Properties Of A Kind Of Multilevel Programming And Algorithms For It

This paper considers a kind of multilevel programming (including the case of linear and nonlinear). Several algorithms are also provided to solve it. The paper consists of four parts. Firstly, we give a simple description of the background of the multilevel programming and some applications of it. Then in the second part, a kind of linear multilevel programming problem (SLMLP) is discussed in detail. Some geometric properties are derived, definition of feasible solution and an equivalence definition are given. We also provide a Branch-and- Bound algorithm to solve it. The numerical result shows that the Branch-and-Bound algorithm works well in solving the medium scale (SL ML?). In the third part, the properties of a kind of nonlinear multilevel programming problem (SNMLP) are analyzed and the feasible solution is defined. Using the theory of reverse convex, a necessary condition at the optimal solution is proven. This gives a new method to solve the multilevel programming. At the same time, we also summarize the algorithms to solve nonlinear bilevel programming and provide a new evolution strategy algorithm to solve (SNMLP). The numerical result shows that it is feasible and efficient. The last part gives a review of the methods of generating linear bilevel programming testing problem and provides some numerical results. These results show that the algorithms we provided are efficient in solving (SLMLP) and (SNMLP).