MULTI-OBJECTIVE EFFICIENT PARAMETRIC OPTIMIZATION

Abstract

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 new parametric hypervolume indicator (pHVI) which measures the space dominated by a given set of data involving both objectives and parameters. The pHVI benefits parametric optimization by enabling the comparison of optimization results, enabling the visualization and detection of optimization convergence, and providing information for an optimization algorithm. MO-EPO uses response surface models of expensive functions to find and evaluate a designs expected to improve the solution and/or models. With new information, response surface models are updated and the process is repeated. "Improvement" is measured by the pHVI metric allowing for the consideration of any number of objectives and parameters.

The novel MO-EPO algorithm is demonstrated on a number of analytical benchmarking problems and two distinct morphing applications with various numbers of objectives and parameters. 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. Both the pHVI metric and the MO-EPO algorithm are significant contributions to parametric optimization methodology and engineering design.