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 optimiza-tion, especially when complex physics and high-fidelity computationally-expensive solvers areinvolved in the process and a global optimum is sought after. In order to have a deeper insightinto this problem and indicate possible remedies, the present paper studies the effects of bothdesign-space dimensionality reduction (DR) and optimization methods on the shape optimiza-tion efficiency. Linear and non-linear DR methods are used for the design-space DR, basedon principal component analysis and deep autoencoders. Global and hybrid global/local deter-ministic derivative-free optimization algorithms (Deterministic Particle Swarm Optimization,DIviding RECTangles, Dolphin Pod Optimization, LSDFPSO, and DIRMIN-2) are applied tothe original and the reduced-dimensionality design-spaces, investigating their efficiency andeffectiveness. Example application is shown for the shape optimization of a destroyer-typevessel sailing in calm water at fixed speed