Correlation-concerned Bayesian Optimization for Multi-Objective Airfoil Design

Airfoil design based on Bayesian optimization generally involves high-fidelity simulations, whose crux in terms of efficiency has always challenged existing optimization frameworks. Theoretically, fully mining the useful information in the evaluated samples is expected to speed up the optimization process. In this paper, a multi-objective Bayesian optimization framework explicitly modeling objective correlations is proposed for airfoil design to make the most of the expensive simulations, where a convolved multiple output Gaussian process (CMOGP) surrogate model and a correlated Pareto-frontier entropy search (cPFES) infill sampling strategy are incorporated respectively for reliable capture of the complex relationships involved and final acquisition of well-distributed Pareto airfoils. Specially, a correlation-concerned representative Pareto-frontier sampling method is also proposed to guide candidate selection in cPFES to a prospective optimization direction efficiently. Comparative results on synthetic problems and an airfoil aerodynamic-stealth design problem demonstrate that modeling objective correlations contributes to both the improvement in prediction accuracy for promising regions and the accelerated convergence to a superior and well-distributed Pareto-frontier within a limited budget. It indicates potential practicability of the proposed framework for multi-objective airfoil design as well as other engineering optimization problems to alleviate efficiency issues.