中文摘要：

针对双层规划的求解问题，提出一种层次风驱动优化算法．初始化上层优化变量后，首先对下层规划进行求解，满足约束条件的同时，更新下层规划中的空气质点速度和位置；然后，利用风驱动优化算法对上层规划问题进行求解：最后，在优化解集合中，选择上下层规划目标值次序之和最小的解作为最终优化解．实验结果表明，所提出的层次风驱动算法是一种有效的求解双层规划问题的方法．

英文摘要：

A hierarchical wind driven optimization（WDO） method is proposed to solve the bi-level programming problem. Firstly, the WDO method is used to optimize the lower level programming problem after initializing the upper level variables, and the positions and velocities of air parcels in the lower level are updated. Then the solutions of the upper level are optimized by using the WDO method with the constrained conditions. Finally, the solutions with the minimum sum of sequences of the two level results are selected as the final solution from the solution set. The experimental results of the proposed algorithm show the effectiveness of the proposed hierarchical wind driven optimization for solving the bi-level programming problems.