A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespa...A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespan and an LPT-LS algorithm is proposed.Non-resumable jobs are first scheduled in a machine by the longest processing time（LPT） rule,and then resumable jobs are scheduled by the list scheduling（LS） rule.And the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the resumable jobs（denoted as S2） are discussed.When S2 is longer than the spare time of the machine after the non-resumable jobs are assigned by the LPT rule,it is equal to 1.When S2 falls in between the spare time of the machine by the LPT rule and the optimal schedule rule,it is less than 2.When S2 is less than the spare time of the machine by the optimal schedule rule,it is less than 2.Finally,numerical examples are presented for verification.展开更多
In this paper we consider a single-machine scheduling model with deteriorating jobs and simultaneous learning, and we introduce polynomial solutions for single machine makespan minimization, total flow times minimizat...In this paper we consider a single-machine scheduling model with deteriorating jobs and simultaneous learning, and we introduce polynomial solutions for single machine makespan minimization, total flow times minimization and maximum lateness minimization corresponding to the first and second special cases of our model under some agreeable conditions. However, corresponding to the third special case of our model, we show that the optimal schedules may be different from those of the classical version for the above objective functions.展开更多
In a CPM network, the longest path problem is one of the most important subjects. According to the intrinsic principle of CPM network, the length of the paths between arbitrary two nodes is presented. Furthermore, the...In a CPM network, the longest path problem is one of the most important subjects. According to the intrinsic principle of CPM network, the length of the paths between arbitrary two nodes is presented. Furthermore, the length of the longest path from start node to arbitrary node and from arbitrary node to end node is proposed. In view of a scheduling problem of two activities with float in the CPM scheduling, we put forward Barycenter Theory and prove this theory based on the algorithm of the length of the longest path. By this theory, we know which activity should be done firstly. At last, we show our theory by an example.展开更多
Motivated by industrial applications we study a single-machine scheduling problem in which all the jobs are mutu- ally independent and available at time zero.The machine processes the jobs sequentially and it is not i...Motivated by industrial applications we study a single-machine scheduling problem in which all the jobs are mutu- ally independent and available at time zero.The machine processes the jobs sequentially and it is not idle if there is any job to be pro- cessed.The operation of each job cannot be interrupted.The machine cannot process more than one job at a time.A setup time is needed if the machine switches from one type of job to another.The objective is to find an optimal schedule with the minimal total jobs’completion time.While the sum of jobs’processing time is always a constant,the objective is to minimize the sum of setup times.Ant colony optimization(ACO)is a meta-heuristic that has recently been applied to scheduling problem.In this paper we propose an improved ACO-Branching Ant Colony with Dynamic Perturbation(DPBAC)algorithm for the single-machine schedul- ing problem.DPBAC improves traditional ACO in following aspects:introducing Branching Method to choose starting points;im- proving state transition rules;introducing Mutation Method to shorten tours;improving pheromone updating rules and introduc- ing Conditional Dynamic Perturbation Strategy.Computational results show that DPBAC algorithm is superior to the traditional ACO algorithm.展开更多
In a local search algorithm,one of its most important features is the definition of its neighborhood which is crucial to the algorithm's performance.In this paper,we present an analysis of neighborhood combination...In a local search algorithm,one of its most important features is the definition of its neighborhood which is crucial to the algorithm's performance.In this paper,we present an analysis of neighborhood combination search for solv-ing the single-machine scheduling problem with sequence-dependent setup time with the objective of minimizing total weighted tardiness(SMSWT).First,We propose a new neighborhood structure named Block Swap(B1)which can be con-sidered as an extension of the previously widely used Block Move(B2)neighborhood,and a fast incremental evaluation technique to enhance its evaluation efficiency.Second,based on the Block Swap and Block Move neighborhoods,we present two kinds of neighborhood structures:neighborhood union(denoted by B1UB2)and token-ring search(denoted by B1→B2),both of which are combinations of B1 and B2.Third,we incorporate the neighborhood union and token-ring search into two representative metaheuristic algorithms:the Iterated Local Search Algorithm(ILSnew)and the Hybrid Evolutionary Algorithm(HEA_(new))to investigate the performance of the neighborhood union and token-ring search.Exten-sive experiments show the competitiveness of the token-ring search combination mechanism of the two neighborhoods.Tested on the 120 public benchmark instances,our HEA_(new)has a highly competitive performance in solution quality and computational time compared with both the exact algorithms and recent metaheuristics.We have also tested the HEA,new algorithm with the selected neighborhood combination search to deal with the 64 public benchmark instances of the single-machine scheduling problem with sequence-dependent setup time.HEAnew is able to match the optimal or the best known results for all the 64 instances.In particular,the computational time for reaching the best well-known results for five chal-lenging instances is reduced by at least 61.25%.展开更多
In this paper,we consider the single-machine scheduling with step-deteriorating jobs and rejection.Each job is either rejected by paying a rejection penalty,or accepted and processed on the single machine,and the actu...In this paper,we consider the single-machine scheduling with step-deteriorating jobs and rejection.Each job is either rejected by paying a rejection penalty,or accepted and processed on the single machine,and the actual processing time of each accepted job is a step function of its starting time and the common deteriorating date.The objective is to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs.For the case of common deteriorating penalty,we first show that the problem is NP-hard in the ordinary sense.Then we present two pseudo-polynomial algorithms and a 2-approximation algorithm.Furthermore,we propose a fully polynomial time approximation scheme.For the case of common normal processing time,we present two pseudo-polynomial time algorithms,a 2-approximation algorithm and a fully polynomial time approximation scheme.展开更多
