Studies On Algorithms For The Multi-objective Bi-level Programming

At first we states mainly the multi-follower programming model, and simply introduces how the bi-level programming brings and it's research background, including the extensive applied fields and prospects of the bi-level programming problem and the main research results related to bi-level programming so far, finally we introduce the problem which we are going to deal with and results.Secondly we introduce the part of preparative knowledge. Including the basic theory and knowledge about the linear programming and the bi-level programming, the duality theory and the means of dealing with the linear programming taking advantage of the duality theory, the Kuhn-Tucker conditions, the optimal-conditions of the bi-level programming, and the step method by which we solve the multi-objective single programming problem and so on.In succession we mainly analyses the relations of the optimal solution, the efficient extreme point and the duality problem of subtract problem of multi-objective bi-level linear programming by taking advantage of theorem of the linear programming based on the thinking of converting the Bi-level Programming to the equivalent single programming. The authors present a new algorithm for multi-objective bi-level linear programming. At last the feasibility of the new algorithm is proved by using an example.Subsequently we analyses the relations of the optimal solution, the Descartes product of efficient extreme point sets and the duality problem of subtract problem of multi-follower bi-level linear programming by taking advantage of theorem of the linear programming. Then the authors present a new algorithm for multi-follower bi-level linear programming. At last the feasibility of the new algorithm is proved by using an example.And then we converts problem of multi-objective bi-level programming into problem of multi-objective single programming problem making by taking advantage of Kuhn-Tucker condition of vector optional problem , at the same time we present improving step method to solve the multi-objective single programming problem making to attain The non-inferior solution sets, analyses the relations of the non-inferior solution of problem of multi-objective single programming problem, objective satisfactoriness and the best satisfaction solution of the multi-objective bi-level programming, Then the authors present a new algorithm for multi-objective bi-level programming ; At last the feasibility of the new algorithm is proved by using an example, and comparing to before we attain the better results.Finally discussions and future research plans are concluded.