Optimal parameters selection of the genetic algorithm for global optimization

The purpose of this work is to summarize the results of research concerning the application of genetic algorithms, since in solving problems of complex systems optimization situations often make it difficult or impossible to use classical methods. To solve this problem, research is carried out on the functions of Akli, Rastrigin, Shekel, complaints handling functions and Rosenbrock functions. The studies are conducted on three starting point scattering algorithms: LPτ sequence, UDC sequences and universal random variation. As a result of the analysis, the option of initialization, selection, recombination, mutation and coding of this algorithm according to given test functions for the data of the scatter of initial points is chosen. The effective parameters of the genetic algorithm according to the results of research are established.


Introduction
Nowadays, the genetic algorithm for global optimization [1][2][3][4] has many options for the algorithm parameters. When applying this algorithm in practice, it is necessary to know which options to use in the first place, i.e. what options of parameters give the greatest efficiency, more precisely, what combination of them gives the greatest efficiency on test functions.
The efficiency of the algorithms will be calculated in three directions: by the value of the function, by the number of steps of the algorithm, by the running time of the algorithm. Studies were conducted on Ackley, Rastrigin, Shekel, Grivanka and Rosenbrock functions [2,5,6]. LP sequence [3,7], UDC sequence, uniform random scatter -very interesting and effective scatter algorithms of initial points. Recent studies in this area were carried out in the works of the scientist [4,8,9].
These studies are applied to specific practical problems, the goal was not to average these parameters, to test for a large number of practical tasks of a test function complex type [1,10]. LP-sequences are an algorithm for scattering points based on a matrix of irreducible Marshal polynomials. UDC sequences are an algorithm for absolutely points uniform distribution over all coordinates in a multidimensional space, regardless of the scatter points number [3,5,8]. Uniform random scatter is a stochastic point scatter algorithm using the normal distribution law.

Experimental part
Block-scheme of the genetic algorithm, which is on study, is presented in Figure 1. The algorithm is standard and consists of five steps: population initialization, assessment of fitness for each individual in population, selection, recombination and mutation. 3 parts of their chromosomes. As a result, the offspring appears, usually the most suitable for further "life". The offspring mutates with time, i.e. changes some of its "genes". This continues until an individual is fit enough.
The study was conducted on test functions: the Acley function, the Rastrigin function, the Shekel function, the Grivanka function and Rosenbrock function.
Algorithm inputs:  The size of the studied patterns space -2.

Results and discussion
As it is known, the goal of the optimization algorithm is to find the extremum as accurately as possible, faster and cheaper. Therefore, it is necessary to take into account the obtained results.
The optimal, in absolute value, the parameters of the genetic algorithm (initialization -Init, selection -Sel, recombination -Rec, mutation -Mut, coding -Cod) were determined, for each test function optimized for each point of view (Tables 1-5).   It is not possible to draw conclusions about the optimal, on average, values of the genetic algorithm parameters for all test functions, since the optimal values of each parameter for each test function are different.
To identify the optimal, on average, values of the parameters of the genetic algorithm for all test functions, it is necessary, using new comparison methodology, to identify with a certain level of significance which options of parameters differ significantly from each other, and which do not. Only in this case, it is possible to determine the optimal, on average, parameter values of the genetic algorithm for all test functions.

Conclusion
In this study, the genetic algorithm for global optimization was analyzed. The studies were carried out on the Akli, Rastrigin, Shekel, Grivanka and Rosenbrock function. The studies were conducted on three initial point spread algorithms: LP sequence, UDC sequence, uniform random variation.
As a result, the best variant of initialization, selection, recombination, mutation, coding of the given algorithm on the given test functions for the given algorithms of the spread of initial points was revealed.