This review article provides a comprehensive analysis of nesting optimization algorithms in the shipbuilding industry,emphasizing their role in improving material utilization,minimizing waste,and enhancing production ...This review article provides a comprehensive analysis of nesting optimization algorithms in the shipbuilding industry,emphasizing their role in improving material utilization,minimizing waste,and enhancing production efficiency.The shipbuilding process involves the complex cutting and arrangement of steel plates,making the optimization of these operations vital for cost-effectiveness and sustainability.Nesting algorithms are broadly classified into four categories:exact,heuristic,metaheuristic,and hybrid.Exact algorithms ensure optimal solutions but are computationally demanding.In contrast,heuristic algorithms deliver quicker results using practical rules,although they may not consistently achieve optimal outcomes.Metaheuristic algorithms combine multiple heuristics to effectively explore solution spaces,striking a balance between solution quality and computational efficiency.Hybrid algorithms integrate the strengths of different approaches to further enhance performance.This review systematically assesses these algorithms using criteria such as material dimensions,part geometry,component layout,and computational efficiency.The findings highlight the significant potential of advanced nesting techniques to improve material utilization,reduce production costs,and promote sustainable practices in shipbuilding.By adopting suitable nesting solutions,shipbuilders can achieve greater efficiency,optimized resource management,and superior overall performance.Future research directions should focus on integrating machine learning and real-time adaptability to further enhance nesting algorithms,paving the way for smarter,more sustainable manufacturing practices in the shipbuilding industry.展开更多
Wind farm layout optimization is a critical challenge in renewable energy development,especially in regions with complex terrain.Micro-siting of wind turbines has a significant impact on the overall efficiency and eco...Wind farm layout optimization is a critical challenge in renewable energy development,especially in regions with complex terrain.Micro-siting of wind turbines has a significant impact on the overall efficiency and economic viability of wind farm,where the wake effect,wind speed,types of wind turbines,etc.,have an impact on the output power of the wind farm.To solve the optimization problem of wind farm layout under complex terrain conditions,this paper proposes wind turbine layout optimization using different types of wind turbines,the aim is to reduce the influence of the wake effect and maximize economic benefits.The linear wake model is used for wake flow calculation over complex terrain.Minimizing the unit energy cost is taken as the objective function,considering that the objective function is affected by cost and output power,which influence each other.The cost function includes construction cost,installation cost,maintenance cost,etc.Therefore,a bi-level constrained optimization model is established,in which the upper-level objective function is to minimize the unit energy cost,and the lower-level objective function is to maximize the output power.Then,a hybrid evolutionary algorithm is designed according to the characteristics of the decision variables.The improved genetic algorithm and differential evolution are used to optimize the upper-level and lower-level objective functions,respectively,these evolutionary operations search for the optimal solution as much as possible.Finally,taking the roughness of different terrain,wind farms of different scales and different types of wind turbines as research scenarios,the optimal deployment is solved by using the algorithm in this paper,and four algorithms are compared to verify the effectiveness of the proposed algorithm.展开更多
Given the power system balancing challenges induced by high-penetration renewable energy integration,this study systematically reviews international balancing mechanism practices and conducts an in-depth deconstructio...Given the power system balancing challenges induced by high-penetration renewable energy integration,this study systematically reviews international balancing mechanism practices and conducts an in-depth deconstruction of Germany’s balancing group mechanism(BGM).Building on this foundation,this research pioneers the integration of virtual power plants(VPPs)with the BGM in the Chinese context to overcome the limitations of traditional single-entity regulation models in flexibility provision and economic efficiency.A balancing responsibility framework centered on VPPs is innovatively proposed and a regional multi-entity collaboration and bi-level responsibility transfer architecture is constructed.This architecture enables cross-layer coordinated optimization of regional system costs and VPP revenues.The upper layer minimizes regional operational costs,whereas the lower layer enhances the operational revenues of VPPs through dynamic gaming between deviation regulation service income and penalty costs.Compared with traditional centralized regulation models,the proposed method reduces system operational costs by 29.1%in typical regional cases and increases VPP revenues by 24.9%.These results validate its dual optimization of system economics and participant incentives through market mechanisms,providing a replicable theoretical paradigm and practical pathway for designing balancing mechanisms in new power systems.展开更多
