Differential evolution variants for searching D- and A-optimal designs for nonlinear models in the bioscience

Abstract Evolutionary-based evolution differential (DE) and swarm-based particle swarm optimization (PSO) are two exemplary nature-inspired algorithms widely used in computer engineering, computer science and artificial intelligence for tackling all kinds of complex optimization problems. Like any popular metaheuristic algorithm, DE has many variants, which are modifications of the original algorithm, that enhance their performances in various ways. This paper investigates the effectiveness of DE and its variants for finding two commonly used D - and A -optimal designs to estimate model parameters. The variants include JADE, CoDE, SHADE, and LSHADE. Our goals are to (i) discuss DE and introduce its variants, and show that, as a sample application, they can perform well for finding optimal designs for complex models, (ii) ascertain whether the algorithms perform equally well and if not, identify which ones or one that appears to be more effective, and (iii) compare their performances with REX, a state-of-the-art algorithm in statistis for tackling optimal design problems. We conduct simulations using frequently used nonlinear models in biostatistics and show that DE and its variants generally perform well with one of its variants, the LSHADE algorithm, generally outperforms the others, including the REX algorithm for finding D and A -optimal designs.