28. July 2022

Finding Fast-to-Compute Proxies for Engineering Optimization Problems

Due to their time-consuming evaluation function, requiring a simulator run, it is difficult to understand the characteristics of engineering optimization problems that make them hard for optimization algorithms. Moreover, it makes it impossible to perform many optimization runs with these problems and to tune optimization algorithms towards improving their performance on such problems.

To overcome these obstacles, an approach towards learning the characteristics of engineering optimization problems, with special emphasis on automotive crash, was recently published. The idea is based on using exploratory landscape analysis (ELA) features, which are features of the optimization landscape that can be computed, based on an existing set of simulated designs (for example, following a design of experiments approach). The method is based on 68 carefully selected ELA features for characterizing the optimization problems, and is applied to ten automotive crashworthiness optimization problem instances for side crash settings (four rocker panel designs, three side pole positions).

Comparing the 68-dimensional ELA features to those of a standard academic test function set, the black box optimization benchmark (BBOB), the standard test functions turn out to be very different from the automotive crash problem instances. However, using a randomized test function generator for generating 1000 different test functions, functions which exhibit an ELA feature vector that is very close (in Euclidean distance) to the automotive crash problem’s feature vector can be identified. The hypothesis that landscape similarity can be measured by ELA feature vector distance is confirmed both by visual inspection of the 2-dimensional objective function landscapes and by comparing the performance of an optimization algorithm on function pairs that have small ELA vector distance. The results indicate that the pipeline can be used to systematically generate objective functions with characteristics identical to real-world engineering design problems, which however are very fast to evaluate. This way, these “proxy-functions” can be used to tune the optimization algorithm’s performance for the real-world problem.

The corresponding article “Learning the Characteristics of Engineering Optimization Problems with Applications in Automotive Crash” received the best paper award in the real-world applications track at the Genetic and Evolutionary Computation Conference (GECCO) in Boston, MA, July 9 – 13. The processing pipeline is available at https://github.com/fx-long/CEOELA.

Acknowledgement: The contribution of the paper was written as part of the joint project newAIDE under the consortium leadership of BMW AG with the partners Altair Engineering GmbH, divis intelligent solutions GmbH, MSC Software GmbH, Technical University of Munich, TWT GmbH. The project is supported by the Federal Ministry for Economic Affairs and Climate Action (BMWK) on the basis of a decision by the German Bundestag.