Additive manufacturing(AM)has attracted significant attention in recent years based on its wide range of applications and growing demand.AM offers the advantages of production flexibility and design freedom.In this st...Additive manufacturing(AM)has attracted significant attention in recent years based on its wide range of applications and growing demand.AM offers the advantages of production flexibility and design freedom.In this study,we considered a practical variant of the batch-processing-machine(BPM)scheduling problem that arises in AM industries,where an AM machine can process multiple parts simultaneously,as long as the twodimensional rectangular packing constraint is not violated.Based on the set-partitioning formulation of our mixed-integer programming(MIP)model,a branch-and-price(B&P)algorithm was developed by embedding a column-generation technique into a branchand-bound framework.Additionally,a novel labelling algorithm was developed to accelerate the column-generation process.Ours is the first study to provide a B&P algorithm to solve the BPM scheduling problem in the AM industry.We tested the performance of our algorithm using a modern MIP solver(Gurobi)and real data from a 3D printing factory.The results demonstrate that for most instances tested,our algorithm produces results similar or identical to those of Gurobi with reasonable computation time and outperforms Gurobi in terms of solution quality and running time on some large instances.展开更多
Safe and efficient sortie scheduling on the confined flight deck is crucial for maintaining high combat effectiveness of the aircraft carrier.The primary difficulty exactly lies in the spatiotemporal coordination,i.e....Safe and efficient sortie scheduling on the confined flight deck is crucial for maintaining high combat effectiveness of the aircraft carrier.The primary difficulty exactly lies in the spatiotemporal coordination,i.e.,allocation of limited supporting resources and collision-avoidance between heterogeneous dispatch entities.In this paper,the problem is investigated in the perspective of hybrid flow-shop scheduling problem by synthesizing the precedence,space and resource constraints.Specifically,eight processing procedures are abstracted,where tractors,preparing spots,catapults,and launching are virtualized as machines.By analyzing the constraints in sortie scheduling,a mixed-integer planning model is constructed.In particular,the constraint on preparing spot occupancy is improved to further enhance the sortie efficiency.The basic trajectory library for each dispatch entity is generated and a delayed strategy is integrated to address the collision-avoidance issue.To efficiently solve the formulated HFSP,which is essentially a combinatorial problem with tightly coupled constraints,a chaos-initialized genetic algorithm is developed.The solution framework is validated by the simulation environment referring to the Fort-class carrier,exhibiting higher sortie efficiency when compared to existing strategies.And animation of the simulation results is available at www.bilibili.com/video/BV14t421A7Tt/.The study presents a promising supporting technique for autonomous flight deck operation in the foreseeable future,and can be easily extended to other supporting scenarios,e.g.,ammunition delivery and aircraft maintenance.展开更多
Ship outfitting is a key process in shipbuilding.Efficient and high-quality ship outfitting is a top priority for modern shipyards.These activities are conducted at different stations of shipyards.The outfitting plan ...Ship outfitting is a key process in shipbuilding.Efficient and high-quality ship outfitting is a top priority for modern shipyards.These activities are conducted at different stations of shipyards.The outfitting plan is one of the crucial issues in shipbuilding.In this paper,production scheduling and material ordering with endogenous uncertainty of the outfitting process are investigated.The uncertain factors in outfitting equipment production are usually decision-related,which leads to difficulties in addressing uncertainties in the outfitting production workshops before production is conducted according to plan.This uncertainty is regarded as endogenous uncertainty and can be treated as non-anticipativity constraints in the model.To address this problem,a stochastic two-stage programming model with endogenous uncertainty is established to optimize the outfitting job scheduling and raw material ordering process.A practical case of the shipyard of China Merchants Heavy Industry Co.,Ltd.is used to evaluate the performance of the proposed method.Satisfactory results are achieved at the lowest expected total cost as the complete kit rate of outfitting equipment is improved and emergency replenishment is reduced.展开更多
Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power sta...Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.展开更多
Thedeployment of the Internet of Things(IoT)with smart sensors has facilitated the emergence of fog computing as an important technology for delivering services to smart environments such as campuses,smart cities,and ...Thedeployment of the Internet of Things(IoT)with smart sensors has facilitated the emergence of fog computing as an important technology for delivering services to smart environments such as campuses,smart cities,and smart transportation systems.Fog computing tackles a range of challenges,including processing,storage,bandwidth,latency,and reliability,by locally distributing secure information through end nodes.Consisting of endpoints,fog nodes,and back-end cloud infrastructure,it provides advanced capabilities beyond traditional cloud computing.In smart environments,particularly within smart city transportation systems,the abundance of devices and nodes poses significant challenges related to power consumption and system reliability.To address the challenges of latency,energy consumption,and fault tolerance in these environments,this paper proposes a latency-aware,faulttolerant framework for resource scheduling and data management,referred to as the FORD framework,for smart cities in fog environments.This framework is designed to meet the demands of time-sensitive applications,such as those in smart transportation systems.The FORD framework incorporates latency-aware resource scheduling to optimize task execution in smart city environments,leveraging resources from both fog and cloud environments.Through simulation-based executions,tasks are allocated to the nearest available nodes with minimum latency.In the event of execution failure,a fault-tolerantmechanism is employed to ensure the successful completion of tasks.Upon successful execution,data is efficiently stored in the cloud data center,ensuring data integrity and reliability within the smart city ecosystem.展开更多
