Efficient global optimization of constrained mixed variable problems

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.

MVMOO: Mixed variable multi-objective optimisation

“…Prior work by Halstrup has looked at the application of the Gower distance metric for use in enabling Bayesian single objective optimisation techniques to be used on mixed variable systems. This work was further developed by Pelamatti et al [32] in which they compared the currently available techniques for optimising mixed variable systems utilising Gaussian approaches. They found the suggested methodology adopted by Halstrup performed comparatively well to other techniques whilst offering the benefit of a reduced number of hyperparameters.…”

Derivative-free mixed binary necklace optimization for cyclic-symmetry optimal design problems

“…In [36], Gaussian process kernels that are products of continuous and discrete kernels are integrated into an EGO method framework; the resulting mixed categorical (involving integer variables not related to effective quantities) optimization problem is then solved by NOMAD. The strengths and weaknesses of various types of kernels for Gaussian processes are discussed in [38].…”

A bi-level methodology for solving large-scale mixed categorical structural optimization

“…In the context of structural optimization problems, various surrogate-based optimization strategies have been extended to categorical variables (Filomeno Coelho, 2014;Müller et al, 2013;Herrera et al, 2014;Roy et al, 2017Roy et al, , 2019Garrido-Merchán and Hernández-Lobato, 2018;Pelamatti et al, 2019). One of the main challenges of such approaches is related to their efficiency when handling large dimension categorical design space.…”

“…Furthermore, a definition of a neighborhood is often required during the construction of the surrogate model. As an example, in (Pelamatti et al, 2019), the neighborhood is defined through an appropriate kernel definition. In these approaches, once the surrogate model is built, the optimizer still faces a large scale discrete optimization problem.…”