FBCA: Flexible Besiege and Conquer Algorithm for Multi-Layer Perceptron Optimization Problems.

A Multi-Layer Perceptron (MLP), as the basic structure of neural networks, is an important component of various deep learning models such as CNNs, RNNs, and Transformers. Nevertheless, MLP training faces significant challenges, with a large number of saddle points and local minima in its non-convex optimization space, which can easily lead to gradient vanishing and premature convergence. Compared with traditional heuristic algorithms relying on a population-based parallel search, such as GA, GWO, DE, etc., the Besiege and Conquer Algorithm (BCA) employs a one-spot update strategy that provides a certain level of global optimization capability but exhibits clear limitations in search flexibility. Specifically, it lacks fast detection, fast adaptation, and fast convergence. First, the fixed sinusoidal amplitude limits the accuracy of fast detection in complex regions. Second, the combination of a random location and fixed perturbation range limits the fast adaptation of global convergence. Finally, the lack of a hierarchical adjustment under a single parameter (BCB) hinders the dynamic transition from exploration to exploitation, resulting in slow convergence. To address these limitations, this paper proposes a Flexible Besiege and Conquer Algorithm (FBCA), which improves search flexibility and convergence capability through three new mechanisms: (1) the sine-guided soft asymmetric Gaussian perturbation mechanism enhances local micro-exploration, thereby achieving a fast detection response near the global optimum; (2) the exponentially modulated spiral perturbation mechanism adopts an exponential spiral factor for fast adaptation of global convergence; and (3) the nonlinear cognitive coefficient-driven velocity update mechanism improves the convergence performance, realizing a more balanced exploration-exploitation process. In the IEEE CEC 2017 benchmark function test, FBCA ranked first in the comprehensive comparison with 12 state-of-the-art algorithms, with a win rate of 62% over BCA in 100-dimensional problems. It also achieved the best performance in six MLP optimization problems, showing excellent convergence accuracy and robustness, proving its excellent global optimization ability in complex nonlinear MLP optimization training. It demonstrates its application value and potential in optimizing neural networks and deep learning models.