# A hybrid short-term load forecasting model developed by factor and feature selection algorithms using improved grasshopper optimization algorithm and principal component analysis

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## Abstract

Hybrid load forecasting models analyze linear and nonlinear components separately. If hybrid models were integrated with factor and feature selection algorithms, they would improve significantly. In the hybrid model proposed by this paper, the initial data were decomposed by an empirical mode decomposition (EMD) model. The linear component was analyzed through the autoregressive integrated moving average (ARIMA) method and the nonlinear component by a neural network (NN) and weighted by the improved flower pollination algorithm (IFPA). With the nonlinear component, the input load demand variable was decomposed by a wavelet transform (WT). In this paper, the improved grasshopper optimization algorithm (IGOA) and the principal component analysis (PCA) were employed to determine the input feature and input factor, respectively. Therefore, the proposed model was composed of EMD, IGOA, PCA, ARIMA, IFPA, NN, and WT algorithms. Finally, Iran’s Electricity Market (IEM) data were used to show improvements in the precision of the proposed forecasting model.

## Keywords

Empirical mode decomposition Improved flower pollination algorithm Improved grasshopper optimization algorithm Neural network Principal component analysis Short-Term Load Forecasting## Abbreviations

- EPMs
Energy planning models

- STLF
Short-term load forecasting

- EMD
Empirical mode decomposition

- IMF
Intrinsic mode function

- ARIMA
Autoregressive integrated moving average

- PCA
Principal component analysis

- GOA
Grasshopper optimization algorithm

- IGOA
Improved grasshopper optimization algorithm

- NN
Neural network

- WTNN
Wavelet transform neural network

- DWT
Discrete wavelet transform

- MRA
Multi-resolution analysis

- db5
Daubechies of order 5

- IFPA
Improved flower pollination algorithm

- MAPE
Mean absolute percent error

- MAE
Mean absolute error

- RMSE
Root mean square error

- IEM
Iran electricity market

## Variables, indexes, and constants

- \( h_{k} \left( t \right) \)
Subtracting signal on stage

*k*- \( y\left( t \right) \)
Input signal

- \( M_{k} \left( t \right) \)
Averaging upper and lower envelope curves on stage

*k*- \( D_{k } \)
Termination criterion on stage

*k*- \( r \)
Remaining amount

- \( X_{i} \)
Position of the

*i*th grasshopper- \( S_{i} \)
Social interaction of the

*i*th grasshopper- \( G_{i} \)
Gravity of the

*i*th grasshopper- \( A_{i} \)
Wind forecast for the

*i*th grasshopper- \( d_{ij} \)
Distance between the

*i*th and*j*th grasshopper- \( \hat{d}_{IJ} \)
A unit vector between two grasshoppers

- \( s\left( r \right) \)
Function defining social forces

- \( G_{i} \)
Gravity constant of the

*i*th grasshopper- \( \hat{e}_{g} \)
Unit vector toward the Earth center

- \( N \)
Number of grasshoppers

- \( {\text{ub}}_{d} \)
Higher bands of the dimensions

*d*- \( {\text{lb}}_{d} \)
Lower bands of the dimensions

*d*- \( X_{i}^{\text{levy}} \)
Levy flight

- \( X_{i}^{*} \)
Position of the

*i*th grasshopper after applying an update- \( X_{i}^{*} \)
The position of the

*i*th grasshopper- \( X_{i}^{\text{op}} \)
Opposite position of the

*i*th grasshopper- \( {\text{LB}} \)
Lower bounds of the search space

- \( {\text{UB}} \)
Upper bounds of the search space

- \( u\left[ m \right] \)
Empirical mean results vector

- \( B \)
The distance-to-mean matrix

- \( V \)
Covariance matrix

*C*- \( g\left[ m \right] \)
The cumulative energy for selection

- \( \Delta^{d} y_{t} \)
The decomposed components of load after the second difference

- \( x\left( t \right) \)
The signal wavelength

*M*Transfer parameter

*N*Scale parameter

*T*Discrete time

- \( \varPsi \)
Mother transfer function

## Notes

### Acknowledgements

Hereby, the researchers thank the Science and Research Branch of the Islamic Azad University, the Industrial Engineering Department, and Niroo Research, Iran, for their contributing assistance and guidance in initial planning of the proposed model and data collection and analysis.

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