The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an exa...The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.展开更多
Satellite constellation design for space optical systems is essentially a multiple-objective optimization problem. In this work, to tackle this challenge, we first categorize the performance metrics of the space optic...Satellite constellation design for space optical systems is essentially a multiple-objective optimization problem. In this work, to tackle this challenge, we first categorize the performance metrics of the space optical system by taking into account the system tasks（i.e., target detection and tracking）. We then propose a new non-dominated sorting genetic algorithm（NSGA） to maximize the system surveillance performance. Pareto optimal sets are employed to deal with the conflicts due to the presence of multiple cost functions. Simulation results verify the validity and the improved performance of the proposed technique over benchmark methods.展开更多
Homing trajectory planning is a core task of autonomous homing of parafoil system.This work analyzes and establishes a simplified kinematic mathematical model,and regards the homing trajectory planning problem as a ki...Homing trajectory planning is a core task of autonomous homing of parafoil system.This work analyzes and establishes a simplified kinematic mathematical model,and regards the homing trajectory planning problem as a kind of multi-objective optimization problem.Being different from traditional ways of transforming the multi-objective optimization into a single objective optimization by weighting factors,this work applies an improved non-dominated sorting genetic algorithm Ⅱ(NSGA Ⅱ) to solve it directly by means of optimizing multi-objective functions simultaneously.In the improved NSGA Ⅱ,the chaos initialization and a crowding distance based population trimming method were introduced to overcome the prematurity of population,the penalty function was used in handling constraints,and the optimal solution was selected according to the method of fuzzy set theory.Simulation results of three different schemes designed according to various practical engineering requirements show that the improved NSGA Ⅱ can effectively obtain the Pareto optimal solution set under different weighting with outstanding convergence and stability,and provide a new train of thoughts to design homing trajectory of parafoil system.展开更多
Optimization of antenna array pattern used in a spaceborne Synthetic Aperture Radar (SAR) system is considered in this study. A robust evolutionary algorithm, Non-dominated Sorting Genetic Algorithms (the improved NS...Optimization of antenna array pattern used in a spaceborne Synthetic Aperture Radar (SAR) system is considered in this study. A robust evolutionary algorithm, Non-dominated Sorting Genetic Algorithms (the improved NSGA-Ⅱ), is applied on a spaceborne SAR antenna pattern design. The system consists of two objective functions with two constraints. Pareto fronts are generated as a result of multi-objective optimization. After being validated by a test problem ZDT4, the algorithms are used to synthesize spaceborne SAR antenna radiation pattern. The good results with low Ambi- guity-to-Signal Ratio (ASR) and high directivity are obtained in the paper.展开更多
With the recent boom in unmanned aerial vehicle (UAV) technology, many UAV applications involving complex and risky tasks in military and civilian fields have emerged, such as military strikes and disaster monitoring....With the recent boom in unmanned aerial vehicle (UAV) technology, many UAV applications involving complex and risky tasks in military and civilian fields have emerged, such as military strikes and disaster monitoring. Task allocation for UAVs is the process of planning the division of work among UAVs, controlled from ground stations by human operators. This study formulates the UAV task-allocation problem as an extended traveling salesman problem and presents a novel UAV task-allocation model for complex air concentration monitoring tasks. Then, an optimized non-dominated sorting genetic algorithm III (NSGA-III) based on a twin-exclusion mechanism, hierarchical objective-domination operator, and segmented gene encoding (i.e., NSGA-III-TEHOD) is developed to solve complex task-allocation problems involving multiple UAVs, hierarchical objectives, obstacles, and ambient wind. The algorithm is tested in several simulations, and the results demonstrate that the new algorithm outperforms NSGA-III, non-dominated sorting genetic algorithm II (NSGA-II), and genetic algorithm (GA) in terms of efficiency of global convergence and early maturation prevention and is available for the hierarchical objective-optimization problems.展开更多
In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Mo...In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II(NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy(E), peak crushing force(Fmax) and mass of the structure(W) as three conflicting objective functions. In the multi-objective optimization problem(MOP), E and Fmax are defined by polynomial models extracted using the software GEvo M based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point(NIP)method and technique for ordering preferences by similarity to ideal solution(TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.展开更多
