In recent years, optimization-based design has emerged as a powerful approach to developing efficient and innovative mechanical structures. However, its practical use in structural mechanics remains highly challenging, primarily due to the high computational cost of simulations and the lack of gradient information in many real-world applications. As a consequence, the field often relies on derivative-free black-box optimization algorithms.
This thesis investigates the ability of the state-of-the-art black-box optimization algorithms to address some of the most important challenges in structural mechanics, with a particular focus on scenarios characterized by high dimensionality and limited evaluation budgets. Evolutionary algorithms such as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and Bayesian Optimization (BO), are widely adopted in this context. However, both approaches face significant limitations when confronted with the aforementioned challenges. In addition, due to modeling inaccuracies, it may be desirable not to output a single solution but rather a diverse set of candidate solutions. In this work, we propose refinements to CMA-ES to improve its ability to generate diverse solutions, thereby enhancing its applicability to complex mechanical optimization problems.
The main contributions are as follows. First, we carry out an empirical comparison of BO-based algorithms and CMA-ES on the Black-box Optimization Benchmarking (BBOB) test suite under small budget constraints, clarifying their potential and limitations in this scenario. Second, we design and evaluate a tailored optimization strategy, CMA-ES-Diversity Search (CMA-ES-DS), to more effectively address the quest to output batches of diverse solutions. Third, we contribute to the development of a novel benchmark suite named MechBench comprising realistic structural mechanics optimization tasks, and we provide an in-depth analysis demonstrating how it complements the BBOB suite. This aims to strengthen the connection between optimization and structural mechanics by providing practical tools and insights that promote the broader adoption of modern optimization strategies in engineering.