The geometric optimization of crystal structures is a procedure widely used in Chemistry that changes the geometrical placement of the particles inside a structure. It is called structural relaxation and constitutes a local minimization problem with a non-convex objective function whose domain complexity increases according to the number of particles involved. In this work we study the performance of the two most popular first order optimization methods in structural relaxation. Although frequently employed, there is a lack of their study in this context from an algorithmic point of view. We run each algorithm in combination with a constant step size, which provides a benchmark for the methods' analysis and direct comparison. We also design dynamic step size rules and study how these improve the two algorithms' performance. Our results show that there is a trade-off between convergence rate and the possibility of an experiment to succeed, hence we construct a function to assign utility to each method based on our respective preference. The function is built according to a recently introduced model of preference indication concerning algorithms with deadline and their run time. Finally, building on all our insights from the experimental results, we provide algorithmic recipes that best correspond to each of the presented preferences and select one recipe as the optimal for equally weighted preferences. Alongside our results we present our open source Python software veltiCRYS, which was used to perform the geometric optimization experiments. Our implementation, can be easily edited to accommodate other energy functions and is especially targeted for testing different methods in structural relaxation.

翻译：晶体结构的几何优化是化学领域广泛使用的一项技术，通过调整结构内部粒子的几何排布实现优化。该过程称为结构弛豫，本质上是一个非凸目标函数的局部最小化问题，其定义域复杂度随粒子数量的增加而升高。本文研究了结构弛豫中最常用的两种一阶优化方法的性能表现。尽管这些方法在实际中频繁使用，但当前缺乏从算法角度针对该场景的深入分析。我们采用恒定步长与各算法相结合，为方法分析与直接比较提供了基准。同时设计了动态步长规则，并探究了这些规则如何提升两种算法的性能。结果表明收敛速度与实验成功可能性之间存在权衡关系，因此我们构建了一个基于各自偏好的效用分配函数。该函数依据近期提出的一种关于带截止时间算法及其运行时间的偏好指示模型建立。最终，基于对实验结果的全部洞见，我们提供了能最佳匹配各类偏好的算法方案，并从中选取了均衡偏好下的最优方案。除研究结果外，我们还开源了用于几何优化实验的Python软件包veltiCRYS。该实现易于修改以适应不同能量函数，尤其针对结构弛豫中不同方法的测试场景。