# Hybridizing Deep Learning and Neuroevolution: Application to the Spanish Short-Term Electric Energy Consumption Forecasting

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## Abstract

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## 1. Introduction

- We propose a new general-purpose approach based on deep learning for big data time-series forecasting. Due to the high computational cost of the deep learning, we adopted a distributed computing solution in order to be able to process large time series.
- The hyper-parameter tuning and optimization of the deep neural networks is a key factor for obtaining competitive results. Usually, the hyper-parameters of a deep neural network are pre-fixed previously or computed by a grid search, which performs an exhaustive search through the whole set of established hyper-parameters. However, the grid search presents an important limitation: it works with discrete values, which greatly limits the fine-tuning of the vast majority of hyper-parameters. Thus, an evolutionary search is proposed to find the hyper-parameters.
- We conduct a wide experimentation using Spanish electricity consumption registered over 10 years, with measurements recorded every 10 min. Results show a mean relative error of 1.44%, demonstrating the high potential of the proposed approach, also compared to other forecasting strategies.
- We evaluate our proposal predictive accuracy and compare it with a strategy based on deep learning using a grid search for setting the hyper parameters. The evolutionary search showed to be effective in order to achieve higher accuracy.
- In addition, we compare the approach with seven state-of-the-art forecasting algorithms such as ARIMA, decision tree, an algorithm based on gradient boosting, random forest, evolutionary decision trees, a standard neural network and an ensemble proposed in [14], outperforming all of them.
- We analyze how the size of the historical window affects the accuracy of the model. We found that when using the past 168 values as input features to predict the next 24 values the best results were obtained.

## 2. Related Works

## 3. Data and Methodology

#### 3.1. Data

#### 3.2. Methodology

#### 3.2.1. Parameters of the Neural Network

#### 3.2.2. Genetic Algorithm Parameters

#### 3.2.3. Description of the Methodology

## 4. Experimental Results

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Correlation plots for the original time-series. (

**a**) AutoCorrelation Function (ACF); (

**b**) Partial AutoCorrelation Function (PACF).

**Figure 2.**Dataset pre-processing. w determines the amount of historical data used, while h represents the prediction horizon.

w | #Rows | #Columns | File Size (In MB) |
---|---|---|---|

24 | 20,742 | 48 | 6 |

48 | 20,741 | 72 | 9 |

72 | 20,740 | 96 | 11.9 |

96 | 20,739 | 120 | 14.9 |

120 | 20,738 | 144 | 17.9 |

144 | 20,737 | 168 | 20.9 |

168 | 20,736 | 192 | 23.9 |

Parameter | Values |
---|---|

Layers | From 2 to 100 |

Neurons | From 10 to 1000 |

Lambda ($\lambda $) | From 0 to 1 × 10${}^{-10}$ |

Rho ($\rho $) | From 0.99 to 1 |

Epsilon ($\u03f5$) | From 0 to 1 × 10${}^{-12}$ |

Activation function | From 0 to 3 |

Distribution function | From 0 to 7 |

End metric | From 0 to 7 |

Operator | Value |
---|---|

Population size | 50 |

Generations | 100 |

Limit of generations | 50 |

Crossover probability | 0.8 |

Mutation probability | 0.1 |

Elitisms probability | 0.05 |

h | Layers | Neurons | $\mathit{\lambda}$ | $\mathit{\rho}$ | $\mathit{\u03f5}$ | Activation | Distribution | End Metric |
---|---|---|---|---|---|---|---|---|

1 | 52 | 942 | 4.09× 10${}^{-10}$ | 1.00 | 6.43 × 10${}^{-12}$ | Tanh | Gaussian | Deviance |

2 | 68 | 921 | 0 | 1.00 | 0 | Maxout | Huber | MSE |

3 | 75 | 880 | 0 | 1.00 | 0 | Maxout | Huber | Deviance |

4 | 68 | 921 | 0 | 1.00 | 0 | Maxout | Huber | MSE |

5 | 88 | 504 | 0 | 1.00 | 0 | Maxout | Huber | Deviance |

6 | 80 | 789 | 0 | 1.00 | 0 | Maxout | Huber | MSE |

7 | 74 | 892 | 0 | 1.00 | 0 | Maxout | Huber | RMSLE |

8 | 46 | 300 | 0 | 1.00 | 0 | Maxout | Huber | MAE |

9 | 75 | 889 | 5.57 × 10${}^{-10}$ | 0.99 | 6.74 × 10${}^{-10}$ | Tanh | Gaussian | Mean per class error |

10 | 25 | 852 | 0 | 1.00 | 0 | Maxout | Huber | RMSLE |

11 | 58 | 843 | 3.69 × 10${}^{-10}$ | 1.00 | 2.45 × 10${}^{-10}$ | Tanh | Gaussian | RMSE |

12 | 41 | 491 | 0 | 1.00 | 0 | Maxout | Huber | RMSLE |

13 | 17 | 552 | 0 | 0.99 | 0 | Maxout | Huber | MSE |

14 | 26 | 661 | 0 | 0.99 | 0 | Maxout | Huber | MAE |

15 | 89 | 811 | 5.61 × 10${}^{-10}$ | 0.99 | 4.23 × 10${}^{-10}$ | Tanh | Gaussian | RMSE |

