The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod mod...The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod model for its portfolio problem. The model is a multistage stochastic programming which considers transaction costs, cash flow between time periods, and the matching of asset and liability; it does not depend on the assumption for normality of return distribution. Additionally, an investment constraint is added. The numerical example manifests that the multiperiod model can more effectively assist the property-liability insurer to determine the optimal composition of insurance and investment portfolio and outperforms the single period one.展开更多
This study presented a simulation-based two-stage interval-stochastic programming （STIP） model to support water resources management in the Kaidu-Konqi watershed in Northwest China. The modeling system coupled a dis...This study presented a simulation-based two-stage interval-stochastic programming （STIP） model to support water resources management in the Kaidu-Konqi watershed in Northwest China. The modeling system coupled a distributed hydrological model with an interval two-stage stochastic programing （ITSP）. The distributed hydrological model was used for establishing a rainfall-runoff forecast system, while random parameters were pro- vided by the statistical analysis of simulation outcomes water resources management planning in Kaidu-Konqi The developed STIP model was applied to a real case of watershed, where three scenarios with different water re- sources management policies were analyzed. The results indicated that water shortage mainly occurred in agri- culture, ecology and forestry sectors. In comparison, the water demand from municipality, industry and stock- breeding sectors can be satisfied due to their lower consumptions and higher economic values. Different policies for ecological water allocation can result in varied system benefits, and can help to identify desired water allocation plans with a maximum economic benefit and a minimum risk of system disruption under uncertainty.展开更多
The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and wate...The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and water sectors within a basin. With the precondition of strictly controlling maximum emissions rights, initial water rights were allocated between the first and the second levels of the hierarchy in order to promote fair and coordinated development across different regions of the basin and coordinated and efficient water use across different water sectors, realize the maximum comprehensive benefits to the basin, promote the unity of quantity and quality of initial water rights allocation, and eliminate water conflict across different regions and water sectors. According to interactive decision-making theory, a principal-subordinate hierarchical interactive iterative algorithm based on the satisfaction degree was developed and used to solve the initial water rights allocation model. A case study verified the validity of the model.展开更多
This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are t...This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.展开更多
This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among...This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.展开更多
This research develops a comprehensive method to solve a combinatorial problem consisting of distribution system reconfiguration, capacitor allocation, and renewable energy resources sizing and siting simultaneously a...This research develops a comprehensive method to solve a combinatorial problem consisting of distribution system reconfiguration, capacitor allocation, and renewable energy resources sizing and siting simultaneously and to improve power system's accountability and system performance parameters. Due to finding solution which is closer to realistic characteristics, load forecasting, market price errors and the uncertainties related to the variable output power of wind based DG units are put in consideration. This work employs NSGA-II accompanied by the fuzzy set theory to solve the aforementioned multi-objective problem. The proposed scheme finally leads to a solution with a minimum voltage deviation, a maximum voltage stability, lower amount of pollutant and lower cost. The cost includes the installation costs of new equipment, reconfiguration costs, power loss cost, reliability cost, cost of energy purchased from power market, upgrade costs of lines and operation and maintenance costs of DGs. Therefore, the proposed methodology improves power quality, reliability and security in lower costs besides its preserve, with the operational indices of power distribution networks in acceptable level. To validate the proposed methodology's usefulness, it was applied on the IEEE 33-bus distribution system then the outcomes were compared with initial configuration.展开更多
Driven by the goal of“carbon neutrality,”the increase in use of renewable energy power systems will be inevitable in the future.Uncontrolled output power and random volatility make it difficult to balance power in r...Driven by the goal of“carbon neutrality,”the increase in use of renewable energy power systems will be inevitable in the future.Uncontrolled output power and random volatility make it difficult to balance power in real time during system operation.Therefore,energy storage is considered to be an effective way to ensure the real-time balance of system power.However,cost of energy storage is relatively expensive.As a solution,energy storage can be used to balance the system power in order to reduce system operating costs.Taking the high proportion of wind power systems as an example,the impact of the“supply side”low-carbon transformation on the economics and reliability of power system operation is explored.In order to solve the problem of power system operation configuration optimization under the background of“carbon neutrality,”this paper establishes a multi-objective programming model.展开更多
