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
针对常规智慧建筑群协同运行过程中存在的数据泄露问题,提出一种基于含均衡约束的均衡问题(equilibrium problem with equilibrium constraints,EPEC)的交互框架,在只共享边界信息的场景下实现智慧建筑群功率协同。搭建了只共享边界信...针对常规智慧建筑群协同运行过程中存在的数据泄露问题,提出一种基于含均衡约束的均衡问题(equilibrium problem with equilibrium constraints,EPEC)的交互框架,在只共享边界信息的场景下实现智慧建筑群功率协同。搭建了只共享边界信息的建筑群双层优化模型,并通过KKT(Karush-Kuhn-Tucker)条件将其转化为带均衡约束的数学规划问题(mathematical program with equilibrium constraints,MPEC)模型,同时采用大M法和强对偶定理对其进行线性化处理,降低求解复杂度。由于建筑群中各个建筑的优化问题相互独立,进一步将多个建筑的MPEC模型联立,形成EPEC模型,并采用对角化算法和双层迭代法实现整体模型的求解。算例结果验证了模型及求解框架的合理性和有效性,在保护建筑用能隐私的前提下实现了建筑群功率协同优化运行。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
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.
文摘针对常规智慧建筑群协同运行过程中存在的数据泄露问题,提出一种基于含均衡约束的均衡问题(equilibrium problem with equilibrium constraints,EPEC)的交互框架,在只共享边界信息的场景下实现智慧建筑群功率协同。搭建了只共享边界信息的建筑群双层优化模型,并通过KKT(Karush-Kuhn-Tucker)条件将其转化为带均衡约束的数学规划问题(mathematical program with equilibrium constraints,MPEC)模型,同时采用大M法和强对偶定理对其进行线性化处理,降低求解复杂度。由于建筑群中各个建筑的优化问题相互独立,进一步将多个建筑的MPEC模型联立,形成EPEC模型,并采用对角化算法和双层迭代法实现整体模型的求解。算例结果验证了模型及求解框架的合理性和有效性,在保护建筑用能隐私的前提下实现了建筑群功率协同优化运行。
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.
