A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ...A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.展开更多
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc...A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.展开更多
With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions ...With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.展开更多
由于网络传输带宽的限制,在网络传输中可能造成数据的丢失.对于同时具有测量数据和控制数据丢失的一类网络控制系统,研究H_2输出反馈控制问题.数据的丢失采用满足Bernoulli分布的二进制随机变量进行表述.利用矩阵不等式方法给出了H_2动...由于网络传输带宽的限制,在网络传输中可能造成数据的丢失.对于同时具有测量数据和控制数据丢失的一类网络控制系统,研究H_2输出反馈控制问题.数据的丢失采用满足Bernoulli分布的二进制随机变量进行表述.利用矩阵不等式方法给出了H_2动态输出反馈控制器存在的充分条件,所设计的控制器使得闭环系统是均方意义下指数稳定并具有给定的H_2性能.采用SLPMM(Sequentially linear programming matrix method)给出相应的控制器求解算法.最后用数值仿真验证了所提出算法的可行性.展开更多
基金supported by the National Natural Science Foundation of China(70771080)the Special Fund for Basic Scientific Research of Central Colleges+2 种基金China University of Geosciences(Wuhan) (CUG090113)the Research Foundation for Outstanding Young TeachersChina University of Geosciences(Wuhan)(CUGQNW0801)
文摘A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)the Fundamental Research Funds for the Central Universities(K50511700004)
文摘A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.
文摘With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.
文摘由于网络传输带宽的限制,在网络传输中可能造成数据的丢失.对于同时具有测量数据和控制数据丢失的一类网络控制系统,研究H_2输出反馈控制问题.数据的丢失采用满足Bernoulli分布的二进制随机变量进行表述.利用矩阵不等式方法给出了H_2动态输出反馈控制器存在的充分条件,所设计的控制器使得闭环系统是均方意义下指数稳定并具有给定的H_2性能.采用SLPMM(Sequentially linear programming matrix method)给出相应的控制器求解算法.最后用数值仿真验证了所提出算法的可行性.
