Research paperAdaptive genetic algorithms used to analyze behavior of complex system
Introduction
As follows from the literature [1], [2], [3], [4], there is still no strict and generally accepted definition of a “complex system”. A considered system is usually identified as complex if its behavior and/or its characteristics satisfy certain specific conditions [5]. In the given study, the term “complex system” is understood to mean such a system whose properties as a whole are not reproduced only through the properties of its separate parts. Obviously, this definition is suitable for a wide variety of systems with heterogeneous “structure” and dynamics, for open natural systems with intermittent, chaotic and nonlinear dynamics. An essential feature of such systems is that their dynamics is defined by a large number of degrees of freedom. Further, according to this definition, the concept of “complex system” is not limited to consideration of some specific (say, physical) systems, but this concept extends to social, biological, ecological, physiological, economic and other systems [6], [7], [8].
Although the internal “structure” of such system can be very specific and complex, evolution of this system is usually characterized by the factors that affect the behavior of this system and by the factors that contain an information generated by this system. Based on information provided by these time-dependent factors, it is possible to analyze the behavior of a complex system. Such treatment is known in cybernetics as the “Black box concept” [9], [10], [11]. The number of these factors/characteristics of a complex system can be very large. Nevertheless, there are reasonable assumptions that greatly simplify the analysis. First, the time dependencies of these factors are correlated. Second, evolution of considered complex system is determined only by the significant factors, and number of these significant factors is finite. Third, during evolution of the system, a factor may change its status from significant to insignificant, and vice versa. Thus, we need a method, which will allow us to select the significant factors. After this, we can construct a correlation model, which takes into account these factors [12], [13], [14], [15], [16].
There are well known methods for the significant factors (variables, subset) selection: such as iteration methods of forward and backward selection [17], correlation methods [18]. However, as known [12], [19], [20], [21], these methods do not provide rigorous selection of the significant factors. As a result, one has to deal with an excessive number of parameters [11], [19], that complicates the subsequent calculations and treatment. The same problem related with the significant factors selection arises also if one uses the ordinary genetic algorithms [11], [19], [22], [23]. In the present work, we demonstrate that this problem can be resolved by means of the method based on the adaptive genetic algorithm. This allows one to construct the nonlinear regression model and to perform the subsequent analysis of complex system.
The paper is organized as follows. The methodology as well as its realization in the frameworks of the genetic algorithms concept are given in Section 2. The approach is applied to analyze the data characterizing a manufacturing company (Section 3) and the meteorological data (Section 4). Concluding remarks are given in Section 5.
Section snippets
Regression equation
Let evolution of a (complex) system over the time range T be characterized by certain set of time-dependent factors, and these factors can be divided into two groups: input factors xi(t) and output factors yj(t):where and ; whereas is the number of all the factors. An output factor yj is factor by means of which evolution of the system is monitored; and it is assumed that number K of the output factors is
Example 1: treatment of the data characterizing a manufacturing company
Let us consider application of the approach for treatment of the time-dependent data characterizing a real manufacturing company, which has cooperation with the enterprises of automobile and oil industry. The data represent quarterly information about the company’s activity for the seven years. On the basis of the data, thirty three time-dependent factors were selected for the subsequent analysis. Herewith, and factors were defined as input and output factors, xi’s and yi’s,
Example 2: meteorological data
As a second example of application of the proposed approach we consider the time-dependent weather data for Szeged – one of the largest city of Hungary located on the Tisza River in the central part of the Carpathian Basin [34]. The available data set represents the hourly values of the nine weather parameters for the period from April 1, 2006 (midnight) to April, 28, 2016 (6 pm). We are focused on the temperature dynamics in this geographic place, and, therefore, it is reasonable to take the
Concluding remarks
We note some important features of the presented approach in a context of the examples considered above.
- (i)
The generalized Kholmogorov–Gabor polynomial (2) applied within the approach is different from the linear regression equationused in the ordinary regression analysis [29]. Polynomial (2) can include the products of the input factors like . As a result, it is possible within the suggested approach to take into account the linear and (more complicated and “hidden”) nonlinear
Acknowledgements
The work of A.V.M. is supported in part by RFBR according to the research project No. 18-02-00407. A.V.M. is thankful to the Ministry of Education and Science for supporting the research in the framework of the state assignment (3.2166.2017/4.6).
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