Surrogate Model Optimization Toolbox

In this document, we introduce the "Surrogate Model Optimization Toolbox," a powerful computational toolkit designed to solve optimization problems efficiently. This toolbox employs surrogate models (also known as metamodels or response surface models) to accelerate the process of finding optimal solutions, significantly reducing computational costs compared to direct optimization methods. For instance, it enables engineers to rapidly design more efficient products through iterative simulation refinement, or helps scientists quickly identify optimal experimental parameters by approximating complex system behaviors. Key implementation features typically include Gaussian Process regression (Kriging), Radial Basis Functions, or Polynomial Chaos Expansions for model construction, coupled with efficient infill criteria like Expected Improvement for iterative optimization. The toolbox's extensible architecture allows integration with various domains including mechanical engineering, computational finance, and scientific computing, making it a widely adopted solution for data-driven optimization challenges. Common functions may include model training with `fitrgp()` for Gaussian Processes, optimization using `bayesopt()` for Bayesian optimization loops, and sensitivity analysis through `sobolAnalysis()` for parameter importance ranking.