Multi-Objective Bayesian Optimization for Design Under Unknown Feasibility Constraints

Abstract Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions and has found applications across engineering, materials science, and machine learning. However, in many practical tasks, feasibility of design is not readily quantifiable. Conventional BO methods often ignore or poorly model design feasibility, leading to impractical or invalid solutions. This work addresses the challenge of integrating feasibility information directly into the BO process. Here we show that modeling feasibility using Gaussian process (GP) classification and treating it as an objective together with other performance objectives in a multi-objective BO setup significantly improves solution quality across different benchmark design tasks. We develop a latent variable Gaussian process classifier for modeling feasibility over categorical design spaces, and use a Dirichlet-based GP classifier for continuous spaces. Our approach provides quantification of feasibility, offering clear optimization guidance. Comparative studies on analytical and real-world test problems demonstrate enhanced performance in terms of both feasibility and optimality. This approach could be extended to a wide range of applications where feasibility is implicit or difficult to define, such as materials discovery, drug design, and chemical process optimization. By re-framing feasibility as a learnable objective, our work opens new avenues for constrained optimization under uncertainty.