Â© 2018 Springer-Verlag GmbH Germany, part of Springer Nature Engineers routinely perform parameter studies to investigate how system response changes over a range of parameter values. This can provide engineering insight into the importance of an exogenous variable, the robustness of a design alternative, or even the validity of simulation models. Parametric optimization is an extension of this concept in which one investigates how the solution to an optimization or equilibrium problem changes over a range of parameter values. It has been applied in economics, process engineering and engineering systems design. Recent work has yielded a general-purpose algorithm for parametric multi-objective optimization, the Predicted Parametric Pareto Genetic Algorithm (P3GA), and demonstrated it on engineering examples. This article advances understanding about the capabilities of P3GA through a suite of test problems of varying scale and application to a multiphysical engineered system: a magnetohydrodynamic thermal transport (MTT) system. We also compare P3GA to iterated application of an established multi-objective optimization algorithm, NSGA-II. Results indicate P3GA outperforms the iterative approach, underscoring the importance of using an algorithm tailored to parametric optimization.