In this article, a novel derivative-free (DF) surrogate-based trust region optimization approach is proposed. In the proposed approach, quadratic surrogate models are constructed and successively updated. The generated surrogate model is then optimized instead of the underlined objective function over trust regions. Truncated conjugate gradients are employed to find the optimal point within each trust region. The approach constructs the initial quadratic surrogate model using few data points of order O(n), where n is the number of design variables. The proposed approach adopts weighted least squares fitting for updating the surrogate model instead of interpolation which is commonly used in DF optimization. This makes the approach more suitable for stochastic optimization and for functions subject to numerical error. The weights are assigned to give more emphasis to points close to the current center point. The accuracy and efficiency of the proposed approach are demonstrated by applying it to a set of classical bench-mark test problems. It is also employed to find the optimal design of RF cavity linear accelerator with a comparison analysis with a recent optimization technique.
Design centering is an optimal design process that seeks for the values of system parameters which maximize the probability of satisfying the design specifications (yield function). In this article, a derivative-free trust region (TR) optimization approach is combined with the generalized space mapping technique to develop a new space mapping (SM) surrogate-based statistical technique for design centering of computationally expensive microwave circuits. The TR optimization approach is well suited for expensive objective functions that have some uncertainty in their values or subject to statistical variations. The principal operation relies on building and successively updating quadratic surrogate models to be optimized instead of the objective function over TRs employing the truncated conjugate gradients. The approach constructs the initial quadratic surrogate model using fewer data points, then updates the surrogate model using a weighted least squares fitting that gives more emphasis to points close to the current center point. Integrating the TR optimization approach with the generalized space mapping technique results in a novel statistical design centering technique for the microwave circuits with a great reduction in computations and simulations needed for the yield optimization process. Design of practical microwave circuits is presented to indicate the effectiveness of the new design centering technique.
System design centering process looks for nominal values of system designable parameters that maximize the probability of satisfying the design specifications (yield function). Statistical design centering implements a statistical analysis method such as Latin hypercube sampling (LHS) for yield function estimation and explicitly optimizes it. In this paper, we introduce a new statistical design centering technique for microwave system design. The technique combines a modified surrogate-based derivative-free trust region (TR) optimization algorithm and the generalized space mapping (GSM) technique. The modified TR algorithm is a derivative-free optimization algorithm that employs quadratic surrogate models to replace the computationally expensive yield function over hyperelliptic trust regions in the optimization process. TR algorithms exhibit global convergence features irrespective the starting point setting. The new design centering approach utilizes the GSM technique to approximate the feasible region in the design parameter space with a sequence of iteratively updated space mapping (SM) surrogates. At each SM iteration, the modified TR algorithm optimizes the yield function for the current SM region approximation to get a better center. Two microwave circuit examples are used to show the effectiveness of the new design centering technique to obtain an optimal design in few SM iterations. In the design process, we employ Sonnet em for the bandstop microstrip filter design and CST Studio Suit for the ultra-wideband (UWB) multiple-inputmultiple-output (MIMO) antenna.
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