Multi-objective optimization in population pharmacokinetic model selection and optimization: application of NSGA-II in pyDarwin

The selection of a “good” model usually involves a combination of objective and subjective criteria. Although many aspects of model quality can be expressed numerically, certain desirable characteristics remain difficult—or even impossible—to quantify precisely. Multi-objective optimization (MOO) provides a systematic way to handle this challenge by explicitly incorporating and balancing both objective (measurable) and subjective (judgment-based) considerations when choosing among candidate solutions. The generated Pareto front represents a set of non-dominated models where no single solution can be improved in one objective without sacrificing the performance in another objective. Using the non-dominated sorting genetic algorithm II (NSGA-II), an implementation of MOO, we simultaneously considered objective function value and number of estimated parameters as competing criteria. Concentration measurements of 17-DMAG, quetiapine, clozapine and ziprasidone were applied to build population pharmacokinetic models through traditional stepwise search, machine learning based single-objective hybrid genetic algorithm (SOHGA) and MOO. Local downhill search with MOO was also assessed in this study. While both objectives improved, models with lower objective function value generally contained more estimated parameters. The number of non-dominated solutions for DMAG, ziprasidone, clozapine, and quetiapine was 17, 9, 9, and 13, respectively. The optimal model selected by SOHGA appeared on the Pareto front for DMAG, ziprasidone and clozapine datasets. Overall, MOO provides objective transparency to the cost of tradeoffs between competing model objectives, allowing researchers to better contextualize subjective criteria (e.g., biological plausibility, improvements in diagnostic plots) when aligning model selection with clinical context.