Reduced‐cost surrogate modeling of input characteristics and design optimization of dual‐band antennas using response features

In this article, a procedure for low‐cost surrogate modeling of input characteristics of dual‐band antennas has been discussed. The number of training data required for construction of an accurate model has been reduced by representing the antenna reflection response to the level of suitably defined feature points. The points are allocated to capture the critical features of the reflection characteristic, such as the frequencies and the levels of the resonances, and supplemented by the additions (infill) points, which is necessary to provide sufficient data that allows restoring the entire response through interpolation. Because the coordinates of the feature points exhibit less nonlinear behavior (as a function of antenna geometry parameters) compared to S‐parameters as a function of frequency, surrogate model construction can be realized with a smaller number of data points. The presented modeling approach is demonstrated using an example of a planar dipole antenna. Also, the feature‐based method is favorably compared to direct modeling of reflection characteristics using kriging. The relevance of the technique is further verified by its application for design optimization.     

Expedited simulation‐driven design optimization of UWB antennas by means of response features

In this work, a method for fast design optimization of broadband antennas is considered. The approach is based on a feature‐based optimization (FBO) concept where reflection characteristics of the structure at hand are formulated in terms of suitably defined feature points. Redefinition of the design problem allows for reducing the design optimization cost, because the dependence of feature point coordinates on antenna dimensions is less nonlinear than for the original frequency characteristics (here, S‐parameters). This results in faster convergence of the optimization algorithm. The cost of the design process is further reduced using variable‐fidelity electromagnetic (EM) simulation models. In case of UWB antennas, the feature points are defined, among others, as the levels of the reflection characteristic at its local in‐band maxima, as well as location of the frequency point which corresponds to acceptable reflection around the lower corner frequency within the UWB band. Also, the number of characteristic points depends on antenna topology and its dimensions. Performance of FBO‐based design optimization is demonstrated using two examples of planar UWB antennas. Moreover, the computational cost of the approach is compared with conventional optimization driven by a pattern search algorithm. Experimental validation of the numerical results is also provided.     

Multi‐objective optimization using metaheuristics: non‐standard algorithms

In recent years, the application of metaheuristic techniques to solve multi‐objective optimization problems has become an active research area. Solving this kind of problems involves obtaining a set of Pareto‐optimal solutions in such a way that the corresponding Pareto front fulfils the requirements of convergence to the true Pareto front and uniform diversity. Most of the studies on metaheuristics for multi‐objective optimization are focused on Evolutionary Algorithms, and some of the state‐of‐the‐art techniques belong this class of algorithms. Our goal in this paper is to study open research lines related to metaheuristics but focusing on less explored areas to provide new perspectives to those researchers interested in multi‐objective optimization. In particular, we focus on non‐evolutionary metaheuristics, hybrid multi‐objective metaheuristics, parallel multi‐objective optimization and multi‐objective optimization under uncertainty. We analyze these issues and discuss open research lines.     

Analysis of circular polarization antenna design trade‐offs using low‐cost EM‐driven multiobjective optimization

Circular polarization (CP) antennas are vital components of modern communication systems. Their design involves handling several requirements such as low reflection and axial ratio (AR) within the frequency range of interest. Small size is an important criterion for antenna mobility which is normally achieved as a by‐product of performance‐oriented modifications of the structure topology. In this work, multiobjective optimization is used in order to identify and analyze design trade‐offs for miniaturized CP antenna including the antenna capability for maintaining small size while retaining acceptable levels of other performance figures. We use a population‐based metaheuristic algorithm to obtain a set of designs which represent the best attainable compromise between the imposed requirements. To maintain a low optimization cost, the algorithm is executed on a cheap approximation model and the results are further corrected to bring them to the EM model accuracy level. Here, the analysis is carried out for a planar CP antenna. Achievable size reduction of the considered structure—while maintaining acceptable performance—is around 11%. Antenna performance in terms of in‐band reflection and AR varies from ?14 to ?10 dB and from 1.3 to 3 dB, respectively. The numerical results are validated by measurements of fabricated antenna prototypes.     

