Diagnostic analysis of metamodels' multivariate dependencies and their impacts in many-objective design optimization

While computers are continually getting faster, physical models of complex systems grow more sophisticated and keep pace. Using metamodels can dramatically reduce the time it takes to evaluate a solution for a complex system; however, while the chief virtue of metamodels is that they approximate more computationally expensive models, this is also their main drawback. Metamodels are approximations, and as such they behave differently than the more sophisticated models they approximate. While the metamodels may be accurate approximations, they may also introduce new interdependencies in the response outputs that may hinder search algorithms during optimization. Understanding the impact of the approximation on the subsequent search thus becomes an important part of the problem as models that were computationally expensive ten to fifteen years ago may now run fast enough for use in optimization. In this paper, we use Sobol0 global sensitivity analysis to compare the search performance of a new auto-adaptive many objective evolutionary algorithm solving a challenging product family design problem with both the original analysis and a second-order response surface approximation of the original analysis. Interdependencies in the response outputs are found to result from the problem formulation used rather than the underlying model in this case. Search operator selection by the auto-adaptive evolutionary algorithm is shown to be consistent with the model sensitivities found by global sensitivity analysis.