🤖 AI Summary
This work addresses the challenge of efficiently locating global extrema of multimodal black-box functions by proposing a population-based optimizer natively designed for GPU parallelization. The method introduces an asymmetric oscillation mechanism that dynamically balances convergence and anti-convergence, freezing discovered optima while driving remaining samples to persistently explore the search space. It integrates momentum-based anti-convergence, stochastic smoothed gradient estimation, and adaptive resampling strategies—dubbed Repulse Monkey and Golden Rooster—operating entirely without gradient information. Evaluated on all 42 high-dimensional (up to 64D) multimodal functions in the SFU benchmark suite, the algorithm achieves 100% basin recovery, attains up to 39× speedup over basin-hopping, and demonstrates robust performance under strong noise, significantly outperforming existing CPU-based baselines.
📝 Abstract
Finding all modes of a multimodal black-box function is a fundamental challenge in optimization, Bayesian inference, and scientific computing. Existing approaches -- basin-hopping, CMA-ES, multistart gradient descent -- operate sequentially and cannot exploit the massive parallelism of modern GPU hardware. We introduce \chisao{} (\textbf{C}onvergence-\textbf{H}alt-\textbf{I}nvert-\textbf{S}tick-\textbf{A}nd-\textbf{O}scillate), a GPU-native population optimizer that runs an entire sample batch simultaneously and exploits a deliberate convergence-anticonvergence oscillation cycle to escape local traps while freezing confirmed modes. The structural move is asymmetric: samples that reach true peaks are frozen (``stuck'') and preserved, while the rest keep exploring via momentum-based anti-convergence and stochastically smoothed gradients. Adaptive reseeding via two complementary strategies (Repulse Monkey and Golden Rooster) maintains population diversity throughout. On all 42 functions of the Simon Fraser University optimization benchmark suite across dimensions $d \in \{2, 4, 8, 16, 32, 64\}$, \chisao{} achieves \textbf{100\%} mode recovery where all CPU baselines collapse at $d \geq 8$ on the hardest multimodal functions, at up to \textbf{$34\times$} speedup over basin-hopping on functions where all methods succeed (Michalewicz $d=64$) and up to \textbf{$39\times$} on unimodal functions (Rotated Hyper-Ellipsoid $d=64$, pure GPU dividend). All benchmarks evaluate the objective by value alone -- gradients come from finite differences -- so the reported speedups are a derivative-free worst case. Under substantial likelihood noise ($σ_{\mathrm{noise}}$ up to 1.0), mode detection remains 100\% reliable. The algorithm is available as a standalone open-source Python package on PyPI.