We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batryev's construction. We demonstrate that such algorithms efficiently optimize physical observables such as axion decay constants or axion-photon couplings in string theory compactifications. For our implementation, we choose a parameterization of triangulations that yields homotopy inequivalent Calabi-Yau threefolds by extending fine, regular triangulations of two-faces, thereby eliminating exponentially large redundancy factors in the map from polytope triangulations to Calabi-Yau hypersurfaces. In particular, we discuss how this encoding renders the entire Kreuzer-Skarke list amenable to a variety of optimization strategies, including but not limited to Genetic Algorithms. To achieve optimal performance, we tune the hyperparameters of our Genetic Algorithm using Bayesian optimization. We find that our implementation vastly outperforms other sampling and optimization strategies like Markov Chain Monte Carlo or Simulated Annealing. Finally, we showcase that our Genetic Algorithm efficiently performs optimization even for the maximal polytope with Hodge numbers $h^{1,1} = 491$, where we use it to maximize axion-photon couplings.

翻译：我们在四维自反多面体的三角剖分中实现遗传算法，通过Batryev构造诱导Calabi-Yau三维超曲面。我们证明此类算法能够高效优化弦论紧化中的物理可观测量，例如轴子衰变常数或轴子-光子耦合。在实现过程中，我们选择了一种三角剖分参数化方案，通过扩展二面的精细正则三角剖分得到同伦不等价的Calabi-Yau三维型，从而消除从多面体三角剖分到Calabi-Yau超曲面映射中指数级别的巨大冗余因子。特别地，我们讨论了这种编码如何使整个Kreuzer-Skarke列表适用于包括但不限于遗传算法的多种优化策略。为达到最优性能，我们使用贝叶斯优化调整遗传算法的超参数。我们发现该实现方法远超其他采样与优化策略（如马尔可夫链蒙特卡洛或模拟退火）。最后，我们展示即使在Hodge数$h^{1,1} = 491$的最大多面体中，该遗传算法仍能高效执行优化——我们将其用于最大化轴子-光子耦合。