  Machine learning-based inverse materials discovery has attracted enormous
attention recently due to its flexibility in dealing with black box models.
Yet, many metaheuristic algorithms are not as widely applied to materials
discovery applications as machine learning methods. There are ongoing
challenges in applying different optimization algorithms to discover crystals
with single- or multi-elemental compositions and how these algorithms differ in
mining the ideal materials. We comprehensively compare 11 different
optimization algorithms for the design of single- and multi-elemental crystals
with targeted properties. By maximizing the bulk modulus and minimizing the
Fermi energy through perturbing the parameterized elemental composition
representations, we estimated the unique counts of elemental compositions, mean
density scan of the objectives space, mean objectives and frequency distributed
over the materials' representations and objectives. We found that
nature-inspired algorithms contain more uncertainties in the defined elemental
composition design tasks, which correspond to their dependency on multiple
hyperparameters. Runge Kutta optimization (RUN) exhibits higher mean objectives
whereas Bayesian optimization (BO) displayed low mean objectives compared with
other methods. Combined with materials count and density scan, we propose that
BO strives to approximate a more accurate surrogate of the design space by
sampling more elemental compositions and hence have lower mean objectives, yet
RUN will repeatedly sample the targeted elemental compositions with higher
objective values. Our work shed light on the automated digital design of
crystals with single- and multi-elemental compositions and is expected to
elicit future studies on materials optimization such as composite and alloy
design based on specific desired properties.