Traditional demand response(DR)programs for energy-intensive industries(EIIs)primarily rely on electricity price signals and often overlook carbon emission factors,limiting their effectiveness in supporting lowcarbon ...Traditional demand response(DR)programs for energy-intensive industries(EIIs)primarily rely on electricity price signals and often overlook carbon emission factors,limiting their effectiveness in supporting lowcarbon transitions.To address this challenge,this paper proposes an electricity–carbon integratedDR strategy based on a bi-level collaborative optimization framework that coordinates the interaction between the grid and EIIs.At the upper level,the grid operatorminimizes generation and curtailment costs by optimizing unit commitment while determining real-time electricity prices and dynamic carbon emission factors.At the lower level,EIIs respond to these dual signals by minimizing their combined electricity and carbon trading costs,considering their participation in medium-and long-term electricity markets,day-ahead spot markets,and carbon emissions trading schemes.The model accounts for direct and indirect carbon emissions,distributed photovoltaic(PV)generation,and battery energy storage systems.This interaction is structured as a Stackelberg game,where the grid acts as the leader and EIIs as followers,enabling dynamic feedback between pricing signals and load response.Simulation studies on an improved IEEE 30-bus system,with a cement plant as a representative user form EIIs,show that the proposed strategy reduces user-side carbon emissions by 7.95% and grid-side generation cost by 4.66%,though the user’s energy cost increases by 7.80% due to carbon trading.Theresults confirmthat the joint guidance of electricity and carbon prices effectively reshapes user load profiles,encourages peak shaving,and improves PV utilization.This coordinated approach not only achieves emission reduction and cost efficiency but also offers a theoretical and practical foundation for integrating carbon pricing into demand-side energy management in future low-carbon power systems.展开更多
Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The ai...Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.展开更多
The design of Human Occupied Vehicle （HOV） is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience depend...The design of Human Occupied Vehicle （HOV） is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience dependence and improve the design, a new Multidisciplinary Design Optimization （MDO） method ＂Bi-Level Integrated System Collaborative Optimization （BLISCO）＂ is applied to the conceptual design of an HOV, which consists of hull module, resistance module, energy module, structure module, weight module, and the stability module. This design problem is defined by 21 design variables and 23 constraints, and its objective is to maximize the ratio of payload to weight. The results show that the general performance of the HOV can be greatly improved by BLISCO.展开更多
In silico approaches for metabolites optimization have been derived from the flood of sequenced and annotated genomes. However, there exist still numerous degrees of freedom in terms of optimization algorithm approach...In silico approaches for metabolites optimization have been derived from the flood of sequenced and annotated genomes. However, there exist still numerous degrees of freedom in terms of optimization algorithm approaches that can be exploited in order to enhance yield of processes which are based on biological reactions. Here, we propose an evolutionary approach aiming to suggest different mutant for augmenting ethanol yield using glycerol as substrate in Escherichia coli. We found that this algorithm, even though is far from providing the global optimum, is able to uncover genes that a global optimizer would be incapable of. By over-expressing accB, eno, dapE, and accA mutants in ethanol production was augmented up to 2 fold compared to its counterpart E. coli BW25113.展开更多
Two-Dimensional Irregular Strip Packing Problem is a classical cutting/packing problem. The problem is to assign, a set of 2-D irregular-shaped items to a rectangular sheet. The width of the sheet is fixed, while its ...Two-Dimensional Irregular Strip Packing Problem is a classical cutting/packing problem. The problem is to assign, a set of 2-D irregular-shaped items to a rectangular sheet. The width of the sheet is fixed, while its length is extendable and has to be minimized. A sequence-based approach is developed and tested. The approach involves two phases;optimization phase and placement phase. The optimization phase searches for the packing sequence that would lead to an optimal (or best) solution when translated to an actual pattern through the placement phase. A Particle Swarm Optimization algorithm is applied in this optimization phase. Regarding the placement phase, a combined algorithm based on traditional placement methods is developed. Competitive results are obtained, where the best solutions are found to be better than, or at least equal to, the best known solutions for 10 out of 31 benchmark data sets. A Statistical Design of Experiments and a random generator of test problems are also used to characterize the performance of the entire algorithm.展开更多