A multi-objective optimization model considering both reliability and maintenance cost is proposed to solve the contradiction between reliability and maintenance cost in high-speed railway catenary system maintenance ...A multi-objective optimization model considering both reliability and maintenance cost is proposed to solve the contradiction between reliability and maintenance cost in high-speed railway catenary system maintenance activities.The non-dominated sorting genetic algorithm 2(NSGA2)is applied to multi-objective optimization,and the optimization result is a set of Pareto solutions.Firstly,multistate failure mode analysis is conducted for the main devices leading to the failure of catenary,and then the reliability and failure mode of the whole catenary system is analyzed.The mathematical relationship between system reliability and maintenance cost is derived considering the existing catenary preventive maintenance mode to improve the reliability of the system.Secondly,an improved NSGA2(INSGA2)is proposed,which strengths population diversity by improving selection operator,and introduces local search strategy to ensure that population distribution is more uniform.The comparison results of the two algorithms before and after improvement on the zero-ductility transition(ZDT)series functions show that the population diversity is better and the solution is more uniform using INSGA2.Finally,the INSGA2 is applied to multi-objective optimization of system reliability and maintenance cost in different maintenance periods.The decision-makers can choose the reasonable solutions as the maintenance plans in the optimization results by weighing the relationship between the system reliability and the maintenance cost.The selected maintenance plans can ensure the lowest maintenance cost while the system reliability is as high as possible.展开更多
Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectivenes...Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.展开更多
Responsive orbits have exhibited advantages in emergencies for their excellent responsiveness and coverage to targets.Generally,there are several conflicting metrics to trade in the orbit design for responsive space.A...Responsive orbits have exhibited advantages in emergencies for their excellent responsiveness and coverage to targets.Generally,there are several conflicting metrics to trade in the orbit design for responsive space.A special multiple-objective genetic algorithm,namely the Nondominated Sorting Genetic AlgorithmⅡ(NSGAⅡ),is used to design responsive orbits.This algorithm has considered the conflicting metrics of orbits to achieve the optimal solution,including the orbital elements and launch programs of responsive vehicles.Low-Earth fast access orbits and low-Earth repeat coverage orbits,two subtypes of responsive orbits,can be designed using NSGAI under given metric tradeoffs,number of vehicles,and launch mode.By selecting the optimal solution from the obtained Pareto fronts,a designer can process the metric tradeoffs conveniently in orbit design.Recurring to the flexibility of the algorithm,the NSGAI promotes the responsive orbit design further.展开更多
This study proposed a design and optimization strategy for a tandem arranged cascade using the Non-dominated Sorting Genetic Algorithm(NSGA) Ⅱ multi-objective optimization algorithm and Back Propagation(BP) neural ne...This study proposed a design and optimization strategy for a tandem arranged cascade using the Non-dominated Sorting Genetic Algorithm(NSGA) Ⅱ multi-objective optimization algorithm and Back Propagation(BP) neural network technology. The NASA Stage 35 was employed as the initial bench mark in the present study and five geometric control parameters were working as the optimization parameters aiming to enhance the aerodynamic performance in terms of total pressure rise and efficiency. Results showed that the feasibility and capability of the proposed optimization strategy was successfully examined. In view of the fact that the initial tandem cascade(directly scaling down from NASA Stage 35) cannot guarantee the aerodynamic performance, first optimization trial was conducted to optimize the initial design. Results showed that the optimum can improve the flow quality whereas the separation on the blade is decayed or even eliminated particularly at the tip and root regions. However, compared with the initial tandem design, the enhancement in total pressure ratio(0.47%) and efficiency(1%) are too small to be noticed. Second investigation was particularly emphasizing on a high turning tandem compressor with an increment by 28°. The pressure rise and efficiency were augmented by 1.44% and 2.34%(compared to the initial tandem design), respectively. An important conclusion can be drawn that the optimization strategy is worthy to be used in high turning compressors with a considerable performance improvement.展开更多
