**1. Introduction**

Antennas are 3D structures, so, at variance of other MW subsystems like filters and couplers, their design has been a matter of intuition and brute-force computations from the beginning (Silver, 1949; Elliott, 1981 just to remember a few). Therefore, an antenna design has been faced at different levels, from simple formulas (Collin, 1985) to sophisticated synthesis techniques (Orchard et al., 1985; Bucci et al., 1994), and from simple heuristic models (Carrel, 1961) to modern global random optimizations, such as GA (Linden & Altshuler, 1996, 1997; Jones & Joines, 1997) and PSO (Baskar et al., 2005), with their heavy computational loads.

Moreover, an antenna design problem is typically divided into two phases, namely an external problem (the evaluation of the antenna currents from the field requirements) and an internal problem (the design of the feed structure needed to achieve those currents, and the input match) (Bucci et al., 1994). In many cases these two phases are almost independent, but for some mutual constraints, as in reflector (Collin, 1985) and slot (Costanzo et al., 2009; Montisci, 2006) or patch (Montisci et al., 2003) array synthesis, since in these cases there is a clear boundary separating the feeding and radiating part of the antenna. In other problems, as in wire antennas design (Johnson & Jasik, 1984), such phases are strictly interconnected, since no clear-cut divides the two parts. For parasitic wire antennas, the interconnection is even stronger, since every element acts as feeding and radiating part at the same time.

The traditional approach to the design of wire antennas starts by choosing a well-defined structure, whose parameters are then optimized. However, a good design requires also a continuous human monitoring, mainly to trim the initial structure to better fit the antenna specifications. A trimming which requires both a deep knowledge and experience in order to effectively change the structure under design. As a matter of fact, such traditional approach is quite expensive, and therefore design techniques without human interaction are

© 2012 Casula and Mazzarella, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Casula and Mazzarella, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of interest, as long as they provide equal, or better, results. This can be achieved only when no initial structure is assumed, since this choice (by necessity fixed in a fully automated procedure) can constrain too strongly the final solution.

Structure-Based Evolutionary Design Applied to Wire Antennas 119

The performance, in the particular problem environment, of each individual computer program in the population is measured by its "fitness". The nature of the fitness measure depends on the problem at hand. Different fitness functions, built from different requirements, can lead to completely different results, each one best fitted to the

The only information which the design process requires to advance in its search within the space of possible solutions are the current population and the fitness of all its individuals. A new population is then generated, by applying simple rules inspired by natural evolution.

• The reproduction simply reproduces in the new population, without any change, a predetermined number of individuals among those who obtained the best fitness. • Crossover is applied on an individual by simply switching one of its nodes with another node from another individual in the population. With a tree-based representation, replacing a node means the replacement of the whole branch. This adds greater effectiveness to the crossover operation, since it exchanges two actual subindividuals with different dimensions. The expressions resulting from a single crossover can be either quite close or very different from their initial parents. The sudden jump from an individual to a very different one is a powerful trap-escaping

• Mutation affects an individual in the population, replacing a whole node in the selected individual, or just the node's information. To maintain integrity, operations must be

Since each individual in the SED approach is a set of unambiguous instructions describing the realization of a generic physical structure, the presented procedure can be extended, in

Before entering into the SED description, some considerations on the name chosen (Casula et al., 2011a) are in order. Koza, in his 1992 paper, coined the name "genetic programming" for his approach. Actually, this name resembles too closely another optimization approach, but with marked differences with the Koza approach, namely the genetic algorithms (GA). We decided to use a different name, better linked to the approach we use, to avoid any ambiguity between very different approaches. In order to better grasp the differences between SED and GA, we can say that GA works on the "nucleotide" (i.e. bit) level, in the sense that the structure is completely defined from the beginning, and only a handful of parameters remain to be optimized. On the other hand, the approach used in SED assumes no "a priori" structure, and it builds up the structure of the individuals as the procedure evolves. Therefore it operates at the "organ" (i.e. physical structure) level, a far more powerful level: it acts on subparts of the whole structure, thus allowing an effective exploration of a far more vast solution space than other design techniques. SED is able to determine both the structure shape and dimensions as an outcome of the procedure, and is therefore a powerful tool for the designer. As a consequence, its solution space has the power of the continuum, while the GA solution space is a discrete one, so it is a very small subspace of the former. Moreover, the

fail-safe, i.e. the type of information the node holds must be taken into account.

The main (meta)-operators used in SED are reproduction, crossover and mutation.

corresponding original requirements.

mechanism.

principle, to any 3D structure.

