## 5 Antenna Synthesis Via an Innovative HYBRID Genetic Algorithm
Standard GAs (SGAs) are very different from those other methods with the optimization aims for the following reasons [16; 17]:  
* These SGAs cooperate with the parameters' coding over computation, not these parameters themselves;
* These SGAs being a multiple-agent hunting process (i.e., a multiple sampling of those hunting spaces);
* These SGAs do not have to make use of those derivatives indeed;
* These SGAs do not apply the deterministic transition schemes, but use some random ones instead. According to the study [18], these SGAs need to be made for every application to obtain the best results. Consequently, an IGA (innovative genetic algorithm) can be suggested to the classes of the problems for antenna combining. Figure 5 shows the specific flow chart of the IGA presented in our paper, and the main characters of the method including:  
* The application for a hybrid coding way;
* The non-correlation among the chromosomes' genes (i.e., the power weights parameters and the genes, which representing the position of those array elements should be optimized synchronously);
* The conception over a prior-knowledge-enhanced operator;
* The design of the scheme for a mind of the adaptive evolution;
* The definition of a hybridization design using the local hunting way. In the SGAs, the individual is coded via a chromosome that is represented by a two-dimensional array, so the optimization problems about the pseudo-Boolean (see from examples [6; 7; 8]) are properly addressed. A coding process is required once the dispersion factors are concerned. Every coefficient can be symbolized via a series of the Q bits. In it, Q = \(log_{2}\) (L), and L being the number of these values that the discrete parameters are able to suppose [11]. However, due to the time consuming coding/decoding processes [12] and the quantization noise, to use the binary coding is disadvantageous and unpractical once the real unknowns are taken in account. Consequently, the real-valued expression is suggested to overtake those drawbacks above [13]. Figure 5: Flowchart of the innovative genetic algorithm. As for an antenna combining of the linear (\(\lambda\)/2) mean spaced matrix (to bypass the effects of those grating lobes), to optimize the different sorts of the parameters is the key, including: Power weight of the active elements \(\{w_{k};k=0,1,2,\ldots,M-1\}\), and number of the active elements, \(M\). In this part, a hybrid coding based on the GA is adopted to address this problem properly. The chromosome is supposed as the structure below:  
\[\overline{\xi}=\{M;b_{0},b_{1},\ldots b_{k-1},b_{k},\ldots b_{N},b_{N-1};w_{0},w_{1},\ldots w_{k-1},w_{k},\ldots w_{N},w_{N-1}\}. \tag{17}\]  
In Equation (17), \(b_{k}\) is a Boolean value (i.e., true or false) giving a status (off or on) of the kth array elements, \(k\) being an integer number of (\(\lambda\)/2) intervals between the left array limit (\(x_{k}=k\,\lambda\)/2) and the kth element, \(w_{k}\) is the related excitation coefficient, and the parameter \(N\) is the number of intervals (\(\lambda\)/2 in length) in which the array length has been dispersed. As for the adopted representation, in order to achieve an admissible method and improve the convergence procedure, the suitable genetic operators should be defined. In the presented application, the mutation keeps a means for investigating the novel regions of addressing space and crossover constitutes in a way to mix the best genes of the present population. In the application some innovative choices have been implemented.