Multi-fidelity Data Driven Expensive Optimization And Its Applications On The Antenna Design

As a key part of radio equipment,antenna is widely used in the fields of communication,radar and etc.Conventional antenna design methods rely on the designers' knowledge of electromagnetic theory and experiences,and it is difficult to find a solution in a short time while facing with challenging requirements.As a novel antenna design method,data driven evolutionary antenna design could consider various requirements together,which reducing the dependence on researchers' experience.Therefore,evolutionary antenna design method is now widely acknowledged.However,with the development of evolutionary antenna,the problem of unaffordable expensive cost produced from the search process gradually came out,which means antenna design problems are belong to expensive problems.For the above problem,data-driven surrogate-assisted optimization,which acts as a very effective global optimization algorithm,has been widely applied in designing problems.By structuring the probabilistic surrogate model and the acquisition function appropriately,the optimization framework can guarantee to get the optimal solution under a few numbers of function evaluations.In addition,various fidelity surrogate models could be regarded as different approximation of real function evaluation,which generates different error and demant different computational cost.It is suitable to apply multi-fidelity data driven evolutionary algorithm to solve.The main purpose of this dissertation is to research multi-fidelity data driven of expensive optimization and its applications on antenna design.The main research work is shown as follows: 1)Two improvements are proposed for hyperparameter estimation during multi-fidelity Gaussian surrogate: a)in order to ensure computational stability and accuracy,an exact formula to calculate regular quantity is designed by analyzing the crash during modeling;b)a method for determining the range of hyperparameter before maximizing likelihood function is proposed,which is rarely discussed before.2)For multi-fidelity Gaussian process model in multi-fidelity optimization,analyzing the impact of correlation,relative evaluation cost and the split among different fidelity functions on the performance of surrogate model,and proposing a general guide for constructing a multi-fidelity Gaussian process model.3)A new algorithm utilizing multiple single-response Gaussian process model is designed for multi-fidelity problems,which is test on multi-fidelity benchmark functions.Results show that in the same condition of computational budget the proposed algorithm could get better solutions than single-fidelity surrogate assisted algorithm.4)A novel robust-enhanced method without additional overhead is proposed.Then applying data-driven surrogate assisted evolutionary algorithms,including single-fidelity and multi-fidelity versions,to design a volcano smoke antenna.Results show it is benefitial to make use of surrogate with limited computational budget.In addition,multi-fidelity data-driven evolutionary algorithm could obtain similar optimal antenna individual compared to single-fidelity case and consume less time cost.There are two innovation points in this paper: a)My work could ensure computational stability and accuracy during modeling and give the range of hyperparameter before maximizing likelihood function,which is rarely discussed in previous research.b)For multi-fidelity Gaussian process model in multi-fidelity optimization,analyzing the impact of correlation,relative evaluation cost,the number of expensive evaluation and the split among different fidelity functions on the performance of surrogate model,and proposing a general guide for constructing a multi-fidelity Gaussian process model.