A Surrogate-Assisted High-Dimensional Mixed-Variable Evolutionary Framework and Its Application to Vehicle Lightweighting Design

In many real-world engineering applications, optimization problems suffer from high-dimensional mixed (continuous-categorical) variables and expensive performance evaluations, which are called HMEOPs. This paper proposes a surrogate-assisted high-dimensional mixed-variable evolutionary framework, named SHIME, for solving HMEOPs. In SHIME, we develop an autoencoding Bayesian neural network (ABNN), which is a dimensionality-reduction-based end-to-end surrogate model. ABNN consists of an autoencoder branch and a Bayesian network branch. The autoencoder branch projects high-dimensional mixed variables into a low-dimensional latent space, obtaining informative latent variables. In the projection, a one-hot encoding layer is employed to convert categorical variables into continuous ones. The Bayesian network branch takes the latent variables as input and outputs predicted objective function values. In this way, ABNN can effectively handle high-dimensional mixed variables and provide accurate objective predictions. Based on ABNN, we further design a surrogate-assisted multispace search mechanism in SHIME. Specifically, in the decision space, mixed-variable differential evolution assisted by ABNN is proposed to preselect high-quality candidates for locating the promising region. Moreover, in the latent space, Bayesian optimization is implemented to improve the quality of the best individual of the population. Therefore, SHIME can achieve an exploration-exploitation tradeoff and find a near-optimal solution within a limited computational budget. We test SHIME on 15 artificial test problems, and the results demonstrate its superior convergence speed and performance against six advanced algorithms. In addition, in two practical applications of vehicle lightweighting design, SHIME improves the design performance by 4.9%-24.4% compared with two competitors.