Generative Multiform Bayesian Optimization.

Area of Science:

• Engineering Optimization
• Computational Design
• Machine Learning

Background:

• Optimizing black-box functions in complex spaces (e.g., airfoil design) is challenging.
• Generative model-based optimization (GMO) maps complex inputs to latent spaces but struggles with determining optimal latent dimensions.
• This difficulty creates a trade-off between solution accuracy and convergence rate.

Purpose of the Study:

• To introduce a novel multiform generative model-based optimization (GMFoO) approach.
• To overcome the limitations of fixed latent dimensions in GMO.
• To enhance optimization performance for complex, expensive objective functions.

Main Methods:

• Developed a generative model promoting positive correlation between multiple latent spaces for knowledge transfer.
• Implemented Bayesian optimization (BO) as the optimizer within the GMFoO framework.
• Designed two strategies for continuous information exchange between latent spaces.

Main Results:

• GMFoO demonstrated improved convergence to superior designs compared to traditional methods.
• The approach was validated on airfoil design, corbel design, and an area maximization problem.
• Effective knowledge transfer and information exchange between latent spaces were achieved.

Conclusions:

• GMFoO offers a promising solution for optimizing expensive black-box functions in complex input spaces.
• Simultaneous optimization across multiple, correlated latent spaces enhances efficiency and accuracy.
• The method provides a robust framework for tackling real-world engineering design problems within limited computational budgets.