The extensive computer-aided search applied in Bena et al. (The tadpole problem, 2020) to find the minimal charge sourced by the fluxes that stabilize all the (flux-stabilizable) moduli of a smooth K3 \(\times \) K3 compactification uses differential evolutionary algorithms supplemented by local searches. We present these algorithms in detail and show that they can also solve our minimization problem for other lattices. Our results support the Tadpole Conjecture: The minimal charge grows linearly with the dimension of the lattice and, for K3 \(\times \) K3, this charge is larger than allowed by tadpole cancellation. Even if we are faced with an NP-hard lattice-reduction problem at every step in the minimization process, we find that differential evolution is a good technique for identifying the regions of the landscape where the fluxes with the lowest tadpole can be found. We then design a “Spider Algorithm,” which is very efficient at exploring these regions and producing large numbers of minimal-tadpole configurations.

广泛的计算机辅助搜索应用于 Bena 等人。（蝌蚪问题，2020 年）找到由稳定平滑 K3 \(\times \)  K3 紧化的所有（通量可稳定）模量的通量产生的最小电荷， 使用由局部搜索补充的差分进化算法。我们详细介绍了这些算法，并表明它们也可以解决我们对其他格的最小化问题。我们的结果支持蝌蚪猜想：最小电荷随着晶格的尺寸线性增长，对于 K3  \(\times \) K3，这个电荷大于蝌蚪抵消所允许的。即使我们在最小化过程的每一步都面临 NP 难点晶格归约问题，我们发现差分进化是一种很好的技术，用于识别可以找到最低蝌蚪通量的景观区域。然后我们设计了一个“蜘蛛算法”，它在探索这些区域和生成大量最小蝌蚪配置方面非常有效。