在传统输配网分离决策的电能市场出清模式中,会出现节点电价过高和风电资源消纳能力不足等问题,为协调输配电网资源与信息不均衡问题,分析输配协同决策下的电力市场特点,构建了输配协同下输电运营商(Transmission System Operator, TSO...在传统输配网分离决策的电能市场出清模式中,会出现节点电价过高和风电资源消纳能力不足等问题,为协调输配电网资源与信息不均衡问题,分析输配协同决策下的电力市场特点,构建了输配协同下输电运营商(Transmission System Operator, TSO)与配电运营商(Distribution System Operator, DSO)电能市场双层出清模式,下层DSO决策利用KKT条件将其转化为均衡约束,经二阶锥的对偶规划与下层KKT的线性化处理,其转化为带均衡约束的数学规划(Mathematical Program with Equilibrium Constraints, MPEC)单层决策模型。实验结果表明,该模型成功调动输配侧资源,降低了市场出清价格,提高了系统经济性,为电力系统运行和市场协调带来积极影响。展开更多
Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front...Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.展开更多
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
Coordinated investment and operations within renewable portfolio standards is one of the key technologies to meet the renewable energy target and realize the economic operations of the power system.This paper proposes...Coordinated investment and operations within renewable portfolio standards is one of the key technologies to meet the renewable energy target and realize the economic operations of the power system.This paper proposes a unified framework of coordinated planning and financial incentives.Joint investment in renewable energy and energy storage and joint optimization of energy and ancillary services are integrated into a unified framework.Various factors are taken into consideration by the social planner in the centralized electricity market,such as the sitting and sizing of renewable energy and energy storage,charge and discharge efficiency of the energy storage,transmission network constraints,reserve capacity,and financial incentives.This framework provides a tool for the social planner to determine the optimal planning scheme of renewable energy and energy storage.The conclusion derived is that the sum of market revenue and financial subsidies of renewable energy and energy storage is exactly equal to their investment cost which is obtained by the Karush-Kuhn-Tucker(KKT)condition of maximizing social welfare problems.A numerical result based on the modified IEEE-39 bus test system demonstrates the effectiveness of the unified framework.The impact of financial incentives,reserve capacity,and production costs on capital investment are studied.展开更多
A fast converging sparse reconstruction algorithm in ghost imaging is presented. It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex ...A fast converging sparse reconstruction algorithm in ghost imaging is presented. It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex optimization. Tests using experimental data show that, compared with the algorithm of Gradient Projection for Sparse Reconstruction (GPSR), the proposed algorithm yields better results with less computation work.展开更多
In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is ef...In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.展开更多
This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set ...This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.展开更多
In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost para...In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. This model is solved with shortages and the unit cost dependent demand is assumed. Hence the cost parameters are imposed here in fuzzy environment. This model has been solved by Kuhn-Tucker conditions method. The results for the model without shortages are obtained as a particular case. The model is illustrated with numerical example.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
The deployment of Relay Nodes (RNs) in 4G LTE-A networks, mainly originating from the wireless backhaul link, provides an excellent network planning tool to enhance system performance. Better coordination between the ...The deployment of Relay Nodes (RNs) in 4G LTE-A networks, mainly originating from the wireless backhaul link, provides an excellent network planning tool to enhance system performance. Better coordination between the base station and relays to mitigate inter-cell interference becomes an important aspect of achieving the required system performance, not only in the single-cell scenario, but also in multi-cell scenarios. In this paper, we model and analyze two basic approaches for designing a 4G LTE-A tri-sectored cellular system. The approaches are based on Antenna Selection Sectored Relaying (ASSR) and Beam Selection Sectored Relaying (BSSR). The main purpose of the proposed schemes is to enhance system performance by improving the quality of the wireless relay backhaul link. In this technique, antenna selection takes into consideration Non-Line-Of-Sight (NLOS) communication, whereas BSSR considers the case of Line-Of-Sight (LOS) communication using heuristic beam forming approach. The resource allocation problem has also been investigated for relay based cooperative LTE-A trisectored cell in the downlink. The best possible location for relay node in the sector, power allocation and MIMO channel modeling is formulated as an optimization problem with the aim of maximizing the end to end link rate and the Signal to Interference plus Noise Ratio (SINR) of 4G LTE-A systems. Power allocation/optimization has been solved by means of the duality equation of the stationary Karush-Kuhn-Tucker (KKT) cond让ion and is used to derive optimal values for the beam forming vector on both the relay as well as the access link. The performance of the proposed scheme is verified through simulations carried out using MATLAB software. The simulation results show a significant improvement in the SINR, throughput capacity, and coverage area of the 4G LTE-A cell, while guaranteeing better quality of service.展开更多
为激励移动式储能系统(mobile energy storage system,MESS)参与电力市场,并在增加自身盈利的同时,在一定程度上缓解电力阻塞,计及转移效用与不确定性,提出一种MESS日前日内两阶段市场竞标策略。首先,在日前阶段,构建MESS参与电力市场...为激励移动式储能系统(mobile energy storage system,MESS)参与电力市场,并在增加自身盈利的同时,在一定程度上缓解电力阻塞,计及转移效用与不确定性,提出一种MESS日前日内两阶段市场竞标策略。首先,在日前阶段,构建MESS参与电力市场双层投标模型,上层旨在决策MESS的时空分布及功率,下层为电力市场出清模型;其次,在日内阶段,采用多场景随机优化方法模拟、分析日内不确定性,并以日前荷电水平和转移计划为参考,基于模型预测控制方法构建MESS参与日内电力市场双层投标模型,上层旨在动态调整MESS实时功率,下层亦为电力市场出清模型;进一步,利用KKT条件和互补松弛理论将双层竞标模型转化为单层线性优化模型,以实现高效求解;最后,以国内某城域互联电力交通网络设计典型仿真案例。仿真结果表明,所提策略能够实现可调配资源的最大化利用,有效缓解电力系统输电阻塞,促进清洁能源消纳。展开更多
文摘在传统输配网分离决策的电能市场出清模式中,会出现节点电价过高和风电资源消纳能力不足等问题,为协调输配电网资源与信息不均衡问题,分析输配协同决策下的电力市场特点,构建了输配协同下输电运营商(Transmission System Operator, TSO)与配电运营商(Distribution System Operator, DSO)电能市场双层出清模式,下层DSO决策利用KKT条件将其转化为均衡约束,经二阶锥的对偶规划与下层KKT的线性化处理,其转化为带均衡约束的数学规划(Mathematical Program with Equilibrium Constraints, MPEC)单层决策模型。实验结果表明,该模型成功调动输配侧资源,降低了市场出清价格,提高了系统经济性,为电力系统运行和市场协调带来积极影响。
文摘Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.