Since COVID-19 was declared as a pandemic in March 2020,the world’s major preoccupation has been to curb it while preserving the economy and reducing unemployment.This paper uses a novel Bi-Level Dynamic Optimal Cont...Since COVID-19 was declared as a pandemic in March 2020,the world’s major preoccupation has been to curb it while preserving the economy and reducing unemployment.This paper uses a novel Bi-Level Dynamic Optimal Control model(BLDOC)to coordinate control between COVID-19 and unemployment.The COVID-19 model is the upper level while the unemployment model is the lower level of the bi-level dynamic optimal control model.The BLDOC model’s main objectives are to minimize the number of individuals infected with COVID-19 and to minimize the unemployed individuals,and at the same time minimizing the cost of the containment strategies.We use the modified approximation Karush–Kuhn–Tucker(KKT)conditions with the Hamiltonian function to handle the bi-level dynamic optimal control model.We consider three control variables:The first control variable relates to government measures to curb the COVID-19 pandemic,i.e.,quarantine,social distancing,and personal protection;and the other two control variables relate to government interventions to reduce the unemployment rate,i.e.,employment,making individuals qualified,creating new jobs reviving the economy,reducing taxes.We investigate four different cases to verify the effect of control variables.Our results indicate that rather than focusing exclusively on only one problem,we need a balanced trade-off between controlling each.展开更多
For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust op...For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust optimization model is constructed with both the center and halfwidth of the most important mechanical performance index described as objective functions and the other requirements on the mechanical performance indices described as constraint functions. To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed. The math?ematical formulae for calculating the feasibility and objective robustness indices and the robustness?based preferential guidelines are proposed for directly ranking various design vectors, which is realized by an algorithm integrating Kriging and nested genetic algorithm. The validity of the proposed method and its superiority to present interval optimization approaches are demonstrated by a numerical example. The robust optimization of the upper beam in a high?speed press with interval material properties demonstrated the applicability and effectiveness of the proposed method in engineering.展开更多
In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective func...In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective function is a classical strongly convex function which may not be smooth.Motivated by the smoothing approaches,we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem.Under some mild conditions,we obtain the convergence rate of the generated sequence,and then based on the analysis framework of S-FISTA,we show the global convergence rate of the proposed algorithm.展开更多
Rapid development of power-to-gas technology provides a potential solution for virtual power plants(VPP)to achieve near-zero carbon emissions.In this paper,a bi-level hybrid stochastic/robust optimization model is pro...Rapid development of power-to-gas technology provides a potential solution for virtual power plants(VPP)to achieve near-zero carbon emissions.In this paper,a bi-level hybrid stochastic/robust optimization model is proposed for low-carbon VPP day-ahead dispatch considering uncertainties from renewable generation and market prices.First,Karush-Kuhn-Tucker optimality conditions are employed to convert the bi-level model to a single level one.Next,the single level problem is decomposed into a master problem in the base case and several subproblems in extreme cases,which can then be solved by using the column-and-constraint generation algorithm iteratively.Numerical results indicate the proposed approach can effectively satisfy system operation constraints including the carbon emission limit,enhance computational efficiency and algorithm robustness compared with the stochastic method,and improve VPP revenue compared with the robust method.展开更多
