Parametric optimization solves optimization problems as a function of uncontrollable or unknown parameters. Such an approach allows an engineer to gather more information than traditional optimization procedures during design. Existing methods for parametric optimization of computationally or monetarily expensive functions can be too time-consuming or impractical to solve. Therefore, new methods for the parametric optimization of expensive functions need to be explored. This work proposes a novel algorithm that leverages the advantages of two existing optimization algorithms. This new algorithm is called the efficient parametric optimization (EPO) algorithm. EPO enables adaptive sampling of a high-fidelity design space using an inexpensive low-fidelity response surface model. Such an approach largely reduces the required number of expensive high-fidelity computations. The proposed method is benchmarked using analytic test problems and used to evaluate a case study requiring finite element analysis. Results show that EPO performs as well as or better than the existing alternative, Predictive Parameterized Pareto Genetic Algorithm (P3GA), for these problems given an allowable number of function evaluations.