaviors of unwillingness to disclose private information.Within the context,a centralized scheduling approach is unfeasible,and a decentralized approach is considered to deal with the targeted problem.This study aims to generate a stable and collaborative solution with high social welfare while simultaneously accommodating consumer agents’preferences under incomplete information.For this purpose,a dynamic iterative auction-based approach based on a decentralized decision-making procedure is developed.In the proposed approach,a dynamic auction procedure is established for dynamic jobs participating in a realtime auction,and a straightforward and easy-to-implement bidding strategy without price is presented to reduce the complexity of bid determination.In addition,an adaptive Hungarian algorithm is applied to solve the winner determination problem efficiently.A theoretical analysis is conducted to prove that the proposed approach is individually rational and that the myopic bidding strategy is a weakly dominant strategy for consumer agents submitting bids.Extensive computational experiments demonstrate that the developed approach achieves high-quality solutions and exhibits considerable stability on largescale problems with numerous consumer agents and jobs.A further multi-agent scheduling problem considering multiple resource agents will be studied in future work.
基金supported by the National Key R&D Program of China(Grant No.2017YFC0805309)Natural Science Foundation of Fujian Province(Grant No.2021J01820)Department of Education of Fujian Province Project(Grant Nos.JAT190294 and JAT210230).
文摘Considering the uncertainty of the speed of horizontal transportation equipment,a cooperative scheduling model of multiple equipment resources in the automated container terminal was constructed to minimize the completion time,thus improving the loading and unloading efficiencies of automated container terminals.The proposed model integrated the two loading and unloading processes of“double-trolley quay crane+AGV+ARMG”and“single-trolley quay crane+container truck+ARMG”and then designed the simulated annealing particle swarm algorithm to solve the model.By comparing the results of the particle swarm algorithm and genetic algorithm,the algorithm designed in this paper could effectively improve the global and local space search capability of finding the optimal solution.Furthermore,the results showed that the proposed method of collaborative scheduling of multiple equipment resources in automated terminals considering hybrid processes effectively improved the loading and unloading efficiencies of automated container terminals.The findings of this study provide a reference for the improvement of loading and unloading processes as well as coordinated scheduling in automated terminals.
基金supported by the Innovation Scientists and Technicians Troop Construction Projects of Henan Province(224000510002)。
文摘Time-Sensitive Network(TSN)with deterministic transmission capability is increasingly used in many emerging fields.It mainly guarantees the Quality of Service(QoS)of applications with strict requirements on time and security.One of the core features of TSN is traffic scheduling with bounded low delay in the network.However,traffic scheduling schemes in TSN are usually synthesized offline and lack dynamism.To implement incremental scheduling of newly arrived traffic in TSN,we propose a Dynamic Response Incremental Scheduling(DR-IS)method for time-sensitive traffic and deploy it on a software-defined time-sensitive network architecture.Under the premise of meeting the traffic scheduling requirements,we adopt two modes,traffic shift and traffic exchange,to dynamically adjust the time slot injection position of the traffic in the original scheme,and determine the sending offset time of the new timesensitive traffic to minimize the global traffic transmission jitter.The evaluation results show that DRIS method can effectively control the large increase of traffic transmission jitter in incremental scheduling without affecting the transmission delay,thus realizing the dynamic incremental scheduling of time-sensitive traffic in TSN.
基金supported by the Natural Science Foundation of Anhui Province(Grant Number 2208085MG181)the Science Research Project of Higher Education Institutions in Anhui Province,Philosophy and Social Sciences(Grant Number 2023AH051063)the Open Fund of Key Laboratory of Anhui Higher Education Institutes(Grant Number CS2021-ZD01).
文摘The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.
基金the supports from National Natural Science Foundation of China(61988101,62073142,22178103)National Natural Science Fund for Distinguished Young Scholars(61925305)International(Regional)Cooperation and Exchange Project(61720106008)。
文摘Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.
