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
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。
