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

  • Mesbaholdin Salami
  • Farzad Movahedi SobhaniEmail author
  • Mohammad Sadegh Ghazizadeh
Original Paper


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.


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



Energy planning models


Short-term load forecasting


Empirical mode decomposition


Intrinsic mode function


Autoregressive integrated moving average


Principal component analysis


Grasshopper optimization algorithm


Improved grasshopper optimization algorithm


Neural network


Wavelet transform neural network


Discrete wavelet transform


Multi-resolution analysis


Daubechies of order 5


Improved flower pollination algorithm


Mean absolute percent error


Mean absolute error


Root mean square error


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 ith grasshopper

\( S_{i} \)

Social interaction of the ith grasshopper

\( G_{i} \)

Gravity of the ith grasshopper

\( A_{i} \)

Wind forecast for the ith grasshopper

\( d_{ij} \)

Distance between the ith and jth grasshopper

\( \hat{d}_{IJ} \)

A unit vector between two grasshoppers

\( s\left( r \right) \)

Function defining social forces

\( G_{i} \)

Gravity constant of the ith 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 ith grasshopper after applying an update

\( X_{i}^{*} \)

The position of the ith grasshopper

\( X_{i}^{\text{op}} \)

Opposite position of the ith 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


Transfer parameter


Scale parameter


Discrete time

\( \varPsi \)

Mother transfer function



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Mesbaholdin Salami
    • 1
  • Farzad Movahedi Sobhani
    • 2
    Email author
  • Mohammad Sadegh Ghazizadeh
    • 3
  1. 1.Department of Industrial Engineering, Central Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Industrial Engineering, Science and Research BranchIslamic Azad UniversityTehranIran
  3. 3.Department of Electrical Engineering, Abbaspour School of EngineeringShahid Beheshti UniversityTehranIran

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