Wu's Method In Multiobjective Programming Problems

The paper deals with the general multi-objective programming problem, and proposes a new method for abtaining the Pareto-optimal solution of a multi-objective optimization problem, which is based on computational algebra and algebraic geometry theory. In the beginning we choose one of the objective functions as the main objective function, and convert the rest of the objective functions into the constraints by introducing parameters. Thus, the multi-objective problem is transformed into a single objective programming problem with parameters. Then we can get the finite kernel by applying the Wu's finite kernel theorem of global optimization of the algebraic systems and obtain the Pareto-optimal solution of multi-objective optimization problem by a brief parametric Analysis. This thesis is composed of three chapters.The first chapter is an introduction, a brief introduction of multi-objective programming background and research progress, Wu Wenjun's method, MMP software and the paper's work.Chapter II to prepare for the knowledge used in the paper, mainly introduces the basic theory of Wu's method and the required knowledge of basic algebra in its applications, and introduces the Wu's characteristic set method in detail. The third chapter, the core of this article, is an application of Wu's method in multi-objective programming. Here, we put forward a new algorithm for solving multi-objective planning, and through linear and nonlinear multi-objective programming examples demonstrate that the method is effective.