Precise control of reflection response in bandwidth‐enhanced planar antennas

In this work, the issues of bandwidth enhancement of planar antennas and the relevance of precise and automated response control through numerical optimization have been investigated. Using an example of a planar antenna with parasitic radiator we illustrate possible effects of even minor modifications of the antenna geometry (here, applied to the ground plane) on its reflection performance. In particular, a proper handling of geometry parameters may lead to considerable broadening of the antenna bandwidth. For the sake of computational efficiency, the adjustment of geometry parameters is carried out using surrogate‐based optimization methods exploiting coarse‐discretization EM simulations as the underlying low‐fidelity antenna model. Additionally, suitably defined penalty function allows us to precisely control the maximum in‐band reflection so that sufficient margin to accommodate possible manufacturing tolerances can be achieved. The optimized designs of the two antenna structures considered in this work exhibit over 1.75 GHz (>31%) and 2.15 GHz (>38%) bandwidth, respectively, for the center frequency of 5.6 GHz. Simulation results are validated using measurements of the fabricated prototypes. Comparison with state‐of‐the‐art designs is also provided. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:653–659, 2016.     

Fast simulation‐driven antenna design using response‐feature surrogates

In this article, a computationally efficient procedure for electromagnetic (EM)‐simulation‐driven design of antennas is presented. Our methodology is based on local approximation models of the antenna response, established using a set of suitably selected characteristic features rather than the entire response (such as reflection versus frequency). The approximation model is utilized to verify the level of satisfying/violating given performance requirements, and to guide the optimization process towards a better design. By exploiting the fact that the dependence of the response features on the designable parameters of the antenna of interest is simple (close to linear or quadratic), the feature‐based optimization converges faster than conventional optimization of frequency‐based EM‐simulated responses. In order to further speed up the design, coarse‐discretization simulations are utilized to estimate the feature gradients with respect to adjustable parameters of the problem at hand. The optimization algorithm is embedded in the trust‐region framework for safeguarding convergence. The proposed technique is demonstrated using two antenna examples. In both the cases, the optimum design is obtained at the computational cost corresponding to a few high‐fidelity EM antenna simulations. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:394–402, 2015.     

Rapid design and size reduction of microwave couplers using variable‐fidelity EM‐driven optimization

In this article, fast electromagnetic (EM) simulation‐driven design optimization of compact microwave couplers is addressed. The main focus is on explicit reduction of the circuit footprint. Our methodology relies on the penalty function approach, which allows us to minimize the circuit area while ensuring equal power split between the output ports and providing a sufficient bandwidth with respect to the return loss and isolation around the operating frequency. Computational efficiency of the design process is achieved by exploiting variable‐fidelity EM simulations, local response surface approximation models, as well as suitable response correction techniques for design tuning. The technique described in this work is demonstrated using two examples of compact rat‐race couplers. The size‐reduction‐oriented designs are compared with performance‐oriented ones to illustrate available design trade‐offs. Final design solutions of the former case illustrate ～92% of miniaturization for both coupler examples (with corresponding fractional bandwidths of 16%). Alternative design solutions pertaining to the latter case show a lesser size reduction (～90% for both examples), but present a much wider bandwidths (～25% for both couplers). The overall computational cost of the design procedure corresponds to about 20 and 10 high‐fidelity coupler simulations for the first and second design example, respectively. Numerical results are also validated experimentally. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:27–35, 2016.     

Rapid design optimization of antennas using space mapping and response surface approximation models

A computationally efficient method for design optimization of antennas is discussed. It combines space mapping, used as the optimization engine, and response surface approximation, used to create the fast surrogate model of the optimized antenna. The surrogate is configured from the response of the coarse‐mesh electromagnetic model of the antenna, and implemented through kriging interpolation. We provide a comprehensive numerical verification of this technique as well as demonstrate its capability to yield a satisfactory design after a few full‐wave simulations of the original structure. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Simulation‐based optimization for rigorous assessment of ground plane modifications in compact UWB antenna design

Introducing ground plane modifications is a popular approach in the design of compact UWB antennas. Yet, specific topological alterations are normally reported on case to case basis without thorough investigations concerning their general suitability for antenna miniaturization. In particular, detailed performance comparison of different ground plane modifications is lacking in the literature. In this article, the effect of selected ground plane modifications on achievable miniaturization rate is considered based on a set of four UWB antennas. EM‐driven optimization is carried out to minimize the antenna footprints while maintaining acceptable matching within the UWB frequency range. In each case, all geometry parameters of the respective structures are utilized in the design process. For the sake of fair comparison, all antennas are implemented on the same dielectric substrate. Our results indicate a clear performance pattern, here, an advantage of the elliptical ground plane slit below the feed line over the rectangular one (average size reduction ratio of 26% versus 19% across the benchmark set). Our conjectures are confirmed by physical measurements of the fabricated antenna prototypes.     

