Research On Solving Nonlinear Bi-level Programming Method Based On Dynamic Differential Evolution Algorithm

The bi-level programming problem(BLPP) is a kind of system optimization problems with hierarchical structure. Because this model can describe the actual system of class relations and more fully reflect the decision maker will have very important theoretical significance and application background in many fields like economy, military, transportation, power engineering and etc.. Firstly, the concept and development of bi-level programming are summarized, on the upper layer and the lower layer optimization relation, the principle and model of problem are introduced, discuss its complexity and reach the optimal conditions, some feasible methods and algorithms of the present problem solving bi-level programming, and these methods and the advantages and disadvantages of the algorithm the analysis, finally introduces the classical test functions of bi-level programming problem set.Because of hierarchical heuristic algorithm for solving nonlinear bi-level programming problems use universality and have advantages,the paper put forward solve the bi-level programming problem by differential evolution algorithm, and analyze the feasibility. Briefly introduces the principle of differential evolution algorithm, due to the shortage of the original differential evolution algorithm for static population renewal, leads to the dynamic concept of difference evolution algorithm and analyzed the dynamic performance of differential evolution algorithm.For nonlinear bi-level programming problems in hierarchical nested structure, this paper proposes a nested nonlinear programming dynamic differential evolution algorithm.In this optimization problem,upper level and lower level are both using dynamic differential evolution algorithm. The upper and lower constraints using augmented penalty function processing,numerical simulation experiment of 24 classical test functions, robustness and convergence rate of the test algorithm, and compared with existing algorithms. The experimental results show that the algorithm is an effective method for solving nonlinear bi-level programming.Because of the nesting principle, we must use a lower level heuristic algorithm to get the lower optimal solution for each upper layer, and the computation cost is very large. On the other hand, if the lower heuristic algorithm falls into the local optimal solution, the corresponding upper level global optimal solution can not be got. Therefore, for a class of upper function and constraint functions is not convex and differentiable requirements and lower level functions can be micro and convex nonlinear bi-level programming problem, first of all through the KKT conditions will bi-level programming problem conversion for monolayer constrained nonlinear programming problems, combined with non fixed multi segment mapping penalty function method and exact penalty function method with no constraints on the constraint conditions, and then put forward a kind of improved dynamic differential evolution algorithm optimization of unconstrained optimization problems are solved. 8 test cases are calculated and compared with the existing algorithms. The test results show that the proposed method is an effective method to solve this kind of bi-level programming problem.In order to improve the algorithm's adaptability, while avoiding the large amount of calculation in the nesting algorithm is proposed based on k-NN nearest neighbor algorithm of agent model based on lower level optimization problem between the approximate relationship. In order to improve the efficiency of the algorithm. In order to improve the accuracy of the surrogate model. Bycombining SQP local search strategy of agent model prediction value for local optimization, and compared with the algorithms in the literature. Experimental results show that the algorithm can improve the prediction accuracy of the surrogate model. And by the comparison in general nested algorithm calculated cost is greatly reduced. It is proved that this algorithm is an effective method to solve the general nonlinear bi-level programming.