文摘In current research on task offloading and resource scheduling in vehicular networks,vehicles are commonly assumed to maintain constant speed or relatively stationary states,and the impact of speed variations on task offloading is often overlooked.It is frequently assumed that vehicles can be accurately modeled during actual motion processes.However,in vehicular dynamic environments,both the tasks generated by the vehicles and the vehicles’surroundings are constantly changing,making it difficult to achieve real-time modeling for actual dynamic vehicular network scenarios.Taking into account the actual dynamic vehicular scenarios,this paper considers the real-time non-uniform movement of vehicles and proposes a vehicular task dynamic offloading and scheduling algorithm for single-task multi-vehicle vehicular network scenarios,attempting to solve the dynamic decision-making problem in task offloading process.The optimization objective is to minimize the average task completion time,which is formulated as a multi-constrained non-linear programming problem.Due to the mobility of vehicles,a constraint model is applied in the decision-making process to dynamically determine whether the communication range is sufficient for task offloading and transmission.Finally,the proposed vehicular task dynamic offloading and scheduling algorithm based on muti-agent deep deterministic policy gradient(MADDPG)is applied to solve the optimal solution of the optimization problem.Simulation results show that the algorithm proposed in this paper is able to achieve lower latency task computation offloading.Meanwhile,the average task completion time of the proposed algorithm in this paper can be improved by 7.6%compared to the performance of the MADDPG scheme and 51.1%compared to the performance of deep deterministic policy gradient(DDPG).
基金the Project Program of Science and Technology on Micro-System Laboratory,No.6142804220101.
文摘In recent years, target tracking has been considered one of the most important applications of wireless sensornetwork (WSN). Optimizing target tracking performance and prolonging network lifetime are two equally criticalobjectives in this scenario. The existing mechanisms still have weaknesses in balancing the two demands. Theproposed heuristic multi-node collaborative scheduling mechanism (HMNCS) comprises cluster head (CH)election, pre-selection, and task set selectionmechanisms, where the latter two kinds of selections forma two-layerselection mechanism. The CH election innovatively introduces the movement trend of the target and establishesa scoring mechanism to determine the optimal CH, which can delay the CH rotation and thus reduce energyconsumption. The pre-selection mechanism adaptively filters out suitable nodes as the candidate task set to applyfor tracking tasks, which can reduce the application consumption and the overhead of the following task setselection. Finally, the task node selection is mathematically transformed into an optimization problem and thegenetic algorithm is adopted to form a final task set in the task set selection mechanism. Simulation results showthat HMNCS outperforms other compared mechanisms in the tracking accuracy and the network lifetime.
基金This research was funded by the NSFC under Grant No.61803279in part by the Qing Lan Project of Jiangsu,in part by the China Postdoctoral Science Foundation under Grant Nos.2020M671596 and 2021M692369+3 种基金in part by the Suzhou Science and Technology Development Plan Project(Key Industry Technology Innovation)under Grant No.SYG202114in part by the Open Project Funding from Anhui Province Key Laboratory of Intelligent Building and Building Energy Saving,Anhui Jianzhu University,under Grant No.IBES2021KF08in part by the Postgraduate Research&Practice Innovation Program of Jiangsu Province under Grant No.KYCX23_3320in part by the Postgraduate Research&Practice Innovation Program of Jiangsu Province under Grant No.SJCX22_1585.
文摘As the current global environment is deteriorating,distributed renewable energy is gradually becoming an important member of the energy internet.Blockchain,as a decentralized distributed ledger with decentralization,traceability and tamper-proof features,is an importantway to achieve efficient consumption andmulti-party supply of new energy.In this article,we establish a blockchain-based mathematical model of multiple microgrids and microgrid aggregators’revenue,consider the degree of microgrid users’preference for electricity thus increasing users’reliance on the blockchainmarket,and apply the one-master-multiple-slave Stackelberg game theory to solve the energy dispatching strategy when each market entity pursues the maximum revenue.The simulation results show that the blockchain-based dynamic game of the multi-microgrid market can effectively increase the revenue of both microgrids and aggregators and improve the utilization of renewable energy.
基金supported by the NationalNatural Science Foundation of China(No.61972118)the Key R&D Program of Zhejiang Province(No.2023C01028).
文摘Cloud service providers generally co-locate online services and batch jobs onto the same computer cluster,where the resources can be pooled in order to maximize data center resource utilization.Due to resource competition between batch jobs and online services,co-location frequently impairs the performance of online services.This study presents a quality of service(QoS)prediction-based schedulingmodel(QPSM)for co-locatedworkloads.The performance prediction of QPSM consists of two parts:the prediction of an online service’s QoS anomaly based on XGBoost and the prediction of the completion time of an offline batch job based on randomforest.On-line service QoS anomaly prediction is used to evaluate the influence of batch jobmix on on-line service performance,and batch job completion time prediction is utilized to reduce the total waiting time of batch jobs.When the same number of batch jobs are scheduled in experiments using typical test sets such as CloudSuite,the scheduling time required by QPSM is reduced by about 6 h on average compared with the first-come,first-served strategy and by about 11 h compared with the random scheduling strategy.Compared with the non-co-located situation,QPSM can improve CPU resource utilization by 12.15% and memory resource utilization by 5.7% on average.Experiments show that the QPSM scheduling strategy proposed in this study can effectively guarantee the quality of online services and further improve cluster resource utilization.
