A hierarchical wind driven optimization method for solving the bi-level programming problem

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 the upper level variables are initialized, and the positions and velocities of air parcels in the lower level are updated. Then the solutions of the upper level are optimized by 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.