Correlation matrices in kriging assisted optimisation of electromagnetic devices

Abstract

Kriging surrogate modelling facilitates efficient decision making regarding where to place the next point for evaluation during optimisation. This is particularly helpful in the design of electromagnetic devices where computationally expensive numerical field modelling needs to be used. The disadvantage, however, is that correlation matrices are required which, for problems with many design variables and multiple objectives, may grow in size leading to the need for page swapping and thus slowing down of what in principle should be a very fast process. In this study several methodologies to reduce the computational resources required in such problems are proposed. The efficiency of the proposed approach is demonstrated using an example of a large multi-parameter optimisation problem where kriging coupled with the average gradient value method is employed.

Robust design optimisation of electromagnetic devices exploiting gradient indices and Kriging

“…Notwithstanding, it should be noted that when using a computer with limited memory there will be difficulties associated with running the numerical simulation software too, which the Kriging model is trying to replace, so the issues of limited available memory are not unique to Kriging formulation; they must, however, be addressed. One possible way forward for much larger practical problems with many variables is to explore the sensitivity of the objective function to changes in all parameters and focus on a subset of such parameters; this idea is pursued in the follow-up work [23].…”

Rapid Prototyping across the Spectrum: RF to Optical 3D Electromagnetic Structures

“…However, a theoretically optimum solution may not be the most robust or stable [49]. Fabrication tolerances and deviations can adversely affect the device performance and thus a pareto front solution, that may not have the best performance but is more stable with parameter uncertainty, may hold the key to physically viable implementations [50]. These techniques have been explored in the context of antenna and antenna arrays as well as micro-/sub-millimeter wave components.…”

Multi-Objective Pareto Optimization of Electromagnetic Devices Exploiting Kriging With Lipschitzian Optimized Expected Improvement

“…However, it was found that large-scale tasks-multi-objective and employing many design variables-may lead to a "combinatorial explosion" when all the required correlation matrices are established between the sample points and the design vectors. The partitioning scheme [4] of the correlation matrices, splitting them into manageable sizes, can mitigate to some extent the burden of storing this massive amount of data, but sacrifices may need to be made in terms of computing efficiency at each iteration to achieve more available physical memory. Therefore, a more efficient method capable of removing this bottleneck is sought.…”