The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because o...The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.展开更多
In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
Micro-nano Earth Observation Satellite(MEOS)constellation has the advantages of low construction cost,short revisit cycle,and high functional density,which is considered a promising solution for serving rapidly growin...Micro-nano Earth Observation Satellite(MEOS)constellation has the advantages of low construction cost,short revisit cycle,and high functional density,which is considered a promising solution for serving rapidly growing observation demands.The observation Scheduling Problem in the MEOS constellation(MEOSSP)is a challenging issue due to the large number of satellites and tasks,as well as complex observation constraints.To address the large-scale and complicated MEOSSP,we develop a Two-Stage Scheduling Algorithm based on the Pointer Network with Attention mechanism(TSSA-PNA).In TSSA-PNA,the MEOS observation scheduling is decomposed into a task allocation stage and a single-MEOS scheduling stage.In the task allocation stage,an adaptive task allocation algorithm with four problem-specific allocation operators is proposed to reallocate the unscheduled tasks to new MEOSs.Regarding the single-MEOS scheduling stage,we design a pointer network based on the encoder-decoder architecture to learn the optimal singleMEOS scheduling solution and introduce the attention mechanism into the encoder to improve the learning efficiency.The Pointer Network with Attention mechanism(PNA)can generate the single-MEOS scheduling solution quickly in an end-to-end manner.These two decomposed stages are performed iteratively to search for the solution with high profit.A greedy local search algorithm is developed to improve the profits further.The performance of the PNA and TSSA-PNA on singleMEOS and multi-MEOS scheduling problems are evaluated in the experiments.The experimental results demonstrate that PNA can obtain the approximate solution for the single-MEOS scheduling problem in a short time.Besides,the TSSA-PNA can achieve higher observation profits than the existing scheduling algorithms within the acceptable computational time for the large-scale MEOS scheduling problem.展开更多
Recently,unmanned aerial vehicle(UAV)-aided free-space optical(FSO)communication has attracted widespread attentions.However,most of the existing research focuses on communication performance only.The authors investig...Recently,unmanned aerial vehicle(UAV)-aided free-space optical(FSO)communication has attracted widespread attentions.However,most of the existing research focuses on communication performance only.The authors investigate the integrated scheduling of communication,sensing,and control for UAV-aided FSO communication systems.Initially,a sensing-control model is established via the control theory.Moreover,an FSO communication channel model is established by considering the effects of atmospheric loss,atmospheric turbulence,geometrical loss,and angle-of-arrival fluctuation.Then,the relationship between the motion control of the UAV and radial displacement is obtained to link the control aspect and communication aspect.Assuming that the base station has instantaneous channel state information(CSI)or statistical CSI,the thresholds of the sensing-control pattern activation are designed,respectively.Finally,an integrated scheduling scheme for performing communication,sensing,and control is proposed.Numerical results indicate that,compared with conventional time-triggered scheme,the proposed integrated scheduling scheme obtains comparable communication and control performance,but reduces the sensing consumed power by 52.46%.展开更多
The dwell scheduling problem for a multifunctional radar system is led to the formation of corresponding optimiza-tion problem.In order to solve the resulting optimization prob-lem,the dwell scheduling process in a sc...The dwell scheduling problem for a multifunctional radar system is led to the formation of corresponding optimiza-tion problem.In order to solve the resulting optimization prob-lem,the dwell scheduling process in a scheduling interval(SI)is formulated as a Markov decision process(MDP),where the state,action,and reward are specified for this dwell scheduling problem.Specially,the action is defined as scheduling the task on the left side,right side or in the middle of the radar idle time-line,which reduces the action space effectively and accelerates the convergence of the training.Through the above process,a model-free reinforcement learning framework is established.Then,an adaptive dwell scheduling method based on Q-learn-ing is proposed,where the converged Q value table after train-ing is utilized to instruct the scheduling process.Simulation results demonstrate that compared with existing dwell schedul-ing algorithms,the proposed one can achieve better scheduling performance considering the urgency criterion,the importance criterion and the desired execution time criterion comprehen-sively.The average running time shows the proposed algorithm has real-time performance.展开更多
Traditional quantum circuit scheduling approaches underutilize the inherent parallelism of quantum computation in the Noisy Intermediate-Scale Quantum(NISQ)era,overlook the inter-layer operations can be further parall...Traditional quantum circuit scheduling approaches underutilize the inherent parallelism of quantum computation in the Noisy Intermediate-Scale Quantum(NISQ)era,overlook the inter-layer operations can be further parallelized.Based on this,two quantum circuit scheduling optimization approaches are designed and integrated into the quantum circuit compilation process.Firstly,we introduce the Layered Topology Scheduling Approach(LTSA),which employs a greedy algorithm and leverages the principles of topological sorting in graph theory.LTSA allocates quantum gates to a layered structure,maximizing the concurrent execution of quantum gate operations.Secondly,the Layerwise Conflict Resolution Approach(LCRA)is proposed.LCRA focuses on utilizing directly executable quantum gates within layers.Through the insertion of SWAP gates and conflict resolution checks,it minimizes conflicts and enhances parallelism,thereby optimizing the overall computational efficiency.Experimental findings indicate that LTSA and LCRA individually achieve a noteworthy reduction of 51.1%and 53.2%,respectively,in the number of inserted SWAP gates.Additionally,they contribute to a decrease in hardware gate overhead by 14.7%and 15%,respectively.Considering the intricate nature of quantum circuits and the temporal dependencies among different layers,the amalgamation of both approaches leads to a remarkable 51.6%reduction in inserted SWAP gates and a 14.8%decrease in hardware gate overhead.These results underscore the efficacy of the combined LTSA and LCRA in optimizing quantum circuit compilation.展开更多