文摘As cloud quantum computing gains broader acceptance,a growing quantity of researchers are directing their focus towards this domain.Nevertheless,the rapid surge in demand for cloud-based quantum computing resources has led to a scarcity,which in turn hampers users from achieving optimal satisfaction.Therefore,cloud quantum computing service providers require a unified analysis and scheduling framework for their quantumresources and user jobs to meet the ever-growing usage demands.This paper introduces a new multi-programming scheduling framework for quantum computing in a cloud environment.The framework addresses the issue of limited quantum computing resources in cloud environments and ensures a satisfactory user experience.It introduces three innovative designs:1)Our framework automatically allocates tasks to different quantum backends while ensuring fairness among users by considering both the cloud-based quantum resources and the user-submitted tasks.2)Multi-programming mechanism is employed across different quantum backends to enhance the overall throughput of the quantum cloud.In comparison to conventional task schedulers,our proposed framework achieves a throughput improvement of more than two-fold in the quantum cloud.3)The framework can balance fidelity and user waiting time by adaptively adjusting scheduling parameters.
基金supported in part by the National Natural Science Foundation of China under Grant 61901128,62273109the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(21KJB510032).
文摘The growing development of the Internet of Things(IoT)is accelerating the emergence and growth of new IoT services and applications,which will result in massive amounts of data being generated,transmitted and pro-cessed in wireless communication networks.Mobile Edge Computing(MEC)is a desired paradigm to timely process the data from IoT for value maximization.In MEC,a number of computing-capable devices are deployed at the network edge near data sources to support edge computing,such that the long network transmission delay in cloud computing paradigm could be avoided.Since an edge device might not always have sufficient resources to process the massive amount of data,computation offloading is significantly important considering the coop-eration among edge devices.However,the dynamic traffic characteristics and heterogeneous computing capa-bilities of edge devices challenge the offloading.In addition,different scheduling schemes might provide different computation delays to the offloaded tasks.Thus,offloading in mobile nodes and scheduling in the MEC server are coupled to determine service delay.This paper seeks to guarantee low delay for computation intensive applica-tions by jointly optimizing the offloading and scheduling in such an MEC system.We propose a Delay-Greedy Computation Offloading(DGCO)algorithm to make offloading decisions for new tasks in distributed computing-enabled mobile devices.A Reinforcement Learning-based Parallel Scheduling(RLPS)algorithm is further designed to schedule offloaded tasks in the multi-core MEC server.With an offloading delay broadcast mechanism,the DGCO and RLPS cooperate to achieve the goal of delay-guarantee-ratio maximization.Finally,the simulation results show that our proposal can bound the end-to-end delay of various tasks.Even under slightly heavy task load,the delay-guarantee-ratio given by DGCO-RLPS can still approximate 95%,while that given by benchmarked algorithms is reduced to intolerable value.The simulation results are demonstrated the effective-ness of DGCO-RLPS for delay guarantee in MEC.
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National Natural Science Foundation of China(62073212).
文摘Improving the cooperative scheduling efficiency of equipment is the key for automated container terminals to copewith the development trend of large-scale ships. In order to improve the solution efficiency of the existing spacetimenetwork (STN) model for the cooperative scheduling problem of yard cranes (YCs) and automated guidedvehicles (AGVs) and extend its application scenarios, two improved STN models are proposed. The flow balanceconstraints in the original model are decomposed, and the trajectory constraints of YCs and AGVs are added toacquire the model STN_A. The coupling constraint in STN_A is updated, and buffer constraints are added toSTN_A so that themodel STN_B is built.As the size of the problem increases, the solution speed of CPLEX becomesthe bottleneck. So a heuristic method containing three groups of heuristic rules is designed to obtain a near-optimalsolution quickly. Experimental results showthat the computation time of STN_A is shortened by 49.47% on averageand the gap is reduced by 1.69% on average compared with the original model. The gap between the solution ofthe heuristic rules and the solution of CPLEX is less than 3.50%, and the solution time of the heuristic rules is onaverage 99.85% less than the solution time of CPLEX. Compared with STN_A, the computation time for solvingSTN_B increases by 58.93% on average.
