Study On Correlation Algorithm Of Solving The Optimal Solution Of Some Two-layer Programming

There are a lot of practical problems in our real life, such as traffic programming,multinational trade, logistics distribution, production programming and other issues which are supposed to be characterized by hierarchy system problems. In this complex system, there may be more than one decision makers, who might also control different objective functions. As conventional mathematical programming models can’t solve this kind of hierarchy problems, people gradually shift to the bi-level programming or multi-layer programming. The bi-level programming model is most simple form of multilevel programming model.Compared to the bi-level programming model,multilevel programming model is more complex, while the latter one cannot do without the former model. Therefore, it’s very necessary and meaningful to study bi-level programming in order to make further study of multilevel programming.Both of bi-level linear programming and bi-level nonlinear programming are analyzed in detail. Solving method which is suitable for characteristics of the model are given in this paper according to different characteristics and the scale of solution model.The special particularity of the constraints and objective function of bi-level linear programming problem determines its optimal solution. Inspired from the single-layer linear programming problem, the optimal solution of the bi-level linear programming in the closed region can be found at the vertices of the constraint domain. This paper presents an improved bi-level linear programming pole method, this method only requires the solution of a related pole by pole combination test, whether the lower level problem the duality gap is equal to zero, we can judge whether the pole is the optimal solution. This method is mainly used to avoid the solution of lower and upper optimal objective function in constraint domain. The solution process is simple and feasible,especially for the bi-level linear programming problem when solving the small scale and the method is not so difficult to calculate, fast, of high precision. But with the expanding scale of problem, with the increasing of the number of poles, it takes too long for solving constrained domain pole, so the penalty function method is given in this paper whose basic idea of the vast majority of function is constructed by a penalty inorder to turn the bi-level programming problem, into single layer one. The method is more advantageous to solve the problem of bi-linear programming problems with large scale or constraint conditions.As for bi-level programming problems that the lower level is nonlinear or both lower and upper one are nonlinear, it’s difficult to transform bi-level programming problem into single layer programming problem by using dual problem so the corresponding punishment is constructed in this paper based on KKT optimality conditions and Lagrange function to solve single mathematical programming problem instead of solving a bi-level nonlinear programming problem.The method of solving the optimal solutions for different types of bi-level programming problems are given in this paper by using the pole algorithm and the penalty function method, and the corresponding numerical experiments are tested.