Hybrid global/local optimization methods in simulation-based shape design

Abstract

Simulation-based design optimization methods integrate computer simulations, design modification tools, and optimization algorithms. In hydrodynamic applications, often objective functions are computationally expensive and noisy, their derivatives are not directly provided, and the existence of local minima cannot be excluded a priori, which motivates the use of deterministic derivative-free global optimization algorithms. DPSO (Deterministic Particle Swarm Optimization), DIRECT (DIviding RECTangles), two well-known derivative-free global optimization algorithms, and FSA (Fish Shoal Algorithm), a novel metaheuristic introduced herein, are described in the present work. Moreover, the enhancement of DIRECT and DPSO is presented based on global/local hybridization with derivative-free line search methods. DPSO, DIRECT, FSA, and three hybrid algorithms (LS-DF PSO, DIRMIN, and DIRMIN-2) are introduced, and assessed on a benchmark of seventy-three analytical functions, providing an effective and efficient guideline for their use in the simulation-based shape design optimization context. The suggested guidelines are applied on ten hull-form optimization problems, using potential flow and RANS solvers, supported by metamodels. The optimizations pertain the high-speed Delft catamaran and an USS Arleigh Burkeclass destroyer ship, namely the DTMB 5415 model, an early and open-to-public version of the DDG-51. Three shape modification techniques, specifically the free-form deformation and the orthogonal basis functions expansion over 2D and 3D subdomains, are introduced, along with the design-space dimensionality reduction by generalized Karhunen-Loève expansion. Hybrid algorithms show a faster convergence towards the global minimum than the original global methods and therefore represent a viable option for shape design optimization. Moreover, FSA shows a better effectiveness compared to the other global algorithm (DPSO and DIRECT), allowing for good expectations for its further improvement with a local hybridization, for the future work.