## 5 Real Coded Mixed Integer Genetic Algorithm  
Genetic algorithm (GA) is one of the optimization and search techniques based on genetics and natural selection, modeled on the idea of [PERSON]'s theory of species origin by means of natural selection. Using this technique, the problem is solved for a different set of inputs, and each set is given some score which is then used as a selection criterion. This set of inputs is called the population of one generation. Before solving the problem again, the set of inputs is changed using elitism, selection, crossover, and mutation functions. The score which is given to an individual solution is in fact the value of a fitness function for a given set of inputs. The idea is to provide an algorithm that evolves toward a globally optimal solution. Figure 12 shows a flowchart of the real coded mixed integer genetic algorithm (RCMIGA) that is defined in [51]. This particular algorithm is selected because of the large number of inputs (in this case, eleven geometric parameters) and the highly nonlinear and discontinuous nature of the problem with many constraints and many local minima. In aerospace engineering, genetic algorithms are used even for the design of the whole aircraft, as in [52]. It is also chosen for washout filter tunning in [44]. This type of GA was chosen because the manufacturing technology requires that the geometric parameters are not continuous values, but there is some accuracy with which it is possible to manufacture parts. From this comes the explanation for the term \"mixed integer\" in the name, it is simply possible to define some variables so that they take only integer values. In addition, \"real coded\" describes that real numbers are used to represent individuals. Obtained integer values can be mapped to available discrete values, these discrete values can be real numbers. Values to which integers are mapped can be arbitrary, but they are more often linearly spaced. As one real engineering problem is analyzed here, limitations inevitably narrow the scope of possible solutions. Due to the need to define limits, the penalty method defined in the paper [53] is used. This method is reflected in the evaluation of nonlinear conditions and by summing the values of nonlinear conditions with the fitness function value. It should be noted that the value for the penalty based on the evaluation of the constraint function is obtained by normalizing the value of the constraint function. Elitism has been implemented to ensure that the best individuals pass from generation to generation unchanged. Despite the fact that they remain unchanged, these individuals,  
Figure 12: Flowchart of real coded mixed integer genetic algorithm. together with others, participate in the selection process so that they can be selected for crossover and mutation, i.e., the application of genetic operators over them. In order to enter the optimization process at all, the first generation of the population is generated based on a uniform distribution. As for every subsequent generation, this initial population must have the parameter values within the defined limits, and if there are integer parameters, they are required to have an integer value. When there is an initial population, it is possible to start the optimization process. First, the elite individuals are separated, and the selection is made. In this case, a selection based on a tournament between two individuals is used. The genetic crossover operator is then applied to the selected individuals, a crossover based on the Laplace distribution. This crossover is defined in the paper [54]. This method has three parameters for adjustment and their values are taken from the same paper. \[a=0,\ b_{real}=0.15,\ b_{int}=0.35 \tag{41}\]  
Then the genetic operator of the mutation is applied, and this mutation is based on the power distribution law. This mutation is defined in the paper [55]. This method has two parameters for adjustment, and their values are taken from the same paper.