Optimization‐Driven Antenna Design Framework With Multiple Performance Constraints

This work proposes an optimization‐driven framework that allows for antenna design with multiple constraints and tradeoff investigation between various objectives. In particular, it allows for antenna size reduction while maintaining other figures of merit (in terms of both electrical and field properties). We demonstrate our framework with UWB antennas size reduction taking into account matching, gain, efficiency, and radiation pattern stability constraints. Furthermore, we compare design tradeoffs between the minimum attainable antenna size and its electrical and field properties using seven design scenarios. The best possible tradeoffs are obtained using rigorous numerical optimization of all geometry parameters of the structure at hand. Two examples of UWB monopole antennas are provided to illustrate that the qualitative performance tradeoffs are very much dependent on a particular antenna topology and material properties of the substrate. Numerical results are supported by experimental validation.     

Meta‐heuristic multi‐ and many‐objective optimization techniques for solution of machine learning problems

Recently, multi‐ and many‐objective meta‐heuristic algorithms have received considerable attention due to their capability to solve optimization problems that require more than one fitness function. This paper presents a comprehensive study of these techniques applied in the context of machine learning problems. Three different topics are reviewed in this work: (a) feature extraction and selection, (b) hyper‐parameter optimization and model selection in the context of supervised learning, and (c) clustering or unsupervised learning. The survey also highlights future research towards related areas.     

Inverse modeling for fast design optimization of small‐size rat‐race couplers incorporating compact cells

In the paper, a framework for computationally‐efficient design optimization of compact rat‐race couplers (RRCs) is discussed. A class of hybrid RRCs with variable operating conditions is investigated, whose size reduction is obtained by replacing ordinary transmission lines with compact microstrip resonant cells (CMRCs). Our approach employs a bottom‐up design strategy leading to the development of compact RRCs through rapid design optimization of its building blocks and a subsequent fine tuning to account for parasitic cross‐coupling effects. The fundamental component of the proposed method is an inverse CMRC surrogate model, covering a wide range of cell electrical parameters, and enabling a convenient adjustment of coupler bandwidth. Having the surrogate model established, it is possible to produce close‐to‐optimum CMRC dimensions at a negligible computational cost. The subsequent correction step requires only up to two electromagnetic simulations of the CMRC. The proposed method is demonstrated by designing an RRC for several operational bandwidths. Experimental results are also provided.     

Computational‐budget‐driven automated microwave design optimization using variable‐fidelity electromagnetic simulations

A robust technique for microwave design optimization is presented. It is based on variable‐fidelity electromagnetic (EM) simulations where the approximate optimum of the “coarser” model becomes an initial design for finding the optimum of the “finer” one. The algorithm automatically switches between the models of different fidelity taking into account the computational budget assumed for the design process. Additional mechanisms enhancing the algorithm include: frequency scaling to reduce the misalignment between the models of different fidelity, as well as the local response surface approximation to reduce the number of EM simulations. The presented technique is particularly suitable for problems where simulation‐driven design is the only option, for example, for wideband antennas and dielectric resonator filters. Our method is demonstrated using two filters and one antenna example. In all cases, the optimal design is obtained at a low computational cost corresponding to a few high‐fidelity simulations of the structure. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Boundary‐based optimization strategies for design of fragment‐type isolation structure in compact MIMO systems

Fragment‐type structures have been used to acquire high isolation in compact multiple‐input and multiple‐output (MIMO) systems. In this paper, two novel optimization strategies, boundary‐based two‐dimensional (2D) median filtering operator and boundary‐based 2D weighted sum filtering operator, are proposed to design fragment‐type isolation structures first when specific boundary conditions are considered in engineering designs. Second, two computer aided optimization techniques are proposed through combining these two operators with MOEA/D‐GO (multi‐objective evolutionary algorithm based on decomposition combined with enhanced genetic operators), respectively. Finally, fragment‐type isolation structures of a compact MIMO PIFAs (planar inverted‐F antennas) system operating at 2.345‐2.36 GHz are designed. Comparison results show that more alternative designs could be found at the expense of searching speed, and both better front‐back‐ratio and wider impedance bandwidth are observed.     

Improved trust‐region gradient‐search algorithm for accelerated optimization of wideband antenna input characteristics

Full‐wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM‐based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate‐assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust‐region‐embedded gradient search with numerical derivatives is proposed for reduced‐cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand‐alone optimization routine or as a building block of surrogate‐assisted procedures.     

