Abstract: A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms.

Abstract: In the present paper, an efficient parallel method for solving complex multicriterial optimization problems, which the optimality criteria can be multiextremal, and the computing of the criteria values can require a large amount of computations in, is proposed. The proposed approach is based on the reduction of the multicriterial problems to the global optimization ones using the minimax convolution of the partial criteria, the dimensionality reduction with the use of the Peano space-filling curves, and the application of the efficient parallel information-statistical global optimization methods. The intensive use of the search information obtained in the course of computations is provided when conducting the computations. The results of the computational experiments demonstrated such an approach to allow reducing the computation costs of solving the multicriterial optimization problems essentially - tens and hundreds times.

Abstract: In this paper, we propose the use of a surrogate model based on mixtures of liner Taylor polynomials for Trust Region methods. The main objective of this model is to reduce the myopia presented in surrogate models based on single low-order Taylor expansions by which, the number of iterations during the optimization process of Trust Region based methods can be increased. The proposed model is built as follows: points are sampled from the search space, at each sampled point a surrogate model of the cost function is built by using a linear Taylor polynomial and then, cost functions can be locally approximated via a convex combination of such surrogate models. The Trust Region framework is then utilized in order to validate the quality of the proposed model. Even more, this model is proven to be fully linear which guaranties the global convergence of Trust Region methods to local optimum solutions. Experimental tests are performed making use of the three-dimensional variational optimization problem from data assimilation with an atmospheric general circulation model. The results reveal that, the use of our proposed surrogate model can improve the quality of the local approximations and even more, their use can decrease the number of iterations needed in order to obtain accurate solutions.

Abstract: In this paper, we discuss a computationally efficient approach to expedite design optimization of broadband hybrid couplers occupying a minimized substrate area. Structure size reduction is achieved here by decomposing an original coupler circuit into low- and high-impedance components and replacing them with electrically equivalent slow-wave lines with reduced physical dimensions. The main challenge is reliable design of computationally demanding low-impedance slow-wave structures that feature a quasi-periodic circuit topology for wideband operation. Our goal is to determine an adequate number of recurrent unit elements as well as to adjust their designable parameters so that the coupler footprint area is minimal. The proposed method involves using surrogate-based optimization with a reconfigurable co-simulation coarse model as the key component enabling design process acceleration. The latter model is composed in Keysight ADS circuit simulator from multiple EM-evaluated data blocks of the slow-wave unit element and theory-based feeding line models. The embedded optimization algorithm is a trust-region-based gradient search with coarse model Jacobian estimation. We exploit a penalty function approach to ensure that the electrical conditions for the slow-wave lines are accordingly satisfied, apart from explicitly minimizing the area of the coupler. The effectiveness of the proposed technique is demonstrated through a design example of two-section 3-dB branch-line coupler. For the given example, we obtain nine circuit design solutions that correspond to the compact couplers whose multi-element slow-wave lines are composed of unit cells ranging from two to ten.

Abstract: Fast and accurate airfoil design under uncertainty using nonintrusive polynomial chaos expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated for the design of airfoil shapes under uncertainty. The proposed approach is illustrated on a numerical example of lift-constrained airfoil drag minimization in transonic viscous flow using the Mach number as an uncertain variable. The results show that compared with the standard problem formulation the proposed approach yields more robust designs. In other words, the designs obtained by the proposed approach are less sensitive to variations in the uncertain variables than those obtained with the standard problem formulation.