Methodology to Optimize Biologically Inspired Algorithms for an Efficient Global Structure Search of TiO₂ Nanoparticles

Biologically inspired optimization algorithms have been successfully applied to a variety of materials optimization problems, but their adaptation, and tuning to these problems is often ad-hoc. This work studies two popular algorithms, particle swarm and differential evolution, to determine how various tuning parameter values affect their relative performance in identifying configurations of TiO₂ nanoparticles. Empirical probability density distributions are created for the convergence rate of each algorithm and the energies of the meta-stable structures they identify. Their sample size is determined using non-parametric tests (Kolmogorov-Smirnov 2-Sample, and Anderson-Darling k-Sample) and the convergence rates of the statistics themselves. The mode of each distribution is used to generate a Pareto Front (PF) of the algorithm’s performance. Each algorithm is tuned until the PF converges, and a surrogate-model-aided inverse-design of tuning parameters is used to accelerate convergence, and tests such as kernel principal component analysis are used to identify correlations in order to provide tuning recommendations and guidelines.