A Nested Weighted Tchebycheff Multi-Objective Bayesian Optimization Approach for Flexibility of Unknown Utopia Estimation in Expensive Black-box Design Problems

TL;DR

This paper introduces a nested weighted Tchebycheff multi-objective Bayesian optimization framework that adaptively selects the best predictive model from a portfolio to improve estimation accuracy in expensive black-box multi-objective problems.

Contribution

It proposes a flexible model selection approach within WTB MOBO, enhancing estimation of unknown utopia points and overall optimization performance in complex black-box problems.

Findings

Improved accuracy in parameter estimation and Pareto solutions.

Reduced function evaluation cost compared to existing MOBO methods.

Effective handling of high-dimensional, multi-modal optimization problems.

Abstract

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.