It has been shown that transverse electric plane waves reflect from certain types of metamaterials with a unit magnitude reflection coefficient (Smith and Schurig, Phys Rev Lett 90 (2003), 077405-1-077405-4).Here we investigate the reflection of transverse magnetic plane waves using a Hertzian dipole over a semi-infinite slab of metamaterial, which is used as a ground plane. (c) 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:899-903, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27454

Evolutionary computation (EC) techniques in design optimization such as genetic algorithms (GA) or efficient global optimization (EGO) require an initial set of data samples (design points) to start the algorithm. They are obtained by evaluating the cost function at selected sites in the input space. A two-dimensional input space can be sampled using a Latin square, a statistical sampling technique which samples a square grid such that there is a single sample in any given row and column. The Latin hypercube is a generalization to any number of dimensions. However, a standard random Latin hypercube can result in initial data sets which may be highly correlated and may not have good space-filling properties. There are techniques which address these issues. We describe and use one technique in this paper.

Efficient Global Optimization (EGO) minimizes expensive cost function evaluations by correlating evaluated parameter sets and respective solutions to model the optimization space. For optimizations requiring destructive testing or lengthy simulations, this computational overhead represents a desirable tradeoff. However, the inspection of the predictor space to determine the next evaluation point can be a time-intensive operation. Although DACE predictor evaluation may be conducted for limited parameters by exhaustive sampling, this method is not extendable to large dimensions. We apply EGO here to the 11-dimensional optimization of a wide-band fragmented patch antenna and present an alternative genetic algorithm approach for selecting the next evaluation point. We compare results achieved with EGO on this optimization problem to previous results achieved with a genetic algorithm.

EGO is an evolutionary, data-adaptive algorithm which can be useful for optimization problems with expensive cost functions. Many antenna design problems qualify since complex computational electromagnetics (CEM) simulations can take significant resources. This makes evolutionary algorithms such as genetic algorithms (GA) or particle swarm optimization (PSO) problematic since iterations of large populations are required. In this paper we discuss multiparameter optimization of a wideband, single-element antenna over a metamaterial ground plane and the interfacing of EGO (optimization) with a full-wave CEM simulation (cost function evaluation).

Chromosome design has been shown to be a crucial element in developing genetic algorithms which approach global solutions without premature convergence. The consecutive positioning of parameters with high-correlations and relevance enhances the creation of genetic building blocks which are likely to persist across recombination to provide genetic inheritance. Incorporating positional gene relevance is challenging, however, in multi-dimensional design problems. We present a hybrid chromosome designed for optimizing a fragmented patch antenna which combines linear and two-dimensional gene representations. We compare previous results obtained with a linear chromosome to solutions obtained with this new hybrid representation.

Efficient Global Optimization (EGO) is a competent evolutionary algorithm which can be useful for problems with expensive cost functions [1,2,3,4,5]. The goal is to find the global minimum using as few function evaluations as possible. Our research indicates that EGO requires far fewer evaluations than genetic algorithms (GAs). However, both algorithms do not always drill down to the absolute minimum, therefore the addition of a final local search technique is indicated. In this paper, we introduce three "endgame" techniques. The techniques can improve optimization efficiency (fewer cost function evaluations) and, if required, they can provide very accurate estimates of the global minimum. We also report results using a different cost function than the one previously used [2,3].

Efficient Global Optimization (EGO) is a competent evolutionary algorithm suited for problems with limited design parameters and expensive cost functions. Many electromagnetics problems, including some antenna designs, fall into this class, as complex electromagnetics simulations can take substantial computational effort. This makes simple evolutionary algorithms such as genetic algorithms or particle swarms very time-consuming for design optimization, as many iterations of large populations are usually required. When physical experiments are necessary to perform tradeoffs or determine effects which may not be simulated, use of these algorithms is simply not practical at all due to the large numbers of measurements required. In this paper we first present a brief introduction to the EGO algorithm. We then present the parasitic superdirective two-element array design problem and results obtained by applying EGO to obtain the optimal element separation and operating frequency to maximize the array directivity. We compare these results to both the optimal solution and results obtained by performing a similar optimization using the Nelder-Mead downhill simplex method. Our results indicate that, unlike the Nelder-Mead algorithm, the EGO algorithm did not become stuck in local minima but rather found the area of the correct global minimum. However, our implementation did not always drill down into the precise minimum and the addition of a local search technique seems to be indicated.

Over the past decade, the Air Force Research Laboratory (AFRL) Antenna Technology Branch at Hanscom AFB has employed the simple genetic algorithm (SGA) as an optimization tool for a wide variety of antenna applications. Over roughly the same period, researchers at the Illinois Genetic Algorithm Laboratory (IlliGAL) at the University of Illinois at Urbana Champaign have developed GA design theory and advanced GA techniques called competent genetic algorithms-GAs that solve hard problems quickly, reliably, and accurately. Recently, under the guidance and direction of the Air Force Office of Scientific Research (AFOSR), the two laboratories have formed a collaboration, the common goal of which is to apply simple, competent, and hybrid GA techniques to challenging antenna problems.This paper is composed of two parts. The first part of this paper summarizes previous research conducted by AFRL at Hanscom for which SGAs were implemented to obtain acceptable solutions to several antenna problems. This research covers diverse areas of interest, including array pattern synthesis, antenna test-bed design, gain enhancement, electrically small single bent wire elements, and wideband antenna elements.The second part of this paper starts by briefly reviewing the design theory and design principles necessary for the invention and implementation of fast, scalable genetic algorithms. A particular procedure, the hierarchical Bayesian optimization algorithm (hBOA) is then briefly outlined, and the remainder of the paper describes collaborative efforts of AFRL and IlliGAL to solve more difficult antenna problems. In particular, recent results of using hBOA to optimize a novel, wideband overlapped subarray system to achieve -35 dB sidelobes over a 20% bandwidth. The problem was sufficiently difficult that acceptable solutions were not obtained using SGAs. The case study demonstrates the utility of using more advanced GA techniques to obtain acceptable solution quality as problem difficulty increases., (c) 2005 Elsevier Ltd. All rights reserved.

An adaptive antenna places nulls in its antenna pattern in the direction of the interfering sources. Adaptive antennas are a subset of smart antennas, and have received considerable interest in the recent wireless revolution. This paper presents a successful application of a genetic algorithm with an experimental antenna for placing a null in the direction of an interference source. The experiment took place at the Air Force Research Laboratory (AFRL)/Sensors Directorate, Hanscom AFB, MA. Results show that a null can be placed down to the noise floor of the measurement system within 20 to 50 power measurements. Thus, the approach to adaptive nulling is a viable means of quickly placing a null in the sidelobes of a phased array antenna