fig4

Figure 4. (A) Scatter plot on the PES generated by an attention-based VAE, colored according to relative energy compared to the global minimum. Black stars indicate agent positions in FA searches, with arrows tracing their evolutionary paths; (B) Performance comparison of 24 independent single BH runs (colored in blue) and 24 independent single FA searches (with 30 agents, colored in red) based on the number of local optimizations vs. energy difference from the global minimum; (C) Comparison between 24 independent FA and parallel BH runs. Both consist of 30 agents in each generation, and start from the same initial structures generated from FA runs. In (B) and (C), lines with markers indicate the mean and shaded regions indicate the standard deviation over 24 independent runs. PES: Potential energy surface; VAE: variational autoencoder; FA: firefly algorithm; BH: