**Abstract**

Multi-objective optimization is an essential component of nearly all engineering design. However, for industrial applications, the design process typically demands running expensive computer code and/or real-world experiments putting the design process at risk of finding suboptimal solutions and/or not meeting budget constraints. As a first step toward a remedy, meta-models are built to mimic the response surface at a much lower query cost. We cover a time-tested technology specifically tailored to limited-data scenarios called Bayesian hybrid modeling (GEBHM) developed and maintained at General Electric (GE) research. GEBHM offers Bayesian mean and principled uncertainty predictions allowing a second technology called intelligent design and analysis of experiments (GE-IDACE/ IDACE) to perform the optimization task using an adaptive sampling strategy. This chapter first covers the theoretical framework of both GEBHM and GE-IDACE. Then, the impact of GEBHM/GE-IDACE is demonstrated on multiple real-world engineering applications including additive manufacturing, combustion testing, and computational fluid dynamic design modeling. GEBHM and GE-IDACE are used daily and extensively within GE with huge impact in the form of 30–90% cost reduction and superior engineering designs of competitive products.

**Keywords:** intelligent design and analysis of computer experiments, GE-IDACE, IDACE, Bayesian hybrid modeling, BHM, GEBHM, GE-BHM, Gaussian process, GP, GE, adaptive sampling, meta-model, surrogate model, uncertainty sampling, Bayesian global optimization, BGO, multi-objective optimization, industrial, industrial design, engineering design, application, real-world, predictive uncertainty, machine learning, ML, artificial intelligence, AI, robust optimization, desirability, expected improvement
