Filled Function Algorithms For Nonlinear Integer Programming Problems

The filled function method is an effective optimization method for solving global optimization problems,is a deterministic algorithm.It is familiar with the principle of simple algorithm and only need to use mature local minimization algorithm.Throughout the development process of the filled function,the key of this algorithm lies in the construction of a kind of simple form,filled function with few parameters and easy to adjust and has good properties.Therefore,the filled function structure and algorithm of innovation is particularly important.In this paper,some improvements and innovations are made on the filled function algorithm for nonlinear integer programming problems,which aim to deepen the theory and improve the effect of the algorithm.The main work is as follows:(1)According to the basic idea of the filling function,a single parameter filled function is constructed for the shortcomings such as the parameter is difficult,the parameter selection is difficult and the adjustment is cumbersome.When the parameter is large enough,the numerical results show that the algorithm is effective;(2)In this paper,we construct a single parameter filled function based on neighborhood search.The improved discrete neighborhood search algorithm is added to the traditional fill function algorithm to avoid the numerical result overflow.Based on the new algorithm,the numerical results show that the algorithm is effective.(3)In this paper,on the basis of the improved filled function definition,constructs a parameterless filled function,not only meet the filling properties,and simply minimizing an objective function,greatly reduces the computation;(4)The previously discussed are unconstrained or box set constraint integer programming problem,then constrained integer programming problem,the idea of penalty function combined with filled function algorithm,discuss the properties of this method,a new algorithm for the design of numerical experiments show that this method is effective and feasible to handle constrained integer programming.