Generating Cheap Representative Functions for Expensive Automotive Crashworthiness Optimization

Abstract

Solving real-world engineering optimization problems, such as automotive crashworthiness optimization, is extremely challenging, because the problem characteristics are oftentimes not well understood. Furthermore, typical hyperparameter optimization approaches that require a large function evaluation budget are computationally hindered, if the function evaluation is expensive, e.g., requires finite element (FE) simulation runs. In this paper, we propose an approach to characterize real-world expensive black-box optimization problems using the exploratory landscape analysis (ELA). Based on these landscape characteristics, we can identify test functions that are fast-to-evaluate and representative for hyperparameter optimization purposes. Focusing on 20 problem instances from automotive crashworthiness optimization, our results reveal that these 20 crashworthiness problems exhibit landscape features different from classical optimization benchmark test suites, such as the widely-used black-box optimization benchmarking (BBOB) problem set. In fact, these 20 problem instances belong to problem classes that are distinct from the BBOB test functions based on the clustering results. Further analysis indicates that, as far as the ELA features concern, they are most similar to problem classes of tree-based test functions. By analyzing the performance of two optimization algorithms with different hyperparameters, namely the covariance matrix adaptation evolutionary strategy (CMA-ES) and Bayesian optimization (BO), we show that the tree-based test functions are indeed representative in terms of predicting the algorithm performances. Following this, such scalable and fast-to-evaluate tree-based test functions have promising potential for automated design of an optimization algorithm for specific real-world problem classes.