Exploration Versus Exploitation Using Kriging Surrogate Modelling In Electromagnetic Design

Electromagnetic design almost always carries a heavy burden of highcomputational cost, with very few exceptions when a very simplistic analytical,empirical or equivalent circuit based model is found to be adequate for performanceprediction. At present, electromagnetic design problem are typically solved using atime-consuming numerical method finite element method. Most of the timethroughout the design process, or at least at later stages, numerical models arerequired to provide necessary accuracy, typically employing3D simulation usingfinite element or related technique which would cause the process becomeextremely time-consuming. Thus for practical purposes, the algorithm we need mustfind the global optimum of objective function with as few objective function calls aspossible, because the information from objective functions is always expensive. As aregression modeling method, kriging method can make predictions based on limitedobservations and it performs especially robust in the multi-objective tasks. As themain research objective, the kriging method will be discussed and tested in the thesis.After reviewing the state-of-the-art methods assisting the kriging method tochoose next location to evaluate, the significance of balancing exploration (searchingthe unknown region with high uncertainty) and exploitation searching the regionwith high confidence has been proved. The current methods like the ExpectedImprovement (EI), the Generalized Expected Improvement (GEI), the Weighted Expected Improvement (WEI) have be tested respectively and compared with eachother in order to analyses the effect of exploration and exploitation. After a set ofdetailed tests, the results presents that the exploration is helpful to search globally,since the exploitation puts a lot of emphasis on searching the region owning sufficientobservations. In some specific tests, if taking too much weight on exploitation, itmight be a risky strategy and cause the kriging model could not find the globaloptimum of objective functions. However, the current methods only can use themanual way of adjusting the tunable weighting parameters to balance the explorationand exploitation, which is hard to fit any practical cases. Thus, as the main works ofthis thesis several novel algorithms using reinforcement learning has been created,which can automatically adjust the weights on the basis of the feedback from thekriging model itself. One of the novel algorithms called Adaptive Weighted ExpectedImprovement (AWEI) method uses the potential error produced by kriging model tocalculate the rewards, but it only consider the short-term advantages. In order toconsider long-term advantages, another algorithm called Surrogate Model basedWeighted Expected Improvement (SMWEI) method was invented which apply thepotential error from kriging model and the random distributed error to build a kind ofsimplified surrogate model for predicting the long-term advantages. A set of practicalexperiments proves the SMWEI method owns the potential that not only it can findthe global optimum of objective functions; as well it can approximate the remainingareas of objective functions relatively well.To complicate research further, the issue of robustness of the design comes intoconsideration related to manufacturing tolerances, material variability, etc whichrequires the designer not only to find the optimum design but also know more aboutits quality, in other words the shape of the objective function must be estimated.Thus, the SMWEI method as a method which can fix the shape of objective functionswell can be improved to use the judgment of robustness of designs. Besides thesingle-objective tasks, the kriging also has been using in the two-objective tasks and multi-objective tasks. In last chapter of thesis, one of the two-objective tasks has beenpresented which is tested by kriging method with the Expected Improvement.