Problems Formulation and Their Solutions for Modeling-Driven Optimization Using Machine Learning

Abstract

We attempt to combine optimization with modeling to construct approximate models of input-output relationships, which are called surrogate models. For modeling, we envision using machine-learning based on input-output data as inequality constraints for error tolerances to be embedded into optimization problems within the framework of the universal approximation theorem, and we refer these combining types of modeling and optimization problems as a modeling-driven optimization problem. Then, as a strategy for solving the modeling-driven optimization problem with a relatively large number of data, we propose the data restriction method, in which modeling-driven optimization problem is replaced with the data restriction problem with a reduced number of inequality constraints for error tolerances corresponding to the set of learning data restricted to a smaller number of elements, and the problems with restricted data are solved sequentially while new approximate models are iteratively constructed in order to improve accuracy of the obtained optimal solution.