Design optimization via surrogate modeling and space mapping: the why, the what, and the how

Abstract

Do you need an engineering design but your optimization algorithms threaten hundreds of costly high-fidelity simulations, and perhaps days or weeks of CPU time? Consider an underlying surrogate model. Take the high-fidelity simulator out of the classical optimization loop. Use space mapping. Optimization via space mapping involves the iterative enhancement of surrogates. Such surrogates arise in a number of ways. A popular approach is through fast-to-compute, physically-based “coarse” models that describe the expensive “fine” model behavior relatively well. A space mapping algorithm then provides excellent designs after only a handful of high-fidelity simulations. Space mapping mimics the way the brain relates new objects or images with familiar objects, images, reality, or experience. The methodology follows the traditional experience and intuition of the engineer, yet is amenable to mathematical treatment. It offers a quantitative explanation for an expert’s “feel” for a problem. Following Bandler’s 1993 concept, space mapping methodology continues to provide success in diverse areas: electronic, photonic, antenna, and magnetic systems; civil, mechanical, and aerospace engineering structures, including automotive crashworthiness design. Corporations that have incorporated space mapping into their design portfolios include Philips, Saab, and Com Dev. We focus on why, when, and how the intuitive space mapping procedure works. We provide microwave engineering examples involving commercial electromagnetic simulators. Two IEEE Microwave Magazine articles complement our presentation, one published in February 2008, the second in December 2008.