This paper investigates network partition and edge server placement problem to exploit the benefit of edge computing for distributed state estimation.A constrained many-objective optimization problem is formulated to ...This paper investigates network partition and edge server placement problem to exploit the benefit of edge computing for distributed state estimation.A constrained many-objective optimization problem is formulated to minimize the cost of edge server deployment,operation,and maintenance,avoid the difference in the partition sizes,reduce the level of coupling between connected partitions,and maximize the inner cohesion of each partition.Capacities of edge server are constrained against underload and overload.To efficiently solve the problem,an improved non-dominated sorting genetic algorithm III(NSGA-III)is developed,with a specifically designed directed mutation operator based on topological characteristics of the partitions to accelerate convergence.Case study validates that the proposed formulations effectively characterize the practical concerns and reveal their trade-offs,and the improved algorithm outperforms existing representative ones for large-scale networks in converging to a near-optimal solution.The optimized result contributes significantly to real-time distributed state estimation.展开更多
This article focuses on decision making for retrofit investment of road networks in order to alleviate severe consequences of roadside tree blowdown during tropical cyclones.The consequences include both the physical ...This article focuses on decision making for retrofit investment of road networks in order to alleviate severe consequences of roadside tree blowdown during tropical cyclones.The consequences include both the physical damage associated with roadside trees and the functional degradation associated with road networks.A trilevel,two-stage,and multiobjective stochastic mathematical model was developed to dispatch limited resources to retrofit the roadside trees of a road network.In the model,a new metric was designed to evaluate the performance of a road network;resilience was considered from robustness and recovery efficiency of a road network.The proposed model is at least a nondeterministic polynomialtime hardness(NP-hard)problem,which is unlikely to be solved by a polynomial time algorithm.Pareto-optimal solutions for this problem can be obtained by a proposed trilevel algorithm.The random forest method was employed to transform the trilevel algorithm into a singlelevel algorithm in order to decrease the computation burden.Roadside tree retrofit of a provincial highway network on Hainan Island,China was selected as a case area because it suffers severely from tropical cyclones every year,where there is an urgency to upgrade roadside trees against tropical cyclones.We found that roadside tree retrofit investment significantly alleviates the expected economic losses of roadside tree blowdown,at the same time that it promotes robustness and expected recovery efficiency of the road network.展开更多
基金Project supported by the National Basic Research Program of China (973 Program) (No. 2007CB714600)
文摘The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.
文摘Satellite constellation design for space optical systems is essentially a multiple-objective optimization problem. In this work, to tackle this challenge, we first categorize the performance metrics of the space optical system by taking into account the system tasks（i.e., target detection and tracking）. We then propose a new non-dominated sorting genetic algorithm（NSGA） to maximize the system surveillance performance. Pareto optimal sets are employed to deal with the conflicts due to the presence of multiple cost functions. Simulation results verify the validity and the improved performance of the proposed technique over benchmark methods.
基金Project(61273138)supported by the National Natural Science Foundation of ChinaProject(14JCZDJC39300)supported by the Key Fund of Tianjin,China
文摘Homing trajectory planning is a core task of autonomous homing of parafoil system.This work analyzes and establishes a simplified kinematic mathematical model,and regards the homing trajectory planning problem as a kind of multi-objective optimization problem.Being different from traditional ways of transforming the multi-objective optimization into a single objective optimization by weighting factors,this work applies an improved non-dominated sorting genetic algorithm Ⅱ(NSGA Ⅱ) to solve it directly by means of optimizing multi-objective functions simultaneously.In the improved NSGA Ⅱ,the chaos initialization and a crowding distance based population trimming method were introduced to overcome the prematurity of population,the penalty function was used in handling constraints,and the optimal solution was selected according to the method of fuzzy set theory.Simulation results of three different schemes designed according to various practical engineering requirements show that the improved NSGA Ⅱ can effectively obtain the Pareto optimal solution set under different weighting with outstanding convergence and stability,and provide a new train of thoughts to design homing trajectory of parafoil system.
