(T-019) Application of NSGA-II and pyDarwin in Multi-objective Optimization for Population Pharmacokinetic (PopPK) Model Selection

Xinnong Li – University at Buffalo; Alex Mazur – Certara, US; Mark Sale – Certara, US; James Craig – Certara, US; Keith Nieforth – Certara, US; Robert Bies – University at Buffalo

Objectives: Model selection typically involves both objective (numerical) and subjective criteria (interpretation of plots and consideration of biological plausibility). Multi-objective optimization (MOO) allows for the simultaneous optimization of multiple criteria. This approach generates a Pareto front, representing a set of non-dominated models where improving performance in one objective would compromise another [1]. An advantage of MOO over single objective optimization is that no, potentially arbitrary, penalties to the OFV are needed. In this study, the main objectives are to identify a set of non-dominated models by simultaneously optimizing objective function value (OFV) and the number of estimated parameters (n_parms), and to evaluate the impact of incorporating local downhill search on the optimization results.

Methods: This study utilized a quetiapine dataset, which was tested by single objective approach in our previously published study [2].

NSGA-II algorithm [3] in pyDarwin [4] was used for multi-objective model selection. In this study, the model selection is driven by two objectives, which are OFV (minus two log likelihood), and n_parms. A local downhill search was also assessed in this study.

The optimization process ran for 20 generations, with 80 models in each generation. The search was combined with local downhill search, which was implemented every 10 generations.

Results: As the generations progressed, the front that included non-dominated models within each generation shifted toward an improved region, optimizing both OFV and model parsimony. The trade-off between two objectives was clearly observed: models with lower OFV generally contained more estimated parameters.

In the search without local downhill search, 10 optimal models were identified on the Pareto front, with OFV ranging from 9996.975 to 10203.494 and n_parms ranging from 7 to 12. One non-dominated model failed the covariance step, and 5 failed the convergence step. When the local downhill search was implemented, 13 nondominated models were selected within the search space. OFV ranges from 9989.829 to 10203.494, and n_parms ranges from 7 to 20. All models with >12 parameters failed the convergence step, indicating a tendency towards overparameterization.

The models selected based on objective criteria are then presented to the user to further examine a manageable set and select one or more “best” models based on subjective criteria, such as biological plausibility and diagnostic graphics.

Conclusions: The MOO method successfully identified a set of non-dominated models within the search space by evaluating OFV and parsimony at the same time. Incorporation of downhill search expanded the exploration area, yielding more non-dominated models. Therefore, integrating the local downhill search into the multi-objective optimization is recommended to enhance the model selection. Overall, the application of NSGA-II successfully generated a set of non-dominated PopPK models, offering greater insight and flexibility for decision-making in model selection.

Citations: [1] M. Kochenderfer and T. Wheeler. Algorithms for optimization. 2019. The MIT Press.
[2] Li X, Sale M, Nieforth K, Bigos KL, Craig J, Wang F, Feng K, Hu M, Bies R, Zhao L. pyDarwin: A Machine Learning Enhanced Automated Nonlinear Mixed-Effect Model Selection Toolbox. Clin Pharmacol Ther. 2024 Apr;115(4):758-773.
[3] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, April 2002.
[4] https://github.com/certara/pyDarwin

Keywords: Multi-objective optimization, Machine learning, Population pharmacokinetic model