In the field of low-carbon building systems,the combination of renewable energy and hydrogen energy systems is gradually gaining prominence.However,the uncertainty of supply and demand and the multi-energy flow coupli...In the field of low-carbon building systems,the combination of renewable energy and hydrogen energy systems is gradually gaining prominence.However,the uncertainty of supply and demand and the multi-energy flow coupling characteristics of this system pose challenges for its optimized scheduling.In light of this,this study focuses on electro-thermal-hydrogen trigeneration systems,first modelling the system's scheduling optimization problem as a Markov decision process,thereby transforming it into a sequential decision problem.Based on this,this paper proposes a reinforcement learning algorithm based on deep deterministic policy gradient improvement,aiming to minimize system operating costs and enhance the system's sustainable operation capability.Experimental results show that compared to traditional reinforcement learning algorithms,the reinforcement learning algorithm based on deep deterministic policy gradient improvement achieves improvements of 12.5%and 22.8%in convergence speed and convergence value,respectively.Additionally,under uncertainty scenarios ranging from 10%to 30%,cost reductions of 2.82%,3.08%,and 2.52%were achieved,respectively,with an average cost reduction of 2.80%across 30 simulated scenarios.Compared to the original algorithm and rule-based algorithms in multi-uncertainty environments,the reinforcement learning algorithm based on improved deep deterministic policy gradients demonstrated superiority in terms of system operating costs and continuous operational capability,effectively enhancing the system's economic and sustainable performance.展开更多
A centralized-distributed scheduling strategy for distribution networks based on multi-temporal and hierarchical cooperative game is proposed to address the issues of difficult operation control and energy optimizatio...A centralized-distributed scheduling strategy for distribution networks based on multi-temporal and hierarchical cooperative game is proposed to address the issues of difficult operation control and energy optimization interaction in distribution network transformer areas,as well as the problem of significant photovoltaic curtailment due to the inability to consume photovoltaic power locally.A scheduling architecture combiningmulti-temporal scales with a three-level decision-making hierarchy is established:the overall approach adopts a centralized-distributed method,analyzing the operational characteristics and interaction relationships of the distribution network center layer,cluster layer,and transformer area layer,providing a“spatial foundation”for subsequent optimization.The optimization process is divided into two stages on the temporal scale:in the first stage,based on forecasted electricity load and demand response characteristics,time-of-use electricity prices are utilized to formulate day-ahead optimization strategies;in the second stage,based on the charging and discharging characteristics of energy storage vehicles and multi-agent cooperative game relationships,rolling electricity prices and optimal interactive energy solutions are determined among clusters and transformer areas using the Nash bargaining theory.Finally,a distributed optimization algorithm using the bisection method is employed to solve the constructed model.Simulation results demonstrate that the proposed optimization strategy can facilitate photovoltaic consumption in the distribution network and enhance grid economy.展开更多
Complex road conditions without signalized intersections when the traffic flow is nearly saturated result in high traffic congestion and accidents,reducing the traffic efficiency of intelligent vehicles.The complex ro...Complex road conditions without signalized intersections when the traffic flow is nearly saturated result in high traffic congestion and accidents,reducing the traffic efficiency of intelligent vehicles.The complex road traffic environment of smart vehicles and other vehicles frequently experiences conflicting start and stop motion.The fine-grained scheduling of autonomous vehicles(AVs)at non-signalized intersections,which is a promising technique for exploring optimal driving paths for both assisted driving nowadays and driverless cars in the near future,has attracted significant attention owing to its high potential for improving road safety and traffic efficiency.Fine-grained scheduling primarily focuses on signalized intersection scenarios,as applying it directly to non-signalized intersections is challenging because each AV can move freely without traffic signal control.This may cause frequent driving collisions and low road traffic efficiency.Therefore,this study proposes a novel algorithm to address this issue.Our work focuses on the fine-grained scheduling of automated vehicles at non-signal intersections via dual reinforced training(FS-DRL).For FS-DRL,we first use a grid to describe the non-signalized intersection and propose a convolutional neural network(CNN)-based fast decision model that can rapidly yield a coarse-grained scheduling decision for each AV in a distributed manner.We then load these coarse-grained scheduling decisions onto a deep Q-learning network(DQN)for further evaluation.We use an adaptive learning rate to maximize the reward function and employ parameterεto tradeoff the fast speed of coarse-grained scheduling in the CNN and optimal fine-grained scheduling in the DQN.In addition,we prove that using this adaptive learning rate leads to a converged loss rate with an extremely small number of training loops.The simulation results show that compared with Dijkstra,RNN,and ant colony-based scheduling,FS-DRL yields a high accuracy of 96.5%on the sample,with improved performance of approximately 61.54%-85.37%in terms of the average conflict and traffic efficiency.展开更多
基金The National Natural Science Foundation of China (No.70971022,71271054)the Scientific Research Innovation Project for College Graduates in Jiangsu Province(No.CXLX_0157)the Scientific Research Foundation of the Education Department of Anhui Province(No.2011sk123)
文摘A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespan and an LPT-LS algorithm is proposed.Non-resumable jobs are first scheduled in a machine by the longest processing time（LPT） rule,and then resumable jobs are scheduled by the list scheduling（LS） rule.And the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the resumable jobs（denoted as S2） are discussed.When S2 is longer than the spare time of the machine after the non-resumable jobs are assigned by the LPT rule,it is equal to 1.When S2 falls in between the spare time of the machine by the LPT rule and the optimal schedule rule,it is less than 2.When S2 is less than the spare time of the machine by the optimal schedule rule,it is less than 2.Finally,numerical examples are presented for verification.
