# Evolutionary Optimization of Case-Based Forecasting Algorithms in Chaotic Environments

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- -
- the system component $X\left(k\right),k=1,\cdots ,N$ of the observed process represents a realization of dynamic chaos and usually takes the form of an oscillatory non-periodic process with a set of false local trends of indefinite duration and
- -
- the noise component $\upsilon \left(k\right),k=1,\cdots ,N$ of the observed process is a nonstationary heteroscedastic process with a non-degenerate autocorrelation function that is time-dependent.

## 3. Results and Discussion

#### 3.1. Implementation of the Computational Precedent Prediction Scheme for Chaotic Processes

#### 3.2. Preliminary Numerical Studies and Results

#### 3.3. Evolutionary Modeling Method Applied to the Problem of Dynamic Adaptation of the Precedent Prediction Algorithm

#### 3.4. Numerical Studies of Evolutionary Adaptation of the Precedent Data Analysis Algorithm

#### 3.5. Specific Features of Evolutionary Adaptation of the Precedent Analysis Algorithm for Chaotic Processes

#### 3.6. Analysis of the Dynamic and Statistical Characteristics of an Unstable Gas-Dynamic System

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Effects of analogous situations used as a prediction and their relationship to the actual predicted process.

**Figure 7.**Dependence of the average value CVO of the precedent prediction score on the value of the filtering coefficients.

**Figure 8.**Dependence of the average value CVO of the precedent prediction score from the model generation number.

**Figure 9.**System and noise components in observations of parameter states of an unstable environment.

**Figure 10.**System component of a process based on cubic spline approximation (green—experimental data a one-day monitoring, blue—spline approximation).

${\mathit{N}}_{\mathit{A}}$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

(4) | 15.82 | 16.53 | 16.37 | 17.14 | 17.15 | 17.36 | 17.37 | 18.68 | 18.5 | 19.3 |

(5) | 15.43 | 17.11 | 15.85 | 16.26 | 16.49 | 16.81 | 17.25 | 18.10 | 19.2 | 18.8 |

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**MDPI and ACS Style**

Musaev, A.; Borovinskaya, E.
Evolutionary Optimization of Case-Based Forecasting Algorithms in Chaotic Environments. *Symmetry* **2021**, *13*, 301.
https://doi.org/10.3390/sym13020301

**AMA Style**

Musaev A, Borovinskaya E.
Evolutionary Optimization of Case-Based Forecasting Algorithms in Chaotic Environments. *Symmetry*. 2021; 13(2):301.
https://doi.org/10.3390/sym13020301

**Chicago/Turabian Style**

Musaev, Alexander, and Ekaterina Borovinskaya.
2021. "Evolutionary Optimization of Case-Based Forecasting Algorithms in Chaotic Environments" *Symmetry* 13, no. 2: 301.
https://doi.org/10.3390/sym13020301