Parameter-Free Filled Function Approach for Integer Optimization Problems

The filled function method is a deterministic algorithm for solving global optimization problems. Most of the existing filled functions contain parameters, exponential terms or logarithmic terms, which not only have no uniform criteria for the selection of parameters and are more difficult to select, but also exponential and logarithmic may lead to numerical result overflow. In this paper, a new parameter-free filled function without exponential and logarithmic terms is proposed, and the filled function has the same local minimizers as the objective function. First, a new filled function is proposed and its properties are analyzed; after that, a corresponding algorithm for the filled function is designed based on this filled function; finally, numerical experiments are conducted on nine commonly used benchmark functions and the performance is compared with the existing filled functions. The experimental results show that the proposed parameter-free filled function algorithm can make the objective function successfully jump out of the current local minimizer and the global optimal solution can be successfully found with better performance.