16 | 98 | 697 | 0 | 1.00 | 0 | Maxout | Huber | MAE |

17 | 74 | 478 | 1.46 × 10${}^{-10}$ | 1.00 | 3.58 × 10${}^{-10}$ | Tanh | Gaussian | Deviance |

18 | 62 | 705 | 2.74 × 10${}^{-10}$ | 0.99 | 6.64 × 10${}^{-10}$ | Tanh | Gaussian | MAE |

19 | 65 | 879 | 0 | 0.99 | 0 | Maxout | Huber | MAE |

20 | 81 | 780 | 7.62 × 10${}^{-10}$ | 0.99 | 5.21 × 10${}^{-10}$ | Tanh | Gaussian | MSE |

21 | 27 | 931 | 0 | 1.00 | 0 | Maxout | Huber | MAE |

22 | 95 | 745 | 0 | 1.00 | 0 | Maxout | Huber | Deviance |

23 | 41 | 923 | 0 | 1.00 | 0 | Maxout | Huber | MSE |

24 | 80 | 754 | 0 | 1.00 | 0 | Maxout | Huber | MAE |

**Table 5.**Average results obtained by different methods for different historical window values. Standard deviation between brackets.

w | |||||||
---|---|---|---|---|---|---|---|

24 | 48 | 72 | 96 | 120 | 144 | 168 | |

NDL | 3.01 (0.90) | 2.38 (0.69) | 2.08 (0.57) | 1.85 (0.55) | 1.60 (0.46) | 1.51 (0.46) | 1.44 (0.42) |

CNN | 4.08 (0.04) | 3.16 (0.03) | 2.69 (0.02) | 2.51 (0.02) | 2.30 (0.02) | 1.71 (0.02) | 1.79 (0.02) |

LSTM | 2.43 (0.03) | 2.05 (0.02) | 1.82 (0.02) | 2.08 (0.02) | 1.74 (0.02) | 1.78 (0.02) | 1.97 (0.02) |

FFNN | 4.51 (0.52) | 3.46 (0.33) | 3.39 (0.30) | 3.12 (0.42) | 2.98 (0.28) | 2.32 (0.29) | 2.46 (0.29) |

ARIMA | 8.82 (5.31) | 8.26 (4.73) | 11.37 (10.43) | 14.03 (13.00) | 6.79 (2.53) | 7.63 (2.54) | 6.92 (2.97) |

DT | 9.52 (1.55) | 9.45 (1.48) | 9.33 (1.39) | 9.40 (1.45) | 9.08 (1.12) | 8.86 (1.01) | 8.79 (0.96) |

GBM | 8.07 (3.82) | 6.59 (2.71) | 5.73 (2.23) | 5.33 (2.08) | 5.02 (1.81) | 4.49 (1.54) | 4.45 (1.56) |

RF | 4.39 (2.13) | 3.69 (1.71) | 2.93 (1.16) | 2.78 (1.04) | 2.45 (0.79) | 2.22 (0.71) | 2.15 (0.69) |

EV | 4.49 (1.91) | 3.98 (1.52) | 3.48 (1.18) | 3.42 (1.15) | 3.19 (0.95) | 3.15 (0.90) | 3.09 (0.84) |

NN | 4.39 (2.23) | 4.27 (2.16) | 4.13 (2.05) | 3.55 (1.56) | 3.15 (1.41) | 2.16 (0.78) | 2.08 (0.74) |

ENSEMBLE | 3.58 (1.65) | 2.95 (1.19) | 2.64 (0.99) | 2.57 (0.97) | 2.38 (0.81) | 1.94 (0.69) | 1.88 (0.67) |

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## Share and Cite

**MDPI and ACS Style**

Divina, F.; Torres Maldonado, J.F.; García-Torres, M.; Martínez-Álvarez, F.; Troncoso, A.
Hybridizing Deep Learning and Neuroevolution: Application to the Spanish Short-Term Electric Energy Consumption Forecasting. *Appl. Sci.* **2020**, *10*, 5487.
https://doi.org/10.3390/app10165487

**AMA Style**

Divina F, Torres Maldonado JF, García-Torres M, Martínez-Álvarez F, Troncoso A.
Hybridizing Deep Learning and Neuroevolution: Application to the Spanish Short-Term Electric Energy Consumption Forecasting. *Applied Sciences*. 2020; 10(16):5487.
https://doi.org/10.3390/app10165487

**Chicago/Turabian Style**

Divina, Federico, José Francisco Torres Maldonado, Miguel García-Torres, Francisco Martínez-Álvarez, and Alicia Troncoso.
2020. "Hybridizing Deep Learning and Neuroevolution: Application to the Spanish Short-Term Electric Energy Consumption Forecasting" *Applied Sciences* 10, no. 16: 5487.
https://doi.org/10.3390/app10165487