文摘In this paper we consider a single-machine scheduling model with deteriorating jobs and simultaneous learning, and we introduce polynomial solutions for single machine makespan minimization, total flow times minimization and maximum lateness minimization corresponding to the first and second special cases of our model under some agreeable conditions. However, corresponding to the third special case of our model, we show that the optimal schedules may be different from those of the classical version for the above objective functions.
基金Sponsored by the National Natural Science Foundation of China(Grant No.70671040)and Specialized Research Fund for the Doctoral Program of High Education(Grant No.20050079008).
文摘In a CPM network, the longest path problem is one of the most important subjects. According to the intrinsic principle of CPM network, the length of the paths between arbitrary two nodes is presented. Furthermore, the length of the longest path from start node to arbitrary node and from arbitrary node to end node is proposed. In view of a scheduling problem of two activities with float in the CPM scheduling, we put forward Barycenter Theory and prove this theory based on the algorithm of the length of the longest path. By this theory, we know which activity should be done firstly. At last, we show our theory by an example.
文摘Motivated by industrial applications we study a single-machine scheduling problem in which all the jobs are mutu- ally independent and available at time zero.The machine processes the jobs sequentially and it is not idle if there is any job to be pro- cessed.The operation of each job cannot be interrupted.The machine cannot process more than one job at a time.A setup time is needed if the machine switches from one type of job to another.The objective is to find an optimal schedule with the minimal total jobs’completion time.While the sum of jobs’processing time is always a constant,the objective is to minimize the sum of setup times.Ant colony optimization(ACO)is a meta-heuristic that has recently been applied to scheduling problem.In this paper we propose an improved ACO-Branching Ant Colony with Dynamic Perturbation(DPBAC)algorithm for the single-machine schedul- ing problem.DPBAC improves traditional ACO in following aspects:introducing Branching Method to choose starting points;im- proving state transition rules;introducing Mutation Method to shorten tours;improving pheromone updating rules and introduc- ing Conditional Dynamic Perturbation Strategy.Computational results show that DPBAC algorithm is superior to the traditional ACO algorithm.
基金supported by the National Natural Science Foundation of China under Grant Nos.62202192,71801218,and 72101094.
文摘In a local search algorithm,one of its most important features is the definition of its neighborhood which is crucial to the algorithm's performance.In this paper,we present an analysis of neighborhood combination search for solv-ing the single-machine scheduling problem with sequence-dependent setup time with the objective of minimizing total weighted tardiness(SMSWT).First,We propose a new neighborhood structure named Block Swap(B1)which can be con-sidered as an extension of the previously widely used Block Move(B2)neighborhood,and a fast incremental evaluation technique to enhance its evaluation efficiency.Second,based on the Block Swap and Block Move neighborhoods,we present two kinds of neighborhood structures:neighborhood union(denoted by B1UB2)and token-ring search(denoted by B1→B2),both of which are combinations of B1 and B2.Third,we incorporate the neighborhood union and token-ring search into two representative metaheuristic algorithms:the Iterated Local Search Algorithm(ILSnew)and the Hybrid Evolutionary Algorithm(HEA_(new))to investigate the performance of the neighborhood union and token-ring search.Exten-sive experiments show the competitiveness of the token-ring search combination mechanism of the two neighborhoods.Tested on the 120 public benchmark instances,our HEA_(new)has a highly competitive performance in solution quality and computational time compared with both the exact algorithms and recent metaheuristics.We have also tested the HEA,new algorithm with the selected neighborhood combination search to deal with the 64 public benchmark instances of the single-machine scheduling problem with sequence-dependent setup time.HEAnew is able to match the optimal or the best known results for all the 64 instances.In particular,the computational time for reaching the best well-known results for five chal-lenging instances is reduced by at least 61.25%.
基金supported by the National Natural Science Foundation of China(Nos.12271295 and 12001313)the Provincial Natural Science Foundation of Shandong(No.ZR2022MA019).
文摘In this paper,we consider the single-machine scheduling with step-deteriorating jobs and rejection.Each job is either rejected by paying a rejection penalty,or accepted and processed on the single machine,and the actual processing time of each accepted job is a step function of its starting time and the common deteriorating date.The objective is to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs.For the case of common deteriorating penalty,we first show that the problem is NP-hard in the ordinary sense.Then we present two pseudo-polynomial algorithms and a 2-approximation algorithm.Furthermore,we propose a fully polynomial time approximation scheme.For the case of common normal processing time,we present two pseudo-polynomial time algorithms,a 2-approximation algorithm and a fully polynomial time approximation scheme.
基金supported by the National Nature Science Foundation of China(NSFC)with grant Nos:72091215/72091210,71921001 and 72022018,and Youth Innovation Promotion Association(Grant No.2021454).
