Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
温室气体排放权交易将给电力系统优化运行带来新的挑战。基于总量管制和排放交易(cap and trade)模式,提出计及排放权交易的机组组合(emission trading unit commitment,ETUC)模型。该模型不仅考虑了排放配额约束,而且考虑了排放权的交...温室气体排放权交易将给电力系统优化运行带来新的挑战。基于总量管制和排放交易(cap and trade)模式,提出计及排放权交易的机组组合(emission trading unit commitment,ETUC)模型。该模型不仅考虑了排放配额约束,而且考虑了排放权的交易。基于二阶锥多面体近似法,提出一种求解ETUC问题的新方法。该方法将ETUC问题转化为混合整数二阶锥规划(mixed integersecond-order cone programming,MISOCP)模型,然后利用多面体近似法将二阶锥约束转化为线性约束,形成解决ETUC问题的混合整数线性规划(mixed integer linear programming,MILP)模型。在10—100机组24时段系统上进行仿真计算,验证所提模型和方法的正确性和有效性。展开更多
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
文摘温室气体排放权交易将给电力系统优化运行带来新的挑战。基于总量管制和排放交易(cap and trade)模式,提出计及排放权交易的机组组合(emission trading unit commitment,ETUC)模型。该模型不仅考虑了排放配额约束,而且考虑了排放权的交易。基于二阶锥多面体近似法,提出一种求解ETUC问题的新方法。该方法将ETUC问题转化为混合整数二阶锥规划(mixed integersecond-order cone programming,MISOCP)模型,然后利用多面体近似法将二阶锥约束转化为线性约束,形成解决ETUC问题的混合整数线性规划(mixed integer linear programming,MILP)模型。在10—100机组24时段系统上进行仿真计算,验证所提模型和方法的正确性和有效性。