The high-energy consumption and high construction density of 5G base stations have greatly increased the demand for backup energy storage batteries.To maximize overall benefits for the investors and operators of base ...The high-energy consumption and high construction density of 5G base stations have greatly increased the demand for backup energy storage batteries.To maximize overall benefits for the investors and operators of base station energy storage,we proposed a bi-level optimization model for the operation of the energy storage,and the planning of 5G base stations considering the sleep mechanism.A multi-base station cooperative system composed of 5G acer stations was considered as the research object,and the outer goal was to maximize the net profit over the complete life cycle of the energy storage.Furthermore,the power and capacity of the energy storage configuration were optimized.The inner goal included the sleep mechanism of the base station,and the optimization of the energy storage charging and discharging strategy,for minimizing the daily electricity expenditure of the 5G base station system.Additionally,genetic algorithm and mixed integer programming were used to solve the bi-level optimization model,analyze the numerical example test comparison of the three types of batteries and the net income of the configuration,and finally verify the validity of the model.Furthermore,the sleep mechanism,the charging and discharging strategy for energy consumption,and the economic benefits for the operators were investigated to provide reference for the 5G base station energy storage configuration.展开更多
For the purpose of dealing with uncertainty factors in engineering optimization problems,this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation.The method analyz...For the purpose of dealing with uncertainty factors in engineering optimization problems,this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation.The method analyzes the effect of uncertain factors to objective and constraints functions,and then the maximal variations to a solution are calculated.In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term;the maximal variation of objective function is taken as a robust index to a solution;linear physical programming is used to adjust the values of quality characteristic and quality variation,and then a bi-level mathematical robust optimal model is constructed.The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions.To demonstrate the proposed method,the design of the two-bar structure acted by concentrated load is presented.In the example the robustness of the normal stress,feasibility of the total volume and the buckling stress are studied.The robust optimal design results show that in the condition of maintaining feasibility robustness,the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.展开更多
This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a ce...This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.展开更多
In order to address the optimal distance toll design problem for cordon-based congestion pricing incorporating the issue of equity,this paper presents a toll user equilibrium( TUE) model based on a transformed network...In order to address the optimal distance toll design problem for cordon-based congestion pricing incorporating the issue of equity,this paper presents a toll user equilibrium( TUE) model based on a transformed network with elastic demand,to evaluate any given toll charge function. A bi-level programming model is developed for determining the optimal toll levels,with the TUE being represented at the lower level.The upper level optimizes the total equity level over the transport network,represented by the Gini coefficient,where a constraint is imposed to the total travel impedance of each OD pair after the levy. A genetic algorithm( GA) is implemented to solve the bi-level model,which is verified by a numerical example.展开更多
文摘This review article provides a comprehensive analysis of nesting optimization algorithms in the shipbuilding industry,emphasizing their role in improving material utilization,minimizing waste,and enhancing production efficiency.The shipbuilding process involves the complex cutting and arrangement of steel plates,making the optimization of these operations vital for cost-effectiveness and sustainability.Nesting algorithms are broadly classified into four categories:exact,heuristic,metaheuristic,and hybrid.Exact algorithms ensure optimal solutions but are computationally demanding.In contrast,heuristic algorithms deliver quicker results using practical rules,although they may not consistently achieve optimal outcomes.Metaheuristic algorithms combine multiple heuristics to effectively explore solution spaces,striking a balance between solution quality and computational efficiency.Hybrid algorithms integrate the strengths of different approaches to further enhance performance.This review systematically assesses these algorithms using criteria such as material dimensions,part geometry,component layout,and computational efficiency.The findings highlight the significant potential of advanced nesting techniques to improve material utilization,reduce production costs,and promote sustainable practices in shipbuilding.By adopting suitable nesting solutions,shipbuilders can achieve greater efficiency,optimized resource management,and superior overall performance.Future research directions should focus on integrating machine learning and real-time adaptability to further enhance nesting algorithms,paving the way for smarter,more sustainable manufacturing practices in the shipbuilding industry.
基金supported by the National Natural Science Foundation of China[Grant No.12461035]Qinghai University Students Innovative Training Program Project[2024-QX-57].