基金supported by the National Natural Science Foundation of China (60873099)
文摘A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金supported in part by the National Natural Science Foundation of China under Grant 51777126。
文摘Coordinated investment and operations within renewable portfolio standards is one of the key technologies to meet the renewable energy target and realize the economic operations of the power system.This paper proposes a unified framework of coordinated planning and financial incentives.Joint investment in renewable energy and energy storage and joint optimization of energy and ancillary services are integrated into a unified framework.Various factors are taken into consideration by the social planner in the centralized electricity market,such as the sitting and sizing of renewable energy and energy storage,charge and discharge efficiency of the energy storage,transmission network constraints,reserve capacity,and financial incentives.This framework provides a tool for the social planner to determine the optimal planning scheme of renewable energy and energy storage.The conclusion derived is that the sum of market revenue and financial subsidies of renewable energy and energy storage is exactly equal to their investment cost which is obtained by the Karush-Kuhn-Tucker(KKT)condition of maximizing social welfare problems.A numerical result based on the modified IEEE-39 bus test system demonstrates the effectiveness of the unified framework.The impact of financial incentives,reserve capacity,and production costs on capital investment are studied.
基金Supported by the Hi-Tech Research and Development Program of China (No. 2011AA120102)
文摘A fast converging sparse reconstruction algorithm in ghost imaging is presented. It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex optimization. Tests using experimental data show that, compared with the algorithm of Gradient Projection for Sparse Reconstruction (GPSR), the proposed algorithm yields better results with less computation work.
文摘In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.
文摘This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.
文摘In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. This model is solved with shortages and the unit cost dependent demand is assumed. Hence the cost parameters are imposed here in fuzzy environment. This model has been solved by Kuhn-Tucker conditions method. The results for the model without shortages are obtained as a particular case. The model is illustrated with numerical example.
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.
文摘The deployment of Relay Nodes (RNs) in 4G LTE-A networks, mainly originating from the wireless backhaul link, provides an excellent network planning tool to enhance system performance. Better coordination between the base station and relays to mitigate inter-cell interference becomes an important aspect of achieving the required system performance, not only in the single-cell scenario, but also in multi-cell scenarios. In this paper, we model and analyze two basic approaches for designing a 4G LTE-A tri-sectored cellular system. The approaches are based on Antenna Selection Sectored Relaying (ASSR) and Beam Selection Sectored Relaying (BSSR). The main purpose of the proposed schemes is to enhance system performance by improving the quality of the wireless relay backhaul link. In this technique, antenna selection takes into consideration Non-Line-Of-Sight (NLOS) communication, whereas BSSR considers the case of Line-Of-Sight (LOS) communication using heuristic beam forming approach. The resource allocation problem has also been investigated for relay based cooperative LTE-A trisectored cell in the downlink. The best possible location for relay node in the sector, power allocation and MIMO channel modeling is formulated as an optimization problem with the aim of maximizing the end to end link rate and the Signal to Interference plus Noise Ratio (SINR) of 4G LTE-A systems. Power allocation/optimization has been solved by means of the duality equation of the stationary Karush-Kuhn-Tucker (KKT) cond让ion and is used to derive optimal values for the beam forming vector on both the relay as well as the access link. The performance of the proposed scheme is verified through simulations carried out using MATLAB software. The simulation results show a significant improvement in the SINR, throughput capacity, and coverage area of the 4G LTE-A cell, while guaranteeing better quality of service.
文摘为激励移动式储能系统(mobile energy storage system,MESS)参与电力市场,并在增加自身盈利的同时,在一定程度上缓解电力阻塞,计及转移效用与不确定性,提出一种MESS日前日内两阶段市场竞标策略。首先,在日前阶段,构建MESS参与电力市场双层投标模型,上层旨在决策MESS的时空分布及功率,下层为电力市场出清模型;其次,在日内阶段,采用多场景随机优化方法模拟、分析日内不确定性,并以日前荷电水平和转移计划为参考,基于模型预测控制方法构建MESS参与日内电力市场双层投标模型,上层旨在动态调整MESS实时功率,下层亦为电力市场出清模型;进一步,利用KKT条件和互补松弛理论将双层竞标模型转化为单层线性优化模型,以实现高效求解;最后,以国内某城域互联电力交通网络设计典型仿真案例。仿真结果表明,所提策略能够实现可调配资源的最大化利用,有效缓解电力系统输电阻塞,促进清洁能源消纳。
