A Derivative-Free Line-Search Algorithm for Simulation-Driven Design Optimization Using Multi-Fidelity Computations

Andrea Serani,Riccardo Pellegrini,Stefano Lucidi,Francesco Rinaldi,Giampaolo Liuzzi,Matteo Diez

doi:10.3390/math10030481

Abstract

The paper presents a multi-fidelity extension of a local line-search-based derivative-free algorithm for nonsmooth constrained optimization (MF-CS-DFN). The method is intended for use in the simulation-driven design optimization (SDDO) context, where multi-fidelity computations are used to evaluate the objective function. The proposed algorithm starts using low-fidelity evaluations and automatically switches to higher-fidelity evaluations based on the line-search step length. The multi-fidelity algorithm is driven by a suitably defined threshold and initialization values for the step length, which are associated to each fidelity level. These are selected to increase the accuracy of the objective evaluations while progressing to the optimal solution. The method is demonstrated for a multi-fidelity SDDO benchmark, namely pertaining to the hull-form optimization of a destroyer-type vessel, aiming at resistance minimization in calm water at fixed speed. Numerical simulations are based on a linear potential flow solver, where seven fidelity levels are used selecting systematically refined computational grids for the hull and the free surface. The method performance is assessed varying the steplength threshold and initialization approach. Specifically, four MF-CS-DFN setups are tested, and the optimization results are compared to its single-fidelity (high-fidelity-based) counterpart (CS-DFN). The MF-CS-DFN results are promising, achieving a resistance reduction of about 12% and showing a faster convergence than CS-DFN. Specifically, the MF extension is between one and two orders of magnitude faster than the original single-fidelity algorithm. For low computational budgets, MF-CS-DFN optimized designs exhibit a resistance that is about 6% lower than that achieved by CS-DFN.

Highlights

Simulation-driven design optimization (SDDO) [1] is an emerging paradigm that offers the possibility to define innovative configurations and optimized designs of complex engineering systems, integrating in a rigorous mathematical framework physics-based computations with numerical optimization algorithms
It should be noted that the MFCS-DFN performance is affected by the step length αand the convergence threshold η, see Algorithm 1
A multi-fidelity extension of the local line-search-based derivative-free approach for nonsmooth constrained optimization (MF-CS-DFN) is introduced for design optimization, which is driven by multi-fidelity computations

Summary

Introduction

Simulation-driven design optimization (SDDO) [1] is an emerging paradigm that offers the possibility to define innovative configurations and optimized designs of complex engineering systems, integrating in a rigorous mathematical framework physics-based computations with numerical optimization algorithms. Methods to reduce the computational cost include linear [4] and nonlinear [5] approaches to design-space dimensionality reduction, adaptive surrogate modeling [6], efficient optimization algorithms [7], and multi-fidelity optimization approaches [8]. Multi-fidelity methods leverage on a fidelity spectrum of computational models (from low to high fidelity), with the objective of maximizing the model accuracy while minimizing the associated computational cost [9,10]. The fidelity spectrum may stem from using different physical models [11,12], spatial and/or time discretizations (e.g., grid size and time step) [13,14,15,16], multidisciplinary coupling (e.g., one- or two-way, tight or loose coupling, etc.) [17,18], degree of solution convergence [19,20], model dimensionality [21,22], and a combination of experimental and numerical data [23,24]

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Results

Conclusion