Response correction techniques for surrogate‐based design optimization of microwave structures

Simulation‐based optimization has become an important design tool in microwave engineering. However, using electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high‐computational cost of an accurate EM simulation. In this article, we present a review of EM‐based design optimization techniques exploiting response‐corrected physically based low‐fidelity models. The surrogate models created through such a correction can be used to yield a reasonable approximation of the optimal design of the computationally expensive structure under consideration (high‐fidelity model). Several approaches using this idea are reviewed including output space mapping, manifold mapping, adaptive response correction, and shape‐preserving response prediction. A common feature of these methods is that they are easy to implement and computationally efficient. Application examples are provided. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Application of bacteria foraging algorithm for the design optimization of multi‐objective Yagi‐Uda array

The design of antenna array with desirable multiple performance parameters such as directivity, input impedance, beam width, and side‐lobe level using any optimization algorithm is a highly challenging task. Bacteria Foraging Algorithm (BFA), as reported by electrical engineers, is the most robust and efficient algorithm in comparison with other presently available algorithms for global optimization of multi‐objective, multi‐parameter design problems. The objective of this article is to apply this new optimization technique, BFA, in the design of Yagi‐Uda array for multi‐objective design parameters. We optimize length and spacing for 6 and 15 elements array to achieve higher directivity, pertinent input impedance, minimum 3‐dB beam width, and maximum front to back ratio both in the E and H planes of the array. At first, we develop a Method of Moments code in MATLAB environment for the Yagi‐Uda array structure for obtaining the above design parameters and then coupled with the BFA for the evaluation of the optimized design parameters. Detail simulation results are included to confirm the design criteria. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2010.     

Efficient multi‐fidelity design optimization of microwave filters using adjoint sensitivity

A simple and robust algorithm for computationally efficient design optimization of microwave filters is presented. Our approach exploits a trust‐region (TR)‐based algorithm that utilizes linear approximation of the filter response obtained using adjoint sensitivity. The algorithm is sequentially executed on a family of electromagnetic (EM)‐simulated models of different fidelities, starting from a coarse‐discretization one, and ending at the original, high‐fidelity filter model to be optimized. Switching between the models is determined using suitably defined convergence criteria. This arrangement allows for substantial cost reduction of the initial stages of the optimization process without compromising the accuracy and resolution of the final design. The performance of our technique is illustrated through the design of a fifth‐order waveguide filter and a coupled iris waveguide filter. We also demonstrate that the multi‐fidelity approach allows for considerable computational savings compared to TR‐based optimization of the high‐fidelity EM model (also utilizing adjoint sensitivity). © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:178–183, 2015.     

Rapid design closure of microwave components by means of feature‐based optimization and adjoint sensitivities

In this article, fast design closure of microwave components using feature‐based optimization (FBO) and adjoint sensitivities is discussed. FBO is one of the most recent optimization techniques that exploits a particular structure of the system response to “flatten” the functional landscape handled during the optimization process, which leads to reducing its computational complexity. When combined with gradient‐based search involving adjoint sensitivities, the design cost becomes even lower, allowing us to find the optimum design using just a few electromagnetic (EM) simulations of the structure at hand. Here, operation and performance of the algorithm is demonstrated using a waveguide filter and a miniaturized microstrip rat‐race coupler (RRC). Comparative studies indicate considerable savings that can be achieved even compared with adjoint‐based gradient search. In case of RRC, numerical results are supported by experimental validation.     

EM‐simulation‐driven design optimization of compact microwave structures using multi‐fidelity simulation models and adjoint sensitivities

Reliable design of miniaturized microwave structures requires utilization of full‐wave electromagnetic (EM) simulation models because other types of representations such as analytical or equivalent circuit models are of insufficient accuracy. This is primarily due to considerable cross‐coupling effects in tightly arranged layouts of compact circuits. Unfortunately, high computational cost of accurate EM analysis makes the dimension adjustment process challenging, particularly for traditional methods based on parameter sweeps, but also for conventional numerical optimization techniques. In this article, low‐cost simulation‐driven designs of compact structures were demonstrated using gradient search with adjoint sensitivities as well as multi‐fidelity EM simulation models. The optimization process was arranged sequentially, with the largest steps taken at the level of coarse‐discretization models. Subsequent fine tuning was realized with the models of higher fidelity. Switching between the models was realized by means of adaptively controlled termination conditions. This allowed for considerable reduction of the design cost compared with single‐level optimization. The approach was illustrated using a compact microstrip rat‐race coupler with two cases considered, that is, (i) bandwidth enhancement, and (ii) minimization of the structure size. In both cases, the optimization cost corresponded to a few high‐fidelity EM simulations of the coupler structure. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:442–448, 2016.