文摘Optimization of antenna array pattern used in a spaceborne Synthetic Aperture Radar (SAR) system is considered in this study. A robust evolutionary algorithm, Non-dominated Sorting Genetic Algorithms (the improved NSGA-Ⅱ), is applied on a spaceborne SAR antenna pattern design. The system consists of two objective functions with two constraints. Pareto fronts are generated as a result of multi-objective optimization. After being validated by a test problem ZDT4, the algorithms are used to synthesize spaceborne SAR antenna radiation pattern. The good results with low Ambi- guity-to-Signal Ratio (ASR) and high directivity are obtained in the paper.
基金the National Key Research and Development Program of China (No. 2017YFC0209902)。
文摘With the recent boom in unmanned aerial vehicle (UAV) technology, many UAV applications involving complex and risky tasks in military and civilian fields have emerged, such as military strikes and disaster monitoring. Task allocation for UAVs is the process of planning the division of work among UAVs, controlled from ground stations by human operators. This study formulates the UAV task-allocation problem as an extended traveling salesman problem and presents a novel UAV task-allocation model for complex air concentration monitoring tasks. Then, an optimized non-dominated sorting genetic algorithm III (NSGA-III) based on a twin-exclusion mechanism, hierarchical objective-domination operator, and segmented gene encoding (i.e., NSGA-III-TEHOD) is developed to solve complex task-allocation problems involving multiple UAVs, hierarchical objectives, obstacles, and ambient wind. The algorithm is tested in several simulations, and the results demonstrate that the new algorithm outperforms NSGA-III, non-dominated sorting genetic algorithm II (NSGA-II), and genetic algorithm (GA) in terms of efficiency of global convergence and early maturation prevention and is available for the hierarchical objective-optimization problems.
文摘In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II(NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy(E), peak crushing force(Fmax) and mass of the structure(W) as three conflicting objective functions. In the multi-objective optimization problem(MOP), E and Fmax are defined by polynomial models extracted using the software GEvo M based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point(NIP)method and technique for ordering preferences by similarity to ideal solution(TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.
文摘A multi-objective optimization model considering both reliability and maintenance cost is proposed to solve the contradiction between reliability and maintenance cost in high-speed railway catenary system maintenance activities.The non-dominated sorting genetic algorithm 2(NSGA2)is applied to multi-objective optimization,and the optimization result is a set of Pareto solutions.Firstly,multistate failure mode analysis is conducted for the main devices leading to the failure of catenary,and then the reliability and failure mode of the whole catenary system is analyzed.The mathematical relationship between system reliability and maintenance cost is derived considering the existing catenary preventive maintenance mode to improve the reliability of the system.Secondly,an improved NSGA2(INSGA2)is proposed,which strengths population diversity by improving selection operator,and introduces local search strategy to ensure that population distribution is more uniform.The comparison results of the two algorithms before and after improvement on the zero-ductility transition(ZDT)series functions show that the population diversity is better and the solution is more uniform using INSGA2.Finally,the INSGA2 is applied to multi-objective optimization of system reliability and maintenance cost in different maintenance periods.The decision-makers can choose the reasonable solutions as the maintenance plans in the optimization results by weighing the relationship between the system reliability and the maintenance cost.The selected maintenance plans can ensure the lowest maintenance cost while the system reliability is as high as possible.
基金supported by the Technology Innovation Program of the Korea Evaluation Institute of Industrial Technology (KEIT)under the Ministry of Trade,Industry and Energy (MOTIE)of Republic of Korea (20012121)by the National Research Foundation of Korea (NRF)grant funded by the Korea government (MSIT) (2022M3J7A106294)。
文摘Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.
文摘Responsive orbits have exhibited advantages in emergencies for their excellent responsiveness and coverage to targets.Generally,there are several conflicting metrics to trade in the orbit design for responsive space.A special multiple-objective genetic algorithm,namely the Nondominated Sorting Genetic AlgorithmⅡ(NSGAⅡ),is used to design responsive orbits.This algorithm has considered the conflicting metrics of orbits to achieve the optimal solution,including the orbital elements and launch programs of responsive vehicles.Low-Earth fast access orbits and low-Earth repeat coverage orbits,two subtypes of responsive orbits,can be designed using NSGAI under given metric tradeoffs,number of vehicles,and launch mode.By selecting the optimal solution from the obtained Pareto fronts,a designer can process the metric tradeoffs conveniently in orbit design.Recurring to the flexibility of the algorithm,the NSGAI promotes the responsive orbit design further.