The present work proposes such an alternative technique which allows to automate the whole project (and not only its repetitive parts), and provide original solutions, not achievable using standard design techniques. This is obtained by describing the whole antenna in terms of elementary parts (wire segments, junctions, and so on), and of their spatial relations (distance, orientation), and searching for high-performance structures by distributing, in the space, groups of these elementary objects. In this way, the final antenna is sought for in an enormous search space, with a very large number of degrees of freedom which leads to better solutions both in terms of performance and overall dimensions. On the other hand, such solution space must be searched for in an effective, and automatic, way in order to get the required antenna. Aim of this work is to describe how to effectively perform an automatic design of wire antennas without an initial choice of the structure, in order to achieve higher performances than those obtainable by using classical design techniques (eg Yagi antennas and log-periodic antennas (Johnson & Jasik, 1984)).

This can be achieved using a new design technique, namely the Structure-based Evolutionary Design (SED), a new global random search method derived by the strategy first proposed by Koza (Koza, 1992). Many optimization techniques recently proposed, such as GA, share the same inspiration, though natural selection is definitely not an optimization process. As a matter of fact, Darwin stated that "the natural system is founded on the descent with modification" (Darwin, 1859), since what is commonly named natural selection is a process leading to biological units better matched to local changing environments. Therefore, from a conceptual point of view, design approaches based on natural selection should be formulated as a search for antennas fulfilling a set of antenna specifications (the *local changing environment*) rather than as optimization of a given performance index. As we will show later, SED allows following this paradigm and in a way closer to how natural selection works. Natural selection has, in fact, a number of peculiar characteristics. First, if we look at it in a functional, or effective, way it works at the organ level. Moreover, it allows an enormous variability, which is limited only by some broad-sense constraints.

Each individual in the SED approach is a "computer program", i.e., a sequential set of unambiguous instructions completely (and uniquely) describing the realization (almost in engineering terms) of the physical structure of an admissible individual. This is a marked difference with GA, where an individual is only a set of physical dimensions and other parameters. In the practical implementation of SED, populations of thousands of individuals, which are traditionally stored as tree structures, are genetically bred using the Darwinian principle of survival and reproduction of the fittest, along with recombination operations appropriate for mating computer programs. Tree structures can be easily evaluated in a recursive manner; every tree node has an operator function and every terminal node has an operand, making mathematical expressions easy to evolve and to be evaluated.

The performance, in the particular problem environment, of each individual computer program in the population is measured by its "fitness". The nature of the fitness measure depends on the problem at hand. Different fitness functions, built from different requirements, can lead to completely different results, each one best fitted to the corresponding original requirements.

The only information which the design process requires to advance in its search within the space of possible solutions are the current population and the fitness of all its individuals. A new population is then generated, by applying simple rules inspired by natural evolution.

The main (meta)-operators used in SED are reproduction, crossover and mutation.

118 Genetic Programming – New Approaches and Successful Applications

procedure) can constrain too strongly the final solution.

Yagi antennas and log-periodic antennas (Johnson & Jasik, 1984)).

of interest, as long as they provide equal, or better, results. This can be achieved only when no initial structure is assumed, since this choice (by necessity fixed in a fully automated

The present work proposes such an alternative technique which allows to automate the whole project (and not only its repetitive parts), and provide original solutions, not achievable using standard design techniques. This is obtained by describing the whole antenna in terms of elementary parts (wire segments, junctions, and so on), and of their spatial relations (distance, orientation), and searching for high-performance structures by distributing, in the space, groups of these elementary objects. In this way, the final antenna is sought for in an enormous search space, with a very large number of degrees of freedom which leads to better solutions both in terms of performance and overall dimensions. On the other hand, such solution space must be searched for in an effective, and automatic, way in order to get the required antenna. Aim of this work is to describe how to effectively perform an automatic design of wire antennas without an initial choice of the structure, in order to achieve higher performances than those obtainable by using classical design techniques (eg

This can be achieved using a new design technique, namely the Structure-based Evolutionary Design (SED), a new global random search method derived by the strategy first proposed by Koza (Koza, 1992). Many optimization techniques recently proposed, such as GA, share the same inspiration, though natural selection is definitely not an optimization process. As a matter of fact, Darwin stated that "the natural system is founded on the descent with modification" (Darwin, 1859), since what is commonly named natural selection is a process leading to biological units better matched to local changing environments. Therefore, from a conceptual point of view, design approaches based on natural selection should be formulated as a search for antennas fulfilling a set of antenna specifications (the *local changing environment*) rather than as optimization of a given performance index. As we will show later, SED allows following this paradigm and in a way closer to how natural selection works. Natural selection has, in fact, a number of peculiar characteristics. First, if we look at it in a functional, or effective, way it works at the organ level. Moreover, it allows

an enormous variability, which is limited only by some broad-sense constraints.

evaluated.

