Derivative-free line-search algorithm for multi-fidelity optimization

The paper presents a multi-fidelity coordinate-search derivative-free algorithm for nonsmooth constrained optimization (MF-CS-DFN), in the context of simulation-based design optimization (SBDO). The objective of the work is the development of an optimization algorithm able to improve the convergence speed of the SBDO process. The proposed algorithm is of a line-search type and can handle objective function evaluations performed with variable accuracy. The algorithm automatically selects the accuracy of the objective function evaluation based an internal steplength parameter. The MF-CS-DFN algorithm starts the optimization with low accuracy and low-cost evaluations of the objective function, then the accuracy (and evaluation cost) is increased. The method is coupled with a potential flow solver whose accuracy is determined by the computational grid size. No surrogate models are used in the current study. The algorithm is applied to the hull-form optimization of a destroyer-type vessel in calm water using 14 hull-shape parameters as design variables. The optimization aims at the total resistance reduction. Seven refinements of the computational grid are used by the multi-fidelity optimizations. Four setups of the MF-CS-DFN algorithm are tested and compared with an optimization performed only on the finest grid. The results show that three of the tested setups achieve better performance than the high-fidelity optimization, converging to a lower resistance value with a reduced computational cost.