The search for Galactic binary gravitational waves is a critical challenge for future space-based gravitational wave detectors, such as LISA. We propose an innovative approach to simultaneously explore gravitational waves originating from Galactic binaries by developing a new local maxima particle swarm optimization algorithm. This new approach effectively addresses the inaccuracies often associated with signal subtraction contamination, a challenge for traditional iterative subtraction methods, particularly when dealing with low signal-to-noise ratio (SNR) signals (e.g., $\mathrm{SNR}<15$). We also account for the effects of overlapping signals and degeneracy noise. To demonstrate the effectiveness of our approach, we use residuals from the LISA mock data challenge (LDC1-4), where 10,982 injected sources with $\mathrm{SNR}\ge 15$ have been removed. For the remaining sources with $\mathrm{SNR}<15$, our method successfully identifies 6,508 signals, yielding a false alarm rate of ${\mathrm{FAS}}_{0.8}=36.8\%$. By focusing on a subset of sources—specifically, those with $f>3\mathrm{mHz}$ and those with $f\le 3\mathrm{mHz}$ but $\mathrm{SNR}\ge 13$—we identify 3,406 signals, with a reduced false alarm rate of ${\mathrm{FAS}}_{0.8}=22.5\%$. We further demonstrate that, within the same detection SNR range, our method achieves a comparable or lower FAS than other existing methods.

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• Gravitational waves