Performance of biologically inspired algorithms tuned on TiO₂ nanoparticle benchmark system

Biologically inspired optimization algorithms (BIOA), such as particle swarm optimization (PSO) and differential evolution (DE), are often applied to a specific problem with the tacit assumptions that each algorithm will have a unique set of “ideal” tuning parameters that provide “best” performance, and that, once tuned, two different optimization algorithms ought to exhibit distinct performance. This work tests those assumptions by systematically comparing PSO and DE applied to identify stable and metastable configurations of a benchmark system, a titania dimer Ti₂O₄, whose energy is described by a modified Matsui-Akaogi pairwise potential. The hypotheses (H) are formally expressed as: (H1) for both PSO and DE there exists a unique, optimal set of tuning parameters that maximize its performance on a given problem; (H2) when running two different BIOAs, one algorithm must demonstrate superior performance over the other. By identifying and studying an approximate Pareto-optimal set of tuning parameters for DE and PSO, H1 is shown to be strictly false for DE, and tentatively false for PSO, while H2 is shown to be false with respect to certain statistics. We further investigate the correlations between key tuning parameters and algorithm performance. Our conclusion may be implemented to further optimize and develop BIOAs applied to materials systems.