Over the past two decades, there has been an explosion in the ability of engineers to create finite element models to simulate the performance of a complex product. Thanks to these advances, the potential for using optimization to improve engineering design is now greater than ever before. However, there are still some gray areas and difficulties in this area. One of the biggest obstacles to the use of optimization is the long runtime of simulations and the lack of gradient information in some of the most complicated simulations, especially in the crashworthiness domain, limiting the set of available solvers to gradient-free black-box optimization algorithms.
A particularly suitable approach for optimization in engineering contexts is the use of surrogate-based algorithms. One of the most commonly used surrogate-based optimization algorithms is Bayesian optimization but the main problem with this approach occurs when the dimension of the domain is high. Since engineering problems are often high dimensional, there is a high need to extend the efficiency of Bayesian optimization to a larger number of parameters.
The main goal of this PhD is to develop efficient Black-Box Optimization Algorithms for high-dimensional problems in structural mechanics. The four key steps that make up the project are: collect and compare algorithms focused on academic problems to evaluate the potential and limitations of state-of-the-art solvers, select and study standard benchmarks in mechanics and perform a Fitness Landscape Analysis on them to identify the main features of typical objective functions in mechanics and quantify the similarity between academic and practical problems. Then, perform an analysis of available open-source finite element method libraries and cluster topology optimization test cases to design a ready-to-use topology optimization benchmark suite and bridge the gap between the optimization and mechanics communities. Finally, perform manual selection using "wizards" and supervised learning approaches ( per-instance algorithm selection ) to enable automated algorithm configuration and hyperparameter optimization, and development of efficient algorithms.
PhD student: Marie Laura SANTONI
PhD supervisors: Carola Doerr
Research laboratory: LIP6 - Laboratoire de recherche en informatique de Sorbonne Université