Each individual in the SED approach is a "computer program", i.e., a sequential set of unambiguous instructions completely (and uniquely) describing the realization (almost in engineering terms) of the physical structure of an admissible individual. This is a marked difference with GA, where an individual is only a set of physical dimensions and other parameters. In the practical implementation of SED, populations of thousands of individuals, which are traditionally stored as tree structures, are genetically bred using the Darwinian principle of survival and reproduction of the fittest, along with recombination operations appropriate for mating computer programs. Tree structures can be easily evaluated in a recursive manner; every tree node has an operator function and every terminal node has an operand, making mathematical expressions easy to evolve and to be


Since each individual in the SED approach is a set of unambiguous instructions describing the realization of a generic physical structure, the presented procedure can be extended, in principle, to any 3D structure.

Before entering into the SED description, some considerations on the name chosen (Casula et al., 2011a) are in order. Koza, in his 1992 paper, coined the name "genetic programming" for his approach. Actually, this name resembles too closely another optimization approach, but with marked differences with the Koza approach, namely the genetic algorithms (GA). We decided to use a different name, better linked to the approach we use, to avoid any ambiguity between very different approaches. In order to better grasp the differences between SED and GA, we can say that GA works on the "nucleotide" (i.e. bit) level, in the sense that the structure is completely defined from the beginning, and only a handful of parameters remain to be optimized. On the other hand, the approach used in SED assumes no "a priori" structure, and it builds up the structure of the individuals as the procedure evolves. Therefore it operates at the "organ" (i.e. physical structure) level, a far more powerful level: it acts on subparts of the whole structure, thus allowing an effective exploration of a far more vast solution space than other design techniques. SED is able to determine both the structure shape and dimensions as an outcome of the procedure, and is therefore a powerful tool for the designer. As a consequence, its solution space has the power of the continuum, while the GA solution space is a discrete one, so it is a very small subspace of the former. Moreover, the typical evolution operators work on actual physical structures, rather than on sequences of bits with no intuitive link to the structure shape. The enormous power of SED fully allows the exploration of more general shapes for the structure. The main drawback is the ill-posedness of the SED, which calls for a regularization procedure.

Structure-Based Evolutionary Design Applied to Wire Antennas 121

After an initial step, where N individuals are picked up at random, an iterative procedure starts, which includes the evaluation of the fitness (appropriate for the problem at hand) for each individual, and the building of the next generation of the population. A larger probability of breeding is assigned to individuals with the highest fitness. The generation of new populations ends only when opportune stopping rules are met (i.e. when the

The solution space, i.e., the set of admissible solutions in which the procedure looks for the optimum, has the power of the continuum. This is the main advantage of SED, since it allows exploring, and evaluating, general structure configurations, but, on the other hand, it can lead to a severely ill-conditioned synthesis problem. As a consequence, a naive implementation usually does not work, since different starting populations lead to completely different final populations, possibly containing only individuals poorly matched to the requirements (a phenomenon similar to the occurrence of traps in optimization

A suitable stabilization is therefore needed. This role can be accomplished by suitable structure requirements, or forced by imposing further constraints, not included in the structure requirements. Whenever possible, the former ones are the better choice, and

Typically, a high number N of individuals for a certain number of generations must be evaluated in order to obtain a good result from the design process. Since each individual can be evaluated independently from each other, the design process is strongly parallelizable,

The Structure-Based Evolutionary Design, based on evolutionary programming, has been devised and applied to the design of broadband parasitic wire arrays for VHF-UHF bands. This requires first to devise a suitable tree representation of wire antennas, well tailored to the SED meta-operators, and then suitable antenna requirements. We consider only antennas with a symmetry plane, and with all element centres on a line. Therefore, each "wire" is actually a symmetric pair of metallic trees, and only one of them must be

In antenna design, the most intuitive fitness function can be built as the "distance" between actual and required far-field behaviour (Franceschetti et al., 1988) or, even more simply, as the antenna gain or SNR (Lo et al., 1966). However, this is not the case for SED. The solution space, i.e., the set of admissible solution in which the procedure looks for the optimum, is composed, in our case, of every Parasitic Dipole Array (PDA) antenna with no limit on the number of wire segments, nor on the size or orientation, represented as real numbers. The design problem is therefore strongly ill-conditioned and, in order to stabilize it, appropriate suitable antenna requirements must be set. Far-field requirements are unable to stabilize the problem, since the far-field degrees of freedom are orders of magnitude less than those of

individual-antenna fulfils, to a prescribed degree, the stated requirement).

procedures).

described.

should be investigated first.

and this can significantly reduce the computation time.

**2.1. SED applied to the design of wire antennas** 

The rest of this chapter is organised as follows:

