An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, ...An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.展开更多
In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programmi...In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.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 anal...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
In recent years,much attention has been devoted to the development and applications of smart grid technologies,with special emphasis on flexible resources such as distributed generations(DGs),energy storages,active lo...In recent years,much attention has been devoted to the development and applications of smart grid technologies,with special emphasis on flexible resources such as distributed generations(DGs),energy storages,active loads,and electric vehicles(EVs).Demand response(DR) is expected to be an effective means for accommodating the integration of renewable energy generations and mitigating their power output fluctuations.Despite their potential contributions to power system secure and economic operation,uncoordinated operations of these flexible resources may result in unexpected congestions in the distribution system concerned.In addition,the behaviors and impacts of flexible resources are normally highly uncertain and complex in deregulated electricity market environments.In this context,this paper aims to propose a DR based congestion management strategy for smart distribution systems.The general framework and procedures for distribution congestion management is first presented.A bi-level optimization model for the day-ahead congestion management based on the proposed framework is established.Subsequently,the robust optimization approach is introduced to alleviate negative impacts introduced by the uncertainties of DG power outputs and market prices.The economic efficiency and robustness of the proposed congestion management strategy is demonstrated by an actual 0.4 kV distribution system in Denmark.展开更多
文摘An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.
文摘In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.
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.
基金supported by National Basic Research Program of China (973 Program) (No. 2013CB228202)National Natural Science Foundsation of China (No. 51477151)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120101110112)a Project by China Southern Power Grid Company (No. K-GD2014-192)
文摘In recent years,much attention has been devoted to the development and applications of smart grid technologies,with special emphasis on flexible resources such as distributed generations(DGs),energy storages,active loads,and electric vehicles(EVs).Demand response(DR) is expected to be an effective means for accommodating the integration of renewable energy generations and mitigating their power output fluctuations.Despite their potential contributions to power system secure and economic operation,uncoordinated operations of these flexible resources may result in unexpected congestions in the distribution system concerned.In addition,the behaviors and impacts of flexible resources are normally highly uncertain and complex in deregulated electricity market environments.In this context,this paper aims to propose a DR based congestion management strategy for smart distribution systems.The general framework and procedures for distribution congestion management is first presented.A bi-level optimization model for the day-ahead congestion management based on the proposed framework is established.Subsequently,the robust optimization approach is introduced to alleviate negative impacts introduced by the uncertainties of DG power outputs and market prices.The economic efficiency and robustness of the proposed congestion management strategy is demonstrated by an actual 0.4 kV distribution system in Denmark.
