Abstract:

Nonlinear integer programming problem is a kind of complex optimization problem. The filled function algorithm is an effective method for solving integer programming problems. It involves an auxiliary function to move successively from one local minimum to another better one. At the same time, the method for using only the local minimization algorithm of mature and popular. However, most of the existing filled functions contain one or two interdependent parameters, which makes it difficult to select and adjust the parameters. And the filled function is a composite function of the objective function, and the objective function itself is more complex. Therefore, it is important to construct a filled function which is simple in form, with fewer parameters and good properties. To solve such problems, in this paper, firstly, we construct a new filled function with one parameter, analyze and prove its filling properties; then, the filled function combined with discrete steepest descent method and proposes a new filled function algorithm; finally, the implementation of the algorithms on six test problems show that the algorithm has good effect and is effective and feasible.

Key words: global optimization, non-linear integer programming, filled function method