  We propose a nested weighted Tchebycheff Multi-objective Bayesian
optimization framework where we build a regression model selection procedure
from an ensemble of models, towards better estimation of the uncertain
parameters of the weighted-Tchebycheff expensive black-box multi-objective
function. In existing work, a weighted Tchebycheff MOBO approach has been
demonstrated which attempts to estimate the unknown utopia in formulating
acquisition function, through calibration using a priori selected regression
model. However, the existing MOBO model lacks flexibility in selecting the
appropriate regression models given the guided sampled data and therefore, can
under-fit or over-fit as the iterations of the MOBO progress, reducing the
overall MOBO performance. As it is too complex to a priori guarantee a best
model in general, this motivates us to consider a portfolio of different
families of predictive models fitted with current training data, guided by the
WTB MOBO; the best model is selected following a user-defined prediction root
mean-square-error-based approach. The proposed approach is implemented in
optimizing a multi-modal benchmark problem and a thin tube design under
constant loading of temperature-pressure, with minimizing the risk of
creep-fatigue failure and design cost. Finally, the nested weighted Tchebycheff
MOBO model performance is compared with different MOBO frameworks with respect
to accuracy in parameter estimation, Pareto-optimal solutions and function
evaluation cost. This method is generalized enough to consider different
families of predictive models in the portfolio for best model selection, where
the overall design architecture allows for solving any high-dimensional
(multiple functions) complex black-box problems and can be extended to any
other global criterion multi-objective optimization methods where prior
knowledge of utopia is required.
