A novel class of single-parameter filled functions for nonsmooth global optimization

Constructing well-behaved filled functions is crucial for the success of filled function algorithms. In this paper, we propose a new class of filled functions specifically designed for nonsmooth optimization problems. The new functions contain only one easy-to-adjust parameter and avoid logarithmic or exponential terms. This design effectively overcomes the issues of parameter sensitivity and computational inefficiency in traditional filled function methods. Theoretical analyses of the proposed filled functions are conducted, and a novel algorithm for unconstrained nonsmooth global optimization is developed. Numerical experiments verify the effectiveness of the proposed algorithm. Comparative results demonstrate its superior performance over the other filled function method.