In this paper, the problem of optimum allocation of repairable and replaceable components in a system is formulated as a Bi-objective stochastic non linear programming problem. The system maintenance time and cost are...In this paper, the problem of optimum allocation of repairable and replaceable components in a system is formulated as a Bi-objective stochastic non linear programming problem. The system maintenance time and cost are random variable and has gamma and normal distribution respectively. A Bi-criteria optimization technique, weighted Tchebycheff is used to obtain the optimum allocation for a system. A numerical example is also presented to illustrate the computational details.展开更多
The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit a...The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.展开更多
Efficient built environment control is essential for balancing energy consumption,thermal comfort,and indoor air quality(IAQ),especially in spaces with highly dynamic and intermittent occupancy patterns.Traditional co...Efficient built environment control is essential for balancing energy consumption,thermal comfort,and indoor air quality(IAQ),especially in spaces with highly dynamic and intermittent occupancy patterns.Traditional control strategies,such as fixed schedules or simple occupancy-based rules,often fail to address the stochastic nature of occupancy behaviors,leading to suboptimal performance.This study proposes a stochastic occupancy-integrated model predictive control(MPC)strategy that advances built environment optimization through several innovative contributions.First,the proposed MPC integrates stochastic occupancy number predictions into its control scheme,enabling multi-objective optimization considering thermal comfort and IAQ for spaces with sudden occupancy changes and irregular usage.Second,the stochastic differential equations(SDE)-based building dynamic models are developed considering the stochasticity and time-inhomogeneity of occupancy heat gains and CO_(2)generations in the prediction of indoor temperature,CO_(2)concentration and energy consumption.Third,a TRNSYS-Python co-simulation platform is established to evaluate the MPC strategy’s performance,addressing the discrepancies between the SDE models used for MPC and the actual process of the target system.Finally,the study comprehensively evaluates the MPC’s multi-dimensional performance under different optimization weight combinations and benchmarks it against two baseline strategies:a fixed-schedule(FIX)strategy and occupancy-based control(OBC)strategies with varying per-person fresh airflow rates.Simulation results demonstrate that the proposed MPC achieves 32%energy savings and 17%IAQ improvement compared to the FIX strategy,and 30%thermal comfort improvement and 20%IAQ improvement with the same energy consumption compared to OBC.These findings highlight the robustness and enhanced performance of the proposed MPC in addressing the complexities of stochastic and time-varying occupancy,offering a state-of-the-art solution for energy-efficient and occupant-centric built environment control.展开更多
Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumptio...Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumption problems with both fixed andproportional transactions costs are investigated in this paper. We model this kind ofdifficult problems as a dynamic stochastic optimization problem, which can cope withdifferent utility functions and any number of time periods. The procedure to solve theresulting complex nonlinear stochastic optimization problem is discussed in detail and abranch-decomposition algorithm is devised.展开更多
The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing ...The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing the agricultural value-added industrial chain.This study uses emergy analysis to comprehensively examine and evaluate the economic benefits,environmental pressures,and sustainable development levels of ICEMFSR in Shucheng County,China.The results show that the ICEMFSR possesses the value of popularization with optimally allocated resources in the studied region,in which the emergy yield ratio(EYR),emergy loading ratio(ELR),and emergy sustainable index(ESI)in this model accounted for 3.59,1.25,and 2.89,respectively.This result indicates a leading position in the national agricultural system.Hence,this study constructs a new model based on the coupling of emergy evaluation and multi-objective linear programming to study ICEMFSR.Consequently,the EYR,ELR,and ESI respectively varied by +24.23%,10.40%,and +38.06%after replanning of ICEMFSR.This variation implies a significant improvement in the sustainable development level of the model.In addition,the optimized scenario design for key substances is proposed based on traceability and the reduce-reuse-recycle principle,including biogasification of crop straw and enhancement of crop scientific planting capacity.展开更多
