Simultaneously search for multi-target Galactic binary gravitational waves

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 (LMPSO) 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., 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 SNR $\ge$ 15 have been removed. For the remaining sources with SNR $<$ 15, our method successfully identifies 6,508 signals, yielding a false alarm rate of $\text{FAS}_{0.8} = 36.8\%$. By focusing on a subset of sources-specifically, those with $f > 3$ mHz and those with $f \le 3$ mHz but SNR $\ge 13$-we identify 3,406 signals, with a reduced false alarm rate of $\text{FAS}_{0.8} = 22.5\%$. We further demonstrate that, within the same detection SNR range, our method achieves a comparable or lower $\text{FAS}$ than other existing methods.