An Algorithm for Multi-Objective Efficient Parametric Optimization

Parametric optimization is the process of solving an optimization problem as a function of currently unknown or changing variables known as parameters. Parametric optimization methods have been shown to benefit engineering design and optimal morphing applications through its specialized problem formulation and specialized algorithms. Despite its benefits to engineering design, existing parametric optimization algorithms (similar to many optimization algorithms) can be inefficient when design analyses are expensive. Since many engineering design problems involve some level of expensive analysis, a more efficient parametric optimization algorithm is needed. Therefore, the multi-objective efficient parametric optimization (MO-EPO) algorithm is developed to allow for the efficient optimization of problems with multiple parameters and objectives. This technique relies on the parametric hypervolume indicator (pHVI) which measures the space dominated by a given set of data involving both objectives and parameters. The novel MO-EPO algorithm is demonstrated on a number of analytical benchmarking problems with various numbers of objectives and parameters. Additionally, a morphing airfoil case study is examined. In each case, MO-EPO is shown to find solutions that are as good as or better than those found from the existing P3GA (i.e., equal or greater pHVI value) when the number of design evaluations is limited.