Surrogate models in evolutionary single-objective optimization: A new taxonomy and experimental study

Engine Calibration With Surrogate-Assisted Bilevel Evolutionary Algorithm

Engine calibration problems are black-box optimization problems which are evaluation costly and most of them are constrained in the objective space. In these problems, decision variables may have different impacts on objectives and constraints, which could be detected by sensitivity analysis. Most existing surrogate-assisted evolutionary algorithms do not analyze variable sensitivity, thus, useless effort may be made on some less sensitive variables. This article proposes a surrogate-assisted bilevel evolutionary algorithm to solve a real-world engine calibration problem. Principal component analysis is performed to investigate the impact of variables on constraints and to divide decision variables into lower-level and upper-level variables. The lower-level aims at optimizing lower-level variables to make candidate solutions feasible, and the upper-level focuses on adjusting upper-level variables to optimize the objective. In addition, an ordinal-regression-based surrogate is adapted to estimate the ordinal landscape of solution feasibility. Computational studies on a gasoline engine model demonstrate that our algorithm is efficient in constraint handling and also achieves a smaller fuel consumption value than other state-of-the-art calibration methods.

A two-stage dominance-based surrogate-assisted evolution algorithm for high-dimensional expensive multi-objective optimization

In the past decades, surrogate-assisted evolutionary algorithms (SAEAs) have become one of the most popular methods to solve expensive multi-objective optimization problems (EMOPs). However, most existing methods focus on low-dimensional EMOPs because a large number of training samples are required to build accurate surrogate models, which is unrealistic for high-dimensional EMOPs. Therefore, this paper develops a two-stage dominance-based surrogate-assisted evolution algorithm (TSDEA) for high-dimensional EMOPs which utilizes the RBF model to approximate each objective function. First, a two-stage selection strategy is applied to select individuals for re-evaluation. Then considering the training time of the model, proposing a novel archive updating strategy to limit the number of individuals for updating. Experimental results show that the proposed algorithm has promising performance and computational efficiency compared to the state-of-the-art five SAEAs.