The energetic optimization problem,e.g.,searching for the optimal switching protocol of certain system parameters to minimize the input work,has been extensively studied by stochastic thermodynamics.In this work,we st...The energetic optimization problem,e.g.,searching for the optimal switching protocol of certain system parameters to minimize the input work,has been extensively studied by stochastic thermodynamics.In this work,we study this problem numerically using iterative dynamic programming.The model systems under investigation are toy actuators consisting of spring-linked beads with loading force imposed on both ending beads.For the simplest case,i.e.,a one-spring actuator driven by tuning the stiffness of the spring,we compare the optimal control protocol of the stiffness for both the overdamped and the underdamped situations,and discuss how inertial effects alter the irreversibility of the driven process and thus modify the optimal protocol.Then,we study the systems with multiple degrees of freedom by constructing oligomer actuators,in which the harmonic interaction between the two ending beads is tuned externally.With the same rated output work,actuators of different constructions demand different minimal input work,reflecting the influence of the internal degrees of freedom on the performance of the actuators.展开更多
A stochastic programming model on the combination of aircraft landing problem and terminal traffic flow management under uncertainty is proposed in this work.In reality,various kinds of uncertainties,including adverse...A stochastic programming model on the combination of aircraft landing problem and terminal traffic flow management under uncertainty is proposed in this work.In reality,various kinds of uncertainties,including adverse weather events,occur more frequently and interrupt air traffic operations.Some of these uncertain events can appear and disappear in a short period.Furthermore,the occurrence of these events affects the flights significantly,delaying the flights or event harming the safety of passengers.Thus,it is essential to respond to these uncertainties to ensure the level of safety at runtime.Runway operation may cease due to strong wind shear,turbulence,microburst or other extreme weather scenarios,is limited due to the restricted airspace capacity,and we extend the problem covering the terminal airspace.The proposed model can significantly reduce the total delay time of aircraft in the computations.展开更多
supported by the Taishan Scholar Construction Engineering by Shandong Government the National Natural Science Foundation of China under Grant Nos.61120106011 and 61203029
文摘The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod model for its portfolio problem. The model is a multistage stochastic programming which considers transaction costs, cash flow between time periods, and the matching of asset and liability; it does not depend on the assumption for normality of return distribution. Additionally, an investment constraint is added. The numerical example manifests that the multiperiod model can more effectively assist the property-liability insurer to determine the optimal composition of insurance and investment portfolio and outperforms the single period one.
基金supported by the National Basic Research Program of China(2010CB951002)the Dr.Western-funded Project of Chinese Academy of Science(XBBS201010 and XBBS201005)+1 种基金the National Natural Sciences Foundation of China (51190095)the Open Research Fund Program of State Key Laboratory of Hydro-science and Engineering(sklhse-2012-A03)
文摘This study presented a simulation-based two-stage interval-stochastic programming （STIP） model to support water resources management in the Kaidu-Konqi watershed in Northwest China. The modeling system coupled a distributed hydrological model with an interval two-stage stochastic programing （ITSP）. The distributed hydrological model was used for establishing a rainfall-runoff forecast system, while random parameters were pro- vided by the statistical analysis of simulation outcomes water resources management planning in Kaidu-Konqi The developed STIP model was applied to a real case of watershed, where three scenarios with different water re- sources management policies were analyzed. The results indicated that water shortage mainly occurred in agri- culture, ecology and forestry sectors. In comparison, the water demand from municipality, industry and stock- breeding sectors can be satisfied due to their lower consumptions and higher economic values. Different policies for ecological water allocation can result in varied system benefits, and can help to identify desired water allocation plans with a maximum economic benefit and a minimum risk of system disruption under uncertainty.
基金supported by the Public Welfare Industry Special Fund Project of the Ministry of Water Resources of China (Grant No. 200701028)the Humanities and Social Science Foundation Program of Hohai University (Grant No. 2008421411)
文摘The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and water sectors within a basin. With the precondition of strictly controlling maximum emissions rights, initial water rights were allocated between the first and the second levels of the hierarchy in order to promote fair and coordinated development across different regions of the basin and coordinated and efficient water use across different water sectors, realize the maximum comprehensive benefits to the basin, promote the unity of quantity and quality of initial water rights allocation, and eliminate water conflict across different regions and water sectors. According to interactive decision-making theory, a principal-subordinate hierarchical interactive iterative algorithm based on the satisfaction degree was developed and used to solve the initial water rights allocation model. A case study verified the validity of the model.
