Branch And Bound Algorithm Of Mixed Integer Nonlinear Programming Problem

This paper mainly studies the method of solving nonlinear integer programming problems and mixed integer nonlinear programming problem. The text is divided into two parts, the main contents are as follows:First,a cutting plane branch-and-bound method is proposed for a class of nonlinear integer programming problems. In this method, the nonlinear feasible region are linearization by the cutting plane equation. At the same time, determining the feasible direction on the subproblems and generating the cutting plane,which can cut off feasible region of no integer solutions and narrow the feasible region.This method can reduce the number of branches.Second, the decomposition method and the convex relaxation method are proposed for mixed integer nonlinear programming problem. In this method, the original problem ues convex relaxation techniques and convert into the dual problem.Then the dual problem is divided into several small problems by useing separation thought.These small problems are solved with dual cutting plane method.This method can simplify the problem, reduce the number of branches and the computation time.The convergence is analyzed and proved.