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
交流潮流约束下的机组组合问题（AC power flow constrained unit commitment,ACUC）是一个非凸的混合整数非线性规划问题,包含大规模的离散变量,极难求解。该文建立了ACUC的分离式模型,引入部分代理割方法,提出了一种新的求解UC问题的...交流潮流约束下的机组组合问题（AC power flow constrained unit commitment,ACUC）是一个非凸的混合整数非线性规划问题,包含大规模的离散变量,极难求解。该文建立了ACUC的分离式模型,引入部分代理割方法,提出了一种新的求解UC问题的分解式算法。并在原始部分代理割（partial surrogate cuts,PSC）法的基础上,为避免在问题规模扩大时过早陷入局部最优解,结合电力系统特征,提出了引入直流潮流相关约束的改进PSC算法,改善解的质量。通过对6节点、IEEE 39节点和118节点系统的仿真计算验证了方法的有效性和适用性,在与其他算法的对比中突显了速度和精度上的优势。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.
文摘交流潮流约束下的机组组合问题（AC power flow constrained unit commitment,ACUC）是一个非凸的混合整数非线性规划问题,包含大规模的离散变量,极难求解。该文建立了ACUC的分离式模型,引入部分代理割方法,提出了一种新的求解UC问题的分解式算法。并在原始部分代理割（partial surrogate cuts,PSC）法的基础上,为避免在问题规模扩大时过早陷入局部最优解,结合电力系统特征,提出了引入直流潮流相关约束的改进PSC算法,改善解的质量。通过对6节点、IEEE 39节点和118节点系统的仿真计算验证了方法的有效性和适用性,在与其他算法的对比中突显了速度和精度上的优势。
