A hybrid one‐then‐two stage algorithm for computationally expensive electromagnetic design optimization

Abstract

Purpose

The purpose of this paper is to propose a surrogate model‐assisted optimization algorithm which effectively searches for the optimum at the earliest opportunity, avoiding the need for a large initial experimental design, which may be wasteful.

Design/methodology/approach

The methodologies of two‐stage and one‐stage selection of points are combined for the first time. After creating a small experimental design, a one‐stage Kriging algorithm is used to search for the optimum for a fixed number of iterations. If it fails to locate the optimum, the points it samples are then used in lieu of a traditional experimental design to initialize a two‐stage algorithm.

Findings

The proposed approach was tested on a mathematical test function. It was found that the optimum could be located, without necessarily constructing an accurate surrogate model first. The algorithm performed well on an electromagnetic design problem, outperforming both a random search and a genetic algorithm, in significantly fewer iterations. The results suggest a new interpretation of surrogate models – merely as tools for constructing a utility function to locate the optimum of an unknown function, as opposed to actual approximations of the unknown function.

Research limitations/implications

The research was carried out on unconstrained problems only. The findings have implications for modern experimental designs, as the proposed algorithm can often locate the optimum without necessarily constructing an accurate surrogate model.

Originality/value

The two paradigms of one‐stage and two‐stage selection of points in surrogate‐model assisted optimization are combined for the first time. Also, it is believed that this is the first time that the methodology ofone‐stage optimization has been used in optimal electromagnetic design.

Citation

Hawe, G. and Sykulski, J. (2007), "A hybrid one‐then‐two stage algorithm for computationally expensive electromagnetic design optimization", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 2, pp. 236-246. https://doi.org/10.1108/03321640710727601