Research paper
Adaptive genetic algorithms used to analyze behavior of complex system

https://doi.org/10.1016/j.cnsns.2018.11.014Get rights and content

Highlights

  • Approach for analysis of evolution of a complex system is suggested.

  • Nonlinear regression model is generated by means of the adaptive genetic algorithm.

  • It becomes possible to identify significant characteristics/factors of complex system behavior.

  • The suggested approach is applied for analysis of the data characterizing a manufacturing company.

Abstract

In the present study, we consider a complex system whose behavior is characterized by set of various time-dependent factors. Some of these factors can characterize the external influences on the system, whereas other factors contain information generated by system. We demonstrate that time-dependence of these factors can be reproduced by the nonlinear regression model. The concrete form of this regression model is constructed on the basis of the genetic algorithms technique. This allows us to predict a possible behavior of the system and to identify the so-called significant factors that have a significant impact on the behavior of the system. To demonstrate validity of the method, we apply it to analyze the data characterizing a manufacturing company and the meteorological data.

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):{x1(t),x2(t),,xi(t),,xM(t)},{y1(t),y2(t),,yj(t),,yK(t)},where i=1,2,,M and j=1,2,,K; whereas (M+K) 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, M=23 and K=10 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 equationy=iaixi.used in the ordinary regression analysis [29]. Polynomial (2) can include the products of the input factors like xixjxk. 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).

References (35)

  • A. Bunde et al.

    Nonlinear memory and risk estimation in financial records

  • M. Bunge

    A general black-box theory

    Philos Sci

    (1963)
  • A.N. Kolmogorov

    Three approaches to the quantitative definition of information

    Probl Inf Transmission

    (1965)
  • D.T. Larose

    Data mining methods and models

    (2006)
  • E.I. George

    The variable selection problem

    J Am Stat Assoc

    (2000)
  • R. Yulmetyev et al.

    Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis

    Phys Rev E

    (2001)
  • R.M. Yulmetyev et al.

    Universal approach to overcoming nonstationarity, unsteadiness and non-markovity of stochastic processes in complex systems

    Physica A

    (2005)
  • Cited by (56)

    • Sustainable design of reinforced concrete structural members using embodied carbon emission and cost optimization

      2021, Journal of Building Engineering
      Citation Excerpt :

      For each solution, calculate the values of the two objective functions (i.e. embodied emissions and costs) and ICVs. Step 4, create offspring solutions taking advantage of the operators of crossover and mutation [50,51], integrate the parent and offspring solutions into a unique pool, and determine non-dominated solutions according to the values of objective functions. Step 5, adopt the fast non-dominated sorting (NSGA-II) method proposed by Deb [52] to select superior individuals as the parents of the next generation.

    View all citing articles on Scopus
    View full text