文摘This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.
文摘This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.
文摘This research develops a comprehensive method to solve a combinatorial problem consisting of distribution system reconfiguration, capacitor allocation, and renewable energy resources sizing and siting simultaneously and to improve power system's accountability and system performance parameters. Due to finding solution which is closer to realistic characteristics, load forecasting, market price errors and the uncertainties related to the variable output power of wind based DG units are put in consideration. This work employs NSGA-II accompanied by the fuzzy set theory to solve the aforementioned multi-objective problem. The proposed scheme finally leads to a solution with a minimum voltage deviation, a maximum voltage stability, lower amount of pollutant and lower cost. The cost includes the installation costs of new equipment, reconfiguration costs, power loss cost, reliability cost, cost of energy purchased from power market, upgrade costs of lines and operation and maintenance costs of DGs. Therefore, the proposed methodology improves power quality, reliability and security in lower costs besides its preserve, with the operational indices of power distribution networks in acceptable level. To validate the proposed methodology's usefulness, it was applied on the IEEE 33-bus distribution system then the outcomes were compared with initial configuration.
文摘Driven by the goal of“carbon neutrality,”the increase in use of renewable energy power systems will be inevitable in the future.Uncontrolled output power and random volatility make it difficult to balance power in real time during system operation.Therefore,energy storage is considered to be an effective way to ensure the real-time balance of system power.However,cost of energy storage is relatively expensive.As a solution,energy storage can be used to balance the system power in order to reduce system operating costs.Taking the high proportion of wind power systems as an example,the impact of the“supply side”low-carbon transformation on the economics and reliability of power system operation is explored.In order to solve the problem of power system operation configuration optimization under the background of“carbon neutrality,”this paper establishes a multi-objective programming model.
文摘In this paper, the problem of optimum allocation of repairable and replaceable components in a system is formulated as a Bi-objective stochastic non linear programming problem. The system maintenance time and cost are random variable and has gamma and normal distribution respectively. A Bi-criteria optimization technique, weighted Tchebycheff is used to obtain the optimum allocation for a system. A numerical example is also presented to illustrate the computational details.
基金the Humanities and Social Science Foundation of the Ministry of Education of China(Grant No.20YJCZH121).
文摘The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.
基金the Research Grants Council(15220323)of the Hong Kong SAR,Chinathe Innovation Fund Denmark to SEM4Cities(IFD No.0143-0004)and RePUP(IFD No.2079-00030B)as well as the ARV project(EU H2020101036723).
文摘Efficient built environment control is essential for balancing energy consumption,thermal comfort,and indoor air quality(IAQ),especially in spaces with highly dynamic and intermittent occupancy patterns.Traditional control strategies,such as fixed schedules or simple occupancy-based rules,often fail to address the stochastic nature of occupancy behaviors,leading to suboptimal performance.This study proposes a stochastic occupancy-integrated model predictive control(MPC)strategy that advances built environment optimization through several innovative contributions.First,the proposed MPC integrates stochastic occupancy number predictions into its control scheme,enabling multi-objective optimization considering thermal comfort and IAQ for spaces with sudden occupancy changes and irregular usage.Second,the stochastic differential equations(SDE)-based building dynamic models are developed considering the stochasticity and time-inhomogeneity of occupancy heat gains and CO_(2)generations in the prediction of indoor temperature,CO_(2)concentration and energy consumption.Third,a TRNSYS-Python co-simulation platform is established to evaluate the MPC strategy’s performance,addressing the discrepancies between the SDE models used for MPC and the actual process of the target system.Finally,the study comprehensively evaluates the MPC’s multi-dimensional performance under different optimization weight combinations and benchmarks it against two baseline strategies:a fixed-schedule(FIX)strategy and occupancy-based control(OBC)strategies with varying per-person fresh airflow rates.Simulation results demonstrate that the proposed MPC achieves 32%energy savings and 17%IAQ improvement compared to the FIX strategy,and 30%thermal comfort improvement and 20%IAQ improvement with the same energy consumption compared to OBC.These findings highlight the robustness and enhanced performance of the proposed MPC in addressing the complexities of stochastic and time-varying occupancy,offering a state-of-the-art solution for energy-efficient and occupant-centric built environment control.