文摘Wind farm layout optimization is a critical challenge in renewable energy development,especially in regions with complex terrain.Micro-siting of wind turbines has a significant impact on the overall efficiency and economic viability of wind farm,where the wake effect,wind speed,types of wind turbines,etc.,have an impact on the output power of the wind farm.To solve the optimization problem of wind farm layout under complex terrain conditions,this paper proposes wind turbine layout optimization using different types of wind turbines,the aim is to reduce the influence of the wake effect and maximize economic benefits.The linear wake model is used for wake flow calculation over complex terrain.Minimizing the unit energy cost is taken as the objective function,considering that the objective function is affected by cost and output power,which influence each other.The cost function includes construction cost,installation cost,maintenance cost,etc.Therefore,a bi-level constrained optimization model is established,in which the upper-level objective function is to minimize the unit energy cost,and the lower-level objective function is to maximize the output power.Then,a hybrid evolutionary algorithm is designed according to the characteristics of the decision variables.The improved genetic algorithm and differential evolution are used to optimize the upper-level and lower-level objective functions,respectively,these evolutionary operations search for the optimal solution as much as possible.Finally,taking the roughness of different terrain,wind farms of different scales and different types of wind turbines as research scenarios,the optimal deployment is solved by using the algorithm in this paper,and four algorithms are compared to verify the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(no.72471087)Beijing Nova Program(no.20250484853)+1 种基金Beijing Natural Science Foundation(no.9242015)National Social Science Foundation of China(no.24&ZD111).
文摘Given the power system balancing challenges induced by high-penetration renewable energy integration,this study systematically reviews international balancing mechanism practices and conducts an in-depth deconstruction of Germany’s balancing group mechanism(BGM).Building on this foundation,this research pioneers the integration of virtual power plants(VPPs)with the BGM in the Chinese context to overcome the limitations of traditional single-entity regulation models in flexibility provision and economic efficiency.A balancing responsibility framework centered on VPPs is innovatively proposed and a regional multi-entity collaboration and bi-level responsibility transfer architecture is constructed.This architecture enables cross-layer coordinated optimization of regional system costs and VPP revenues.The upper layer minimizes regional operational costs,whereas the lower layer enhances the operational revenues of VPPs through dynamic gaming between deviation regulation service income and penalty costs.Compared with traditional centralized regulation models,the proposed method reduces system operational costs by 29.1%in typical regional cases and increases VPP revenues by 24.9%.These results validate its dual optimization of system economics and participant incentives through market mechanisms,providing a replicable theoretical paradigm and practical pathway for designing balancing mechanisms in new power systems.
基金supported by the Science and Technology Project of Yunnan Power Grid Co.,Ltd.under Grant No.YNKJXM20222410.
文摘Traditional demand response(DR)programs for energy-intensive industries(EIIs)primarily rely on electricity price signals and often overlook carbon emission factors,limiting their effectiveness in supporting lowcarbon transitions.To address this challenge,this paper proposes an electricity–carbon integratedDR strategy based on a bi-level collaborative optimization framework that coordinates the interaction between the grid and EIIs.At the upper level,the grid operatorminimizes generation and curtailment costs by optimizing unit commitment while determining real-time electricity prices and dynamic carbon emission factors.At the lower level,EIIs respond to these dual signals by minimizing their combined electricity and carbon trading costs,considering their participation in medium-and long-term electricity markets,day-ahead spot markets,and carbon emissions trading schemes.The model accounts for direct and indirect carbon emissions,distributed photovoltaic(PV)generation,and battery energy storage systems.This interaction is structured as a Stackelberg game,where the grid acts as the leader and EIIs as followers,enabling dynamic feedback between pricing signals and load response.Simulation studies on an improved IEEE 30-bus system,with a cement plant as a representative user form EIIs,show that the proposed strategy reduces user-side carbon emissions by 7.95% and grid-side generation cost by 4.66%,though the user’s energy cost increases by 7.80% due to carbon trading.Theresults confirmthat the joint guidance of electricity and carbon prices effectively reshapes user load profiles,encourages peak shaving,and improves PV utilization.This coordinated approach not only achieves emission reduction and cost efficiency but also offers a theoretical and practical foundation for integrating carbon pricing into demand-side energy management in future low-carbon power systems.
文摘Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.