文摘Additive manufacturing(AM)has attracted significant attention in recent years based on its wide range of applications and growing demand.AM offers the advantages of production flexibility and design freedom.In this study,we considered a practical variant of the batch-processing-machine(BPM)scheduling problem that arises in AM industries,where an AM machine can process multiple parts simultaneously,as long as the twodimensional rectangular packing constraint is not violated.Based on the set-partitioning formulation of our mixed-integer programming(MIP)model,a branch-and-price(B&P)algorithm was developed by embedding a column-generation technique into a branchand-bound framework.Additionally,a novel labelling algorithm was developed to accelerate the column-generation process.Ours is the first study to provide a B&P algorithm to solve the BPM scheduling problem in the AM industry.We tested the performance of our algorithm using a modern MIP solver(Gurobi)and real data from a 3D printing factory.The results demonstrate that for most instances tested,our algorithm produces results similar or identical to those of Gurobi with reasonable computation time and outperforms Gurobi in terms of solution quality and running time on some large instances.
基金the financial support of the National Key Research and Development Plan(2021YFB3302501)the financial support of the National Natural Science Foundation of China(12102077)。
文摘Safe and efficient sortie scheduling on the confined flight deck is crucial for maintaining high combat effectiveness of the aircraft carrier.The primary difficulty exactly lies in the spatiotemporal coordination,i.e.,allocation of limited supporting resources and collision-avoidance between heterogeneous dispatch entities.In this paper,the problem is investigated in the perspective of hybrid flow-shop scheduling problem by synthesizing the precedence,space and resource constraints.Specifically,eight processing procedures are abstracted,where tractors,preparing spots,catapults,and launching are virtualized as machines.By analyzing the constraints in sortie scheduling,a mixed-integer planning model is constructed.In particular,the constraint on preparing spot occupancy is improved to further enhance the sortie efficiency.The basic trajectory library for each dispatch entity is generated and a delayed strategy is integrated to address the collision-avoidance issue.To efficiently solve the formulated HFSP,which is essentially a combinatorial problem with tightly coupled constraints,a chaos-initialized genetic algorithm is developed.The solution framework is validated by the simulation environment referring to the Fort-class carrier,exhibiting higher sortie efficiency when compared to existing strategies.And animation of the simulation results is available at www.bilibili.com/video/BV14t421A7Tt/.The study presents a promising supporting technique for autonomous flight deck operation in the foreseeable future,and can be easily extended to other supporting scenarios,e.g.,ammunition delivery and aircraft maintenance.
基金supported in part by the High-tech ship scientific research project of the Ministry of Industry and Information Technology of the People’s Republic of China,and the National Nature Science Foundation of China(Grant No.71671113)the Science and Technology Department of Shaanxi Province(No.2020GY-219)the Ministry of Education Collaborative Project of Production,Learning and Research(No.201901024016).
文摘Ship outfitting is a key process in shipbuilding.Efficient and high-quality ship outfitting is a top priority for modern shipyards.These activities are conducted at different stations of shipyards.The outfitting plan is one of the crucial issues in shipbuilding.In this paper,production scheduling and material ordering with endogenous uncertainty of the outfitting process are investigated.The uncertain factors in outfitting equipment production are usually decision-related,which leads to difficulties in addressing uncertainties in the outfitting production workshops before production is conducted according to plan.This uncertainty is regarded as endogenous uncertainty and can be treated as non-anticipativity constraints in the model.To address this problem,a stochastic two-stage programming model with endogenous uncertainty is established to optimize the outfitting job scheduling and raw material ordering process.A practical case of the shipyard of China Merchants Heavy Industry Co.,Ltd.is used to evaluate the performance of the proposed method.Satisfactory results are achieved at the lowest expected total cost as the complete kit rate of outfitting equipment is improved and emergency replenishment is reduced.
基金supported in part by the National Natural Science Foundation of China under Grant No.61473066in part by the Natural Science Foundation of Hebei Province under Grant No.F2021501020+2 种基金in part by the S&T Program of Qinhuangdao under Grant No.202401A195in part by the Science Research Project of Hebei Education Department under Grant No.QN2025008in part by the Innovation Capability Improvement Plan Project of Hebei Province under Grant No.22567637H
文摘Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.
基金supported by the Deanship of Scientific Research and Graduate Studies at King Khalid University under research grant number(R.G.P.2/93/45).
文摘Thedeployment of the Internet of Things(IoT)with smart sensors has facilitated the emergence of fog computing as an important technology for delivering services to smart environments such as campuses,smart cities,and smart transportation systems.Fog computing tackles a range of challenges,including processing,storage,bandwidth,latency,and reliability,by locally distributing secure information through end nodes.Consisting of endpoints,fog nodes,and back-end cloud infrastructure,it provides advanced capabilities beyond traditional cloud computing.In smart environments,particularly within smart city transportation systems,the abundance of devices and nodes poses significant challenges related to power consumption and system reliability.To address the challenges of latency,energy consumption,and fault tolerance in these environments,this paper proposes a latency-aware,faulttolerant framework for resource scheduling and data management,referred to as the FORD framework,for smart cities in fog environments.This framework is designed to meet the demands of time-sensitive applications,such as those in smart transportation systems.The FORD framework incorporates latency-aware resource scheduling to optimize task execution in smart city environments,leveraging resources from both fog and cloud environments.Through simulation-based executions,tasks are allocated to the nearest available nodes with minimum latency.In the event of execution failure,a fault-tolerantmechanism is employed to ensure the successful completion of tasks.Upon successful execution,data is efficiently stored in the cloud data center,ensuring data integrity and reliability within the smart city ecosystem.
