On the combined effect of design-space dimensionality reduction and optimization methods on shape optimization efficiency

The curse of dimensionality represents a relevant issue in simulation-based shape optimization, especially when complex physics and high-fidelity computationally-expensive solvers are involved in the process and a global optimum is sought after. In order to have a deeper insight into this problem and indicate possible remedies, the present paper studies the effects of both design-space dimensionality reduction (DR) and optimization methods on the shape optimization efficiency. Linear and non-linear DR methods are used for the design-space DR, based on principal component analysis and deep autoencoders. Global and hybrid global/local deterministic derivative-free optimization algorithms (Deterministic Particle Swarm Optimization, DIviding RECTangles, Dolphin Pod Optimization, LSDFPSO, and DIRMIN-2) are applied to the original and the reduced-dimensionality design-spaces, investigating their efficiency and effectiveness. Example application is shown for the shape optimization of a destroyer-type vessel sailing in calm water at fixed speed.