基金financially supported by the National Natural Science Foundation of China(Grant No.51109132)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110073120015)
文摘The design of Human Occupied Vehicle （HOV） is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience dependence and improve the design, a new Multidisciplinary Design Optimization （MDO） method ＂Bi-Level Integrated System Collaborative Optimization （BLISCO）＂ is applied to the conceptual design of an HOV, which consists of hull module, resistance module, energy module, structure module, weight module, and the stability module. This design problem is defined by 21 design variables and 23 constraints, and its objective is to maximize the ratio of payload to weight. The results show that the general performance of the HOV can be greatly improved by BLISCO.
基金the support of the National BioResource Project(NIG,Japan):E.coli Strain for kindly providing us with the Keio Collection using for our experimental sectionAlso this work is funded by Vicerrectoria de investigaciones at Universidad de los Andes.
文摘In silico approaches for metabolites optimization have been derived from the flood of sequenced and annotated genomes. However, there exist still numerous degrees of freedom in terms of optimization algorithm approaches that can be exploited in order to enhance yield of processes which are based on biological reactions. Here, we propose an evolutionary approach aiming to suggest different mutant for augmenting ethanol yield using glycerol as substrate in Escherichia coli. We found that this algorithm, even though is far from providing the global optimum, is able to uncover genes that a global optimizer would be incapable of. By over-expressing accB, eno, dapE, and accA mutants in ethanol production was augmented up to 2 fold compared to its counterpart E. coli BW25113.
文摘Two-Dimensional Irregular Strip Packing Problem is a classical cutting/packing problem. The problem is to assign, a set of 2-D irregular-shaped items to a rectangular sheet. The width of the sheet is fixed, while its length is extendable and has to be minimized. A sequence-based approach is developed and tested. The approach involves two phases;optimization phase and placement phase. The optimization phase searches for the packing sequence that would lead to an optimal (or best) solution when translated to an actual pattern through the placement phase. A Particle Swarm Optimization algorithm is applied in this optimization phase. Regarding the placement phase, a combined algorithm based on traditional placement methods is developed. Competitive results are obtained, where the best solutions are found to be better than, or at least equal to, the best known solutions for 10 out of 31 benchmark data sets. A Statistical Design of Experiments and a random generator of test problems are also used to characterize the performance of the entire algorithm.
基金The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research Group No.RG-1441-309.
文摘Since COVID-19 was declared as a pandemic in March 2020,the world’s major preoccupation has been to curb it while preserving the economy and reducing unemployment.This paper uses a novel Bi-Level Dynamic Optimal Control model(BLDOC)to coordinate control between COVID-19 and unemployment.The COVID-19 model is the upper level while the unemployment model is the lower level of the bi-level dynamic optimal control model.The BLDOC model’s main objectives are to minimize the number of individuals infected with COVID-19 and to minimize the unemployed individuals,and at the same time minimizing the cost of the containment strategies.We use the modified approximation Karush–Kuhn–Tucker(KKT)conditions with the Hamiltonian function to handle the bi-level dynamic optimal control model.We consider three control variables:The first control variable relates to government measures to curb the COVID-19 pandemic,i.e.,quarantine,social distancing,and personal protection;and the other two control variables relate to government interventions to reduce the unemployment rate,i.e.,employment,making individuals qualified,creating new jobs reviving the economy,reducing taxes.We investigate four different cases to verify the effect of control variables.Our results indicate that rather than focusing exclusively on only one problem,we need a balanced trade-off between controlling each.
基金Supported by National Natural Science Foundation of China(Grant Nos.51775491,51475417,U1608256,51405433)
文摘For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust optimization model is constructed with both the center and halfwidth of the most important mechanical performance index described as objective functions and the other requirements on the mechanical performance indices described as constraint functions. To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed. The math?ematical formulae for calculating the feasibility and objective robustness indices and the robustness?based preferential guidelines are proposed for directly ranking various design vectors, which is realized by an algorithm integrating Kriging and nested genetic algorithm. The validity of the proposed method and its superiority to present interval optimization approaches are demonstrated by a numerical example. The robust optimization of the upper beam in a high?speed press with interval material properties demonstrated the applicability and effectiveness of the proposed method in engineering.
