解非线性两层规划问题的新的遗传算法及全局收敛性

A New Genetic Algorithm for Nonlinear Bilevel Programming Problem and Its Global Convergence

针对两层规划问题本质上的非凸性和不可微性给其数值求解带来极大困难,特别是求非线性两层规划问题的全局最优解,而遗传算法不受这些因素的限制,设计了一种新的有效的遗传算法来解决非线性两层规划问题.该算法充分考虑了两层规划问题的结构特点,使遗传算子更加有效,并且易于产生好的后代.

It is very difficult to determine its solution of bilevel programming problem because of its inherent nonconvexity and nondifferentiability. In particular, it is more difficult to get the global optimal solution of nonlinear bilevel programming problem. But Genetic algorithm has no restrictions on functions involved such as differentiability, convexity and so on. So a new kind of the effective Genetic algorithm for nonlinear bilevel programming problem is presented. This algorithm sufficiently utilizes the specific structure of the problem, such that genetic operator is more effective and better offspring can be produced easily. The theoretical analysis and the numerical simulations show that the new algorithm is used not only simply and easily but also effectively.