基金supported in part by the National Key Research and Development Program of China under Grant No.2021YFF0901300in part by the National Natural Science Foundation of China under Grant Nos.62173076 and 72271048.
文摘The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金supported by the National Natural Science Foundation of China(No.62101587)the National Funded Postdoctoral Researcher Program of China(No.GZC20233578)。
文摘Micro-nano Earth Observation Satellite(MEOS)constellation has the advantages of low construction cost,short revisit cycle,and high functional density,which is considered a promising solution for serving rapidly growing observation demands.The observation Scheduling Problem in the MEOS constellation(MEOSSP)is a challenging issue due to the large number of satellites and tasks,as well as complex observation constraints.To address the large-scale and complicated MEOSSP,we develop a Two-Stage Scheduling Algorithm based on the Pointer Network with Attention mechanism(TSSA-PNA).In TSSA-PNA,the MEOS observation scheduling is decomposed into a task allocation stage and a single-MEOS scheduling stage.In the task allocation stage,an adaptive task allocation algorithm with four problem-specific allocation operators is proposed to reallocate the unscheduled tasks to new MEOSs.Regarding the single-MEOS scheduling stage,we design a pointer network based on the encoder-decoder architecture to learn the optimal singleMEOS scheduling solution and introduce the attention mechanism into the encoder to improve the learning efficiency.The Pointer Network with Attention mechanism(PNA)can generate the single-MEOS scheduling solution quickly in an end-to-end manner.These two decomposed stages are performed iteratively to search for the solution with high profit.A greedy local search algorithm is developed to improve the profits further.The performance of the PNA and TSSA-PNA on singleMEOS and multi-MEOS scheduling problems are evaluated in the experiments.The experimental results demonstrate that PNA can obtain the approximate solution for the single-MEOS scheduling problem in a short time.Besides,the TSSA-PNA can achieve higher observation profits than the existing scheduling algorithms within the acceptable computational time for the large-scale MEOS scheduling problem.
文摘Recently,unmanned aerial vehicle(UAV)-aided free-space optical(FSO)communication has attracted widespread attentions.However,most of the existing research focuses on communication performance only.The authors investigate the integrated scheduling of communication,sensing,and control for UAV-aided FSO communication systems.Initially,a sensing-control model is established via the control theory.Moreover,an FSO communication channel model is established by considering the effects of atmospheric loss,atmospheric turbulence,geometrical loss,and angle-of-arrival fluctuation.Then,the relationship between the motion control of the UAV and radial displacement is obtained to link the control aspect and communication aspect.Assuming that the base station has instantaneous channel state information(CSI)or statistical CSI,the thresholds of the sensing-control pattern activation are designed,respectively.Finally,an integrated scheduling scheme for performing communication,sensing,and control is proposed.Numerical results indicate that,compared with conventional time-triggered scheme,the proposed integrated scheduling scheme obtains comparable communication and control performance,but reduces the sensing consumed power by 52.46%.
基金supported by the National Natural Science Foundation of China(6177109562031007).
文摘The dwell scheduling problem for a multifunctional radar system is led to the formation of corresponding optimiza-tion problem.In order to solve the resulting optimization prob-lem,the dwell scheduling process in a scheduling interval(SI)is formulated as a Markov decision process(MDP),where the state,action,and reward are specified for this dwell scheduling problem.Specially,the action is defined as scheduling the task on the left side,right side or in the middle of the radar idle time-line,which reduces the action space effectively and accelerates the convergence of the training.Through the above process,a model-free reinforcement learning framework is established.Then,an adaptive dwell scheduling method based on Q-learn-ing is proposed,where the converged Q value table after train-ing is utilized to instruct the scheduling process.Simulation results demonstrate that compared with existing dwell schedul-ing algorithms,the proposed one can achieve better scheduling performance considering the urgency criterion,the importance criterion and the desired execution time criterion comprehen-sively.The average running time shows the proposed algorithm has real-time performance.
基金funded by the Natural Science Foundation of Heilongjiang Province(Grant No.LH2022F035)the Cultivation Programme for Young Innovative Talents in Ordinary Higher Education Institutions of Heilongjiang Province(Grant No.UNPYSCT-2020212)the Cultivation Programme for Young Innovative Talents in Scientific Research of Harbin University of Commerce(Grant No.2023-KYYWF-0983).
文摘Traditional quantum circuit scheduling approaches underutilize the inherent parallelism of quantum computation in the Noisy Intermediate-Scale Quantum(NISQ)era,overlook the inter-layer operations can be further parallelized.Based on this,two quantum circuit scheduling optimization approaches are designed and integrated into the quantum circuit compilation process.Firstly,we introduce the Layered Topology Scheduling Approach(LTSA),which employs a greedy algorithm and leverages the principles of topological sorting in graph theory.LTSA allocates quantum gates to a layered structure,maximizing the concurrent execution of quantum gate operations.Secondly,the Layerwise Conflict Resolution Approach(LCRA)is proposed.LCRA focuses on utilizing directly executable quantum gates within layers.Through the insertion of SWAP gates and conflict resolution checks,it minimizes conflicts and enhances parallelism,thereby optimizing the overall computational efficiency.Experimental findings indicate that LTSA and LCRA individually achieve a noteworthy reduction of 51.1%and 53.2%,respectively,in the number of inserted SWAP gates.Additionally,they contribute to a decrease in hardware gate overhead by 14.7%and 15%,respectively.Considering the intricate nature of quantum circuits and the temporal dependencies among different layers,the amalgamation of both approaches leads to a remarkable 51.6%reduction in inserted SWAP gates and a 14.8%decrease in hardware gate overhead.These results underscore the efficacy of the combined LTSA and LCRA in optimizing quantum circuit compilation.
