Efficient global optimization of constrained mixed variable problems

TL;DR

This paper introduces variants of the Efficient Global Optimization algorithm tailored for constrained problems with mixed variables, utilizing a novel Gaussian Process kernel to improve convergence efficiency in complex system design tasks.

Contribution

It proposes new algorithm variants that incorporate a discrete kernel in Gaussian Processes for better optimization of mixed variable problems.

Findings

Fewer function evaluations needed for convergence.

Effective on aerospace design problems.

Outperforms traditional optimization algorithms.

Abstract

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In this paper, several variants of the Efficient Global Optimization algorithm for costly constrained problems depending simultaneously on continuous decision variables as well as on quantitative and/or qualitative discrete design parameters are proposed. The adaptation that is considered is based on a redefinition of the Gaussian Process kernel as a product between the standard continuous kernel and a second kernel representing the covariance between the discrete variable values. Several parameterizations of this discrete kernel, with their respective strengths and weaknesses, are discussed in this paper. The novel algorithms are tested on a number of analytical test-cases and an aerospace related design problem, and it is shown that they require fewer function evaluations in order to converge towards the neighborhoods of the problem optima when compared to more commonly used optimization algorithms.