基金This research is partially supported by the Natural Science Foundation of Shaanxi Province,China(2001SL09)
文摘Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumption problems with both fixed andproportional transactions costs are investigated in this paper. We model this kind ofdifficult problems as a dynamic stochastic optimization problem, which can cope withdifferent utility functions and any number of time periods. The procedure to solve theresulting complex nonlinear stochastic optimization problem is discussed in detail and abranch-decomposition algorithm is devised.
基金supported by National Key R&D Plan[Grant number.2016YFC0502805]National Natural Science Foundation of China[Grant number.71974116]+2 种基金Shandong Natural Science Foundation[Grant number.ZR2019MG009]Shandong Province Social Science Planning Research Project[Grant number.20CGLJ13]Taishan Scholar Project[Grant number.tsqn202103010].
文摘The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing the agricultural value-added industrial chain.This study uses emergy analysis to comprehensively examine and evaluate the economic benefits,environmental pressures,and sustainable development levels of ICEMFSR in Shucheng County,China.The results show that the ICEMFSR possesses the value of popularization with optimally allocated resources in the studied region,in which the emergy yield ratio(EYR),emergy loading ratio(ELR),and emergy sustainable index(ESI)in this model accounted for 3.59,1.25,and 2.89,respectively.This result indicates a leading position in the national agricultural system.Hence,this study constructs a new model based on the coupling of emergy evaluation and multi-objective linear programming to study ICEMFSR.Consequently,the EYR,ELR,and ESI respectively varied by +24.23%,10.40%,and +38.06%after replanning of ICEMFSR.This variation implies a significant improvement in the sustainable development level of the model.In addition,the optimized scenario design for key substances is proposed based on traceability and the reduce-reuse-recycle principle,including biogasification of crop straw and enhancement of crop scientific planting capacity.
文摘The energetic optimization problem,e.g.,searching for the optimal switching protocol of certain system parameters to minimize the input work,has been extensively studied by stochastic thermodynamics.In this work,we study this problem numerically using iterative dynamic programming.The model systems under investigation are toy actuators consisting of spring-linked beads with loading force imposed on both ending beads.For the simplest case,i.e.,a one-spring actuator driven by tuning the stiffness of the spring,we compare the optimal control protocol of the stiffness for both the overdamped and the underdamped situations,and discuss how inertial effects alter the irreversibility of the driven process and thus modify the optimal protocol.Then,we study the systems with multiple degrees of freedom by constructing oligomer actuators,in which the harmonic interaction between the two ending beads is tuned externally.With the same rated output work,actuators of different constructions demand different minimal input work,reflecting the influence of the internal degrees of freedom on the performance of the actuators.
基金supported by grants from the Research Grants Council,the Hong Kong Government(Grant No.PolyU25218321,PolyU15201423)Department of Aeronautical and Aviation Engineering,The Hong Kong Polytechnic University,Hong Kong SAR(RJTT,RJ85,RJJ9)the National Natural Science Foun-dation of China(Grant number:72301229).
文摘A stochastic programming model on the combination of aircraft landing problem and terminal traffic flow management under uncertainty is proposed in this work.In reality,various kinds of uncertainties,including adverse weather events,occur more frequently and interrupt air traffic operations.Some of these uncertain events can appear and disappear in a short period.Furthermore,the occurrence of these events affects the flights significantly,delaying the flights or event harming the safety of passengers.Thus,it is essential to respond to these uncertainties to ensure the level of safety at runtime.Runway operation may cease due to strong wind shear,turbulence,microburst or other extreme weather scenarios,is limited due to the restricted airspace capacity,and we extend the problem covering the terminal airspace.The proposed model can significantly reduce the total delay time of aircraft in the computations.
基金supported by the National Natural Science Foundation of China under Grant Nos.71125005,70871108,and 70810107020Outstanding Talents Funds of Organization Department,Beijing Committee of CPC
文摘supported by the Taishan Scholar Construction Engineering by Shandong Government the National Natural Science Foundation of China under Grant Nos.61120106011 and 61203029
