A novel parameter-free differentiable filled function for global optimization

The filled function method is a prominent approach in global optimization, effectively overcoming the limitations of non-global minimizers by successively locating improved local minima. While its implementation is relatively straightforward, algorithmic efficiency is highly dependent on the properties of the filled function. Although various forms have been developed to enhance performance, most existing versions are either non-differentiable or involve multiple parameters that are difficult to tune. Recent studies have introduced parameter-free or differentiable variants, yet further improvement in both structural simplicity and numerical robustness remains a challenge. To address this, this study proposes a novel filled function that is both completely parameter-free and continuously differentiable, distinguishing it from existing designs that typically achieve only one of these features. The proposed formulation not only eliminates parameter tuning but also ensures smoothness, enabling the direct application of efficient gradient-based solvers. Theoretical analysis establishes its filling properties, while numerical experiments on benchmark functions demonstrate that the method achieves superior convergence efficiency and reliability compared to existing filled function algorithms. These contributions provide a more streamlined and computationally efficient tool for global optimization.