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A novel parameter-free filled function method for global optimization and solving nonlinear equation systems
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AI
DOI：10.1016/j.jfranklin.2026.108479.png)
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Abstract
En 中文
Global optimization is essential for addressing complex real-world problems characterized by non-convexity and numerous local minima. Traditional gradient-based methods often struggle in such scenarios due to poor convergence to local optima rather than the global solution. To overcome this limitation, we propose a novel parameter-free filled function, an auxiliary construct designed to enhance global optimization algorithms by escaping local optima. The proposed function introduces an inverse cosine component to create a continuously differentiable and completely parameter-free formulation that effectively overcomes the common limitations of false smoothing and numerical instability found in existing filled function methods. Theoretical analysis demonstrates the function’s continuous differentiability and its effectiveness in escaping local optima. Building on this formulation, we develop the Non-Parametric Filled Function algorithm (NPFFF), which alternately minimizes the original objective function and the filled function to traverse the search space. NPFFF eliminates the need for manual parameter tuning, simplifying implementation and enhancing robustness. Complexity analysis indicates that constructing the filled function requires only linear time. Experimental results on standard benchmark functions demonstrate that NPFFF achieves faster convergence and higher accuracy than existing methods. Furthermore, NPFFF successfully solves nonlinear systems of equations by transforming them into global optimization tasks.
Keywords:
global optimization
filled function
nonlinear equations
parameter-free
global search
Journal
J
IF:
4.2
Papers:
822
Citations:
0