## 5 Evolutionary Algorithms  
Evolutionary algorithms use mechanisms similar to those connected with the evolution of naturally occurring species. As already mentioned, one of the basic concepts in evolutionary algorithms is an individual. What an individual is depends on the specific problem to which the evolutionary algorithms are applied. In the problem analysed in this study, the individual is a sequence of 5 numbers. Each of these numbers corresponded to one of 5 flotation parameters obtained from the measurements. A population is a group of individuals. Operation of an evolutionary algorithm consists in changing the population of individuals in such a way that they change in the direction set by a particular criterion. The operation of the evolutionary algorithm created to solve the problem is as follows:  
1. The draw of the initial population consisting of \(n=5000\) individuals. Since each individual is 5 numbers, \(5\times 5000\) numbers should be drawn. In addition, the following limits were set on the range of volatility: \(0\leq x_{1}\leq 2\), \(10\leq x_{2}\leq 163\), \(1\leq x_{3}\leq 30\), \(0\leq x_{4}\leq 1\), \(100\leq x_{5}\leq 200\). Furthermore, it is also assumed that \(x_{1}\) and \(x_{4}\) can only be integers. The allocated numbers \(x_{2}\) indicate the middle points of the ranges. The adopted limits concerning the variability ranges also apply to all subsequent stages of the algorithm. 2. Creating another population by merging: - A copy of a previous population (consisting of \(n\) individuals), - \(n\) individuals created as a result of a mutation of individuals from the previous population. The mutation consists in changing one of the numbers included in the individual to a random one or changing an arbitrary bit included in the individual to the opposite one. - \(n\) individuals created as a result of a crossover of individuals from the previous population. The crossover consists in creating a descendant (a new individual) in such a way that each number of which it consists is selected randomly from the first or second parent (parents are individuals from which the descendant was created). It is assumed that the crossover can also consist in creating a descendant in such a way that each bit of which the descendant consists is chosen randomly from the first or second parent. - \(n\) individuals created by searching a certain environment for the best individuals of the previous population. 10 modifications were created from a given individual. Each of the modifications consisted in changing one of the numbers included in this individual by some small value assumed. Since the adopted value can be added or subtracted and the individual consists of 5 numbers, 10 modifications were created from the given individual. Thanks to such a solution, the closest environment of the individual is examined in detail. 3. (Selection--consists in population reduction. Only \(n\) individuals are selected from among the \(n=4\) individuals created previously. It was assumed that the resulting population will consist of 40% of the best individuals (meeting the criterion to the highest degree), 20% of the worst individuals and the remainder of the randomly generated ones. Adding the worst individuals enables the whole population to emerge from local extrema. Adding randomly generated individuals results in the additional search in other space areas. In the problem under consideration, the calculation of the criterion is possible due to the learned neural network. The evaluation of an individual consisted in providing 5 numbers which are the individual (\(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), \(x_{5}\)) for 5 inputs of the learned neural network and calculating on the basis of the values obtained for 3 network outputs (\(\beta\), \(\vartheta\), \(\varepsilon\)) of the criterion values. It was assumed that we are looking for solutions resulting in obtaining maximum \(\beta\), \(\varepsilon\) and minimum \(\vartheta\) values.