Advanced Smoothing Approaches for Global Minimization: Algorithmic Design and Applications
TL;DR
This paper addresses the unconstrained global minimization of continuously differentiable functions by introducing a novel global optimization framework based on the auxiliary function approach, and develops two new local-search-based algorithms that offer superior performance and robustness.
Abstract
This paper addresses the unconstrained global minimization of continuously differentiable functions by introducing a novel global optimization framework based on the auxiliary function approach. First, a robust auxiliary function that remains unaffected by parameter variations is proposed. Building upon this formulation, two new local-search-based algorithms are developed, and their numerical stabilization is thoroughly analyzed. To validate the efficiency and real-world applicability of the proposed approach, the algorithms are evaluated on standard benchmark functions as well as the challenging 25-bar space truss weight optimization problem. Comparative analyses with state-of-the-art methods demonstrate that the proposed algorithms offer superior performance and robustness.