基金the Science and Technology Projects of State Grid Jiangsu Electric Power Company “Design, Regulation and Application of Electric-Hydrogen-Heat Integrated Energy Systems for Low Carbon Buildings, J2024184”.
文摘In the field of low-carbon building systems,the combination of renewable energy and hydrogen energy systems is gradually gaining prominence.However,the uncertainty of supply and demand and the multi-energy flow coupling characteristics of this system pose challenges for its optimized scheduling.In light of this,this study focuses on electro-thermal-hydrogen trigeneration systems,first modelling the system's scheduling optimization problem as a Markov decision process,thereby transforming it into a sequential decision problem.Based on this,this paper proposes a reinforcement learning algorithm based on deep deterministic policy gradient improvement,aiming to minimize system operating costs and enhance the system's sustainable operation capability.Experimental results show that compared to traditional reinforcement learning algorithms,the reinforcement learning algorithm based on deep deterministic policy gradient improvement achieves improvements of 12.5%and 22.8%in convergence speed and convergence value,respectively.Additionally,under uncertainty scenarios ranging from 10%to 30%,cost reductions of 2.82%,3.08%,and 2.52%were achieved,respectively,with an average cost reduction of 2.80%across 30 simulated scenarios.Compared to the original algorithm and rule-based algorithms in multi-uncertainty environments,the reinforcement learning algorithm based on improved deep deterministic policy gradients demonstrated superiority in terms of system operating costs and continuous operational capability,effectively enhancing the system's economic and sustainable performance.
基金funded by the Jilin Province Science and Technology Development Plan Project(20230101344JC).
文摘A centralized-distributed scheduling strategy for distribution networks based on multi-temporal and hierarchical cooperative game is proposed to address the issues of difficult operation control and energy optimization interaction in distribution network transformer areas,as well as the problem of significant photovoltaic curtailment due to the inability to consume photovoltaic power locally.A scheduling architecture combiningmulti-temporal scales with a three-level decision-making hierarchy is established:the overall approach adopts a centralized-distributed method,analyzing the operational characteristics and interaction relationships of the distribution network center layer,cluster layer,and transformer area layer,providing a“spatial foundation”for subsequent optimization.The optimization process is divided into two stages on the temporal scale:in the first stage,based on forecasted electricity load and demand response characteristics,time-of-use electricity prices are utilized to formulate day-ahead optimization strategies;in the second stage,based on the charging and discharging characteristics of energy storage vehicles and multi-agent cooperative game relationships,rolling electricity prices and optimal interactive energy solutions are determined among clusters and transformer areas using the Nash bargaining theory.Finally,a distributed optimization algorithm using the bisection method is employed to solve the constructed model.Simulation results demonstrate that the proposed optimization strategy can facilitate photovoltaic consumption in the distribution network and enhance grid economy.
基金Supported by National Natural Science Foundation of China(Grant No.61803206)Jiangsu Provincial Natural Science Foundation(Grant No.222300420468)Jiangsu Provincial key R&D Program(Grant No.BE2017008-2).
文摘Complex road conditions without signalized intersections when the traffic flow is nearly saturated result in high traffic congestion and accidents,reducing the traffic efficiency of intelligent vehicles.The complex road traffic environment of smart vehicles and other vehicles frequently experiences conflicting start and stop motion.The fine-grained scheduling of autonomous vehicles(AVs)at non-signalized intersections,which is a promising technique for exploring optimal driving paths for both assisted driving nowadays and driverless cars in the near future,has attracted significant attention owing to its high potential for improving road safety and traffic efficiency.Fine-grained scheduling primarily focuses on signalized intersection scenarios,as applying it directly to non-signalized intersections is challenging because each AV can move freely without traffic signal control.This may cause frequent driving collisions and low road traffic efficiency.Therefore,this study proposes a novel algorithm to address this issue.Our work focuses on the fine-grained scheduling of automated vehicles at non-signal intersections via dual reinforced training(FS-DRL).For FS-DRL,we first use a grid to describe the non-signalized intersection and propose a convolutional neural network(CNN)-based fast decision model that can rapidly yield a coarse-grained scheduling decision for each AV in a distributed manner.We then load these coarse-grained scheduling decisions onto a deep Q-learning network(DQN)for further evaluation.We use an adaptive learning rate to maximize the reward function and employ parameterεto tradeoff the fast speed of coarse-grained scheduling in the CNN and optimal fine-grained scheduling in the DQN.In addition,we prove that using this adaptive learning rate leads to a converged loss rate with an extremely small number of training loops.The simulation results show that compared with Dijkstra,RNN,and ant colony-based scheduling,FS-DRL yields a high accuracy of 96.5%on the sample,with improved performance of approximately 61.54%-85.37%in terms of the average conflict and traffic efficiency.