基金financially supported by the National Natural Science Foundation of China(No.51376150)
文摘This study proposed a design and optimization strategy for a tandem arranged cascade using the Non-dominated Sorting Genetic Algorithm(NSGA) Ⅱ multi-objective optimization algorithm and Back Propagation(BP) neural network technology. The NASA Stage 35 was employed as the initial bench mark in the present study and five geometric control parameters were working as the optimization parameters aiming to enhance the aerodynamic performance in terms of total pressure rise and efficiency. Results showed that the feasibility and capability of the proposed optimization strategy was successfully examined. In view of the fact that the initial tandem cascade(directly scaling down from NASA Stage 35) cannot guarantee the aerodynamic performance, first optimization trial was conducted to optimize the initial design. Results showed that the optimum can improve the flow quality whereas the separation on the blade is decayed or even eliminated particularly at the tip and root regions. However, compared with the initial tandem design, the enhancement in total pressure ratio(0.47%) and efficiency(1%) are too small to be noticed. Second investigation was particularly emphasizing on a high turning tandem compressor with an increment by 28°. The pressure rise and efficiency were augmented by 1.44% and 2.34%(compared to the initial tandem design), respectively. An important conclusion can be drawn that the optimization strategy is worthy to be used in high turning compressors with a considerable performance improvement.
基金supported by the Shanghai Sailing Program(No.19YF1423700)the National Key Research and Development Program of China(No.2016YFB0900100)the Key Project of Shanghai Science and Technology Committee(No.18DZ1100303).
文摘This paper investigates network partition and edge server placement problem to exploit the benefit of edge computing for distributed state estimation.A constrained many-objective optimization problem is formulated to minimize the cost of edge server deployment,operation,and maintenance,avoid the difference in the partition sizes,reduce the level of coupling between connected partitions,and maximize the inner cohesion of each partition.Capacities of edge server are constrained against underload and overload.To efficiently solve the problem,an improved non-dominated sorting genetic algorithm III(NSGA-III)is developed,with a specifically designed directed mutation operator based on topological characteristics of the partitions to accelerate convergence.Case study validates that the proposed formulations effectively characterize the practical concerns and reveal their trade-offs,and the improved algorithm outperforms existing representative ones for large-scale networks in converging to a near-optimal solution.The optimized result contributes significantly to real-time distributed state estimation.
基金partially supported by the National Key Research and Development Program of China(2016YFA0602403)the National Natural Science Foundation of China(41621061)the International Center for Collaborative Research on Disaster Risk Reduction(ICCRDRR)
文摘This article focuses on decision making for retrofit investment of road networks in order to alleviate severe consequences of roadside tree blowdown during tropical cyclones.The consequences include both the physical damage associated with roadside trees and the functional degradation associated with road networks.A trilevel,two-stage,and multiobjective stochastic mathematical model was developed to dispatch limited resources to retrofit the roadside trees of a road network.In the model,a new metric was designed to evaluate the performance of a road network;resilience was considered from robustness and recovery efficiency of a road network.The proposed model is at least a nondeterministic polynomialtime hardness(NP-hard)problem,which is unlikely to be solved by a polynomial time algorithm.Pareto-optimal solutions for this problem can be obtained by a proposed trilevel algorithm.The random forest method was employed to transform the trilevel algorithm into a singlelevel algorithm in order to decrease the computation burden.Roadside tree retrofit of a provincial highway network on Hainan Island,China was selected as a case area because it suffers severely from tropical cyclones every year,where there is an urgency to upgrade roadside trees against tropical cyclones.We found that roadside tree retrofit investment significantly alleviates the expected economic losses of roadside tree blowdown,at the same time that it promotes robustness and expected recovery efficiency of the road network.