文摘In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective function is a classical strongly convex function which may not be smooth.Motivated by the smoothing approaches,we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem.Under some mild conditions,we obtain the convergence rate of the generated sequence,and then based on the analysis framework of S-FISTA,we show the global convergence rate of the proposed algorithm.
基金supported by the Shenzhen Science and Technology Program(JCYJ20210324130811031)Tsinghua Shenzhen International Graduate School Interdisciplinary Research and Innovation Fund(JC2021004).
文摘Rapid development of power-to-gas technology provides a potential solution for virtual power plants(VPP)to achieve near-zero carbon emissions.In this paper,a bi-level hybrid stochastic/robust optimization model is proposed for low-carbon VPP day-ahead dispatch considering uncertainties from renewable generation and market prices.First,Karush-Kuhn-Tucker optimality conditions are employed to convert the bi-level model to a single level one.Next,the single level problem is decomposed into a master problem in the base case and several subproblems in extreme cases,which can then be solved by using the column-and-constraint generation algorithm iteratively.Numerical results indicate the proposed approach can effectively satisfy system operation constraints including the carbon emission limit,enhance computational efficiency and algorithm robustness compared with the stochastic method,and improve VPP revenue compared with the robust method.
基金supported by the State Grid Science and Technology Project(KJ21-1-56).
文摘The high-energy consumption and high construction density of 5G base stations have greatly increased the demand for backup energy storage batteries.To maximize overall benefits for the investors and operators of base station energy storage,we proposed a bi-level optimization model for the operation of the energy storage,and the planning of 5G base stations considering the sleep mechanism.A multi-base station cooperative system composed of 5G acer stations was considered as the research object,and the outer goal was to maximize the net profit over the complete life cycle of the energy storage.Furthermore,the power and capacity of the energy storage configuration were optimized.The inner goal included the sleep mechanism of the base station,and the optimization of the energy storage charging and discharging strategy,for minimizing the daily electricity expenditure of the 5G base station system.Additionally,genetic algorithm and mixed integer programming were used to solve the bi-level optimization model,analyze the numerical example test comparison of the three types of batteries and the net income of the configuration,and finally verify the validity of the model.Furthermore,the sleep mechanism,the charging and discharging strategy for energy consumption,and the economic benefits for the operators were investigated to provide reference for the 5G base station energy storage configuration.
基金supported by Program for New Century Excellent Talents in University,Ministry of Education of China(Grant No.NCET-05-0285)
文摘For the purpose of dealing with uncertainty factors in engineering optimization problems,this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation.The method analyzes the effect of uncertain factors to objective and constraints functions,and then the maximal variations to a solution are calculated.In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term;the maximal variation of objective function is taken as a robust index to a solution;linear physical programming is used to adjust the values of quality characteristic and quality variation,and then a bi-level mathematical robust optimal model is constructed.The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions.To demonstrate the proposed method,the design of the two-bar structure acted by concentrated load is presented.In the example the robustness of the normal stress,feasibility of the total volume and the buckling stress are studied.The robust optimal design results show that in the condition of maintaining feasibility robustness,the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.
文摘This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61374195 and 71501038)the Fundamental Research Funds for the Central Universities(Grant No.2242015R30036)the Natural Science Foundation of Jiangsu Province in China(Grant No.BK20150603)
文摘In order to address the optimal distance toll design problem for cordon-based congestion pricing incorporating the issue of equity,this paper presents a toll user equilibrium( TUE) model based on a transformed network with elastic demand,to evaluate any given toll charge function. A bi-level programming model is developed for determining the optimal toll levels,with the TUE being represented at the lower level.The upper level optimizes the total equity level over the transport network,represented by the Gini coefficient,where a constraint is imposed to the total travel impedance of each OD pair after the levy. A genetic algorithm( GA) is implemented to solve the bi-level model,which is verified by a numerical example.
