Based On The Characteristics Of Wu Algorithm Of Integer Programming Problem

Wu’s method, also know as the characteristic setting method, different fromGrobner basis method, fully using the zero set of perspectives to deal with problems,meanwhile, owing to the triangular equations, it is determined by the characteristics ofcolumn is a triangular column form, maintaining its original geometricproperties.Therefore in theorem proving, polynomial equation solving and many otheraspects of a Groebner basis method is more effective. Now Wu’s characteristic methodin mathematical theory, theoretical physics, robotics, and many other fields have beenwidely used.Wu’s method can be for our integer programming problem the answer, althoughearly research is about the research work in this field, but for nonlinear integerprogramming problem it is not effective. However Wu’s characteristic method can solveit. The reason is that Groebner basis algorithm and Wu’s characteristic method cansolve nonlinear algebraic equations with an effective way. With the mathematical andcomputer tools maple and the development of MMP of which the package wsolve, wecould get a Wu’s characteristic set with the help of computer. The main task of thispaper is solving integer programming problem with Wu’s characteristic method.This paper is mainly based on Wu’s characteristic set method to solve the0-1integer programming problem and gives the algorithm and examples(under Maplesystem, realize the algorithm). Compared with Groebner basis method we can draw aconclusion that Wu’s characteristic set method is more effective.On the other hand, the paper introduced the Groebner basis method to solve integerprogramming(un0-1) and we give a Wu’s characteristic set method similarly (no needto calculate the Groebner base), through examples’ comparison shows the improvedalgorithm is effective in a certain range.