# A Hybrid LSTM-Based Genetic Programming Approach for Short-Term Prediction of Global Solar Radiation Using Weather Data

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## Abstract

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## 1. Introduction

_{panel}) for a product family of polycrystalline solar panels. The data recorded include SR measurements with ambient temperature, wind velocity, and ambient relative humidity as effective parameters. The authors claimed that their obtained function outperformed the models related to the Nominal Operating Cell Temperature (NOCT) and Nominal Module Operating Temperature (NMOT) approaches that are considered as the most common ways to obtain the T

_{panel}. In [33], the authors presented a hybrid approach that includes the GP and the Simulated Annealing (SA) heuristic optimization techniques for estimating the GSR. The researchers concluded a prediction equation where the SR is formulated in terms of several climatological and meteorological parameters in two cities of Iran.

## 2. Genetic Programming and Long Short-Term Memory Models

#### 2.1. Genetic Programming

- Measure the fitness value for each individual using a predefined fitness function. This fitness value indicates how the individual function (computer program) suits the problem under consideration.
- Select a set of individuals, based on their fitness values, from the present population using a suitable selection strategy.
- Generate the next population by applying the crossover and mutation operators to selected individuals based on predefined crossover and mutation probabilities.
- Based on a predefined reproduction probability, the clone is based on individuals with the best fitness values to the next population.

#### 2.1.1. GPLearn Framework

- Sub-tree mutation: it takes the winner (a tree) of a random selection and then selects a random sub-tree from it to be replaced. A donor sub-tree is generated at random, and this is inserted into the chosen winner tree to form offspring in the next generation. This type of mutation is considered one of the aggressive mutations. It allows big changes in an individual by replacing a complete sub-tree and all its descendants with totally naïve random components.
- Hoist mutation: it takes the winner of a random selection and selects a random sub-tree from it. Then, a random sub-tree of that sub-tree is selected, and this is lifted (hoisted) into the original sub-tree’s location to produce offspring in the next generation.
- Point mutation: it takes the winner of a random selection and selects random nodes from the winner to be replaced. Functions are replaced by other functions that require the same number of arguments, and other terminals replace terminals. The resulting tree forms offspring in the next generation. Figure 3 depicts the three described types of mutations.

#### 2.1.2. Memetic Programming

#### 2.2. Long Short-Term Memory (LSTM) Models

## 3. Hybrid Approach Development

#### 3.1. Building Base Models

- AirDensity (Kg/m
^{3}): the density of the air - AirTemp_Avg (°C): the average temperature of the air 3 m above the surface
- HeatIndex (°C): the heat index
- RelativeWindSpeed_Max (m/s): the maximum relative wind speed
- RH_ Avg (%): the relative humidity in the air
- SurfaceTemp_Avg (°C): the average temperature 10 cm close to the surface
- SolarRadiation_Avg (W/m
^{2}): the average global solar radiation

- LSTM_1 receives in each input vector the following parameters: Air Density, Max Relative Wind Speed, and Solar Radiation for the current and the $k$ previous 15-min slots.
- LSTM_2 receives in each input vector the following parameters: Air Density, Average Surface Temperature, and Solar Radiation for the current and the $k$ previous 15-min slots.
- LSTM_3 receives in each input vector the following parameters: Average Air Temperature, Heat Index, and Solar Radiation for the current and the $k$ previous 15-min slots.
- LSTM_4 receives in each input vector the following parameters: Average Air Temperature, Relative Humidity, and Solar Radiation for the current and the $k$ previous 15-min slots.
- LSTM_5 receives in each input vector the following parameters: Average Air Temperature, Average Surface Temperature, and Solar Radiation for the current and the $k$ previous 15-min slots.

#### 3.2. Building the Hybrid GP-LSTM Model

- A standard version consists of the primary mutation and crossover operators as is described in Section 2. The parameters of this version of GP module are setup as follows:
- ○
- The population size is set to be equal to 200 individuals. Each individual represents a nonlinear combination formula of the outputs of the base predictors.
- ○
- The set of operators that are used in the internal nodes of the trees that represent the individuals includes the four arithmetic operators: addition (+), difference (−), division (/), and multiplication (*). In addition, it includes the decimal log $log()$, the exponential function ${e}^{()}$ and the square root ($\sqrt{()}$).
- ○
- The depth of each of the trees that represent individuals is equal to eight. The maximum depth allowed for trees in each population is one of the adjustable parameters in a GP evolution process. The depth of each of the binary trees is set to be dynamic. It starts by an initial depth that can be dynamically increased until a selected maximum value is reached.
- ○
- The fitness function evaluates the efficiency of each of the individuals that represent candidate solutions (chromosomes). A fitness function related to the root mean square error (RMSE) has been used.

- ○
- The probability of applying each of the genetic operators (crossover and mutation).
- ○
- The sampling method to select individuals from the current population to participate in generating new individuals for the next generation.

- A hybrid version of the GP algorithm, named MP, consists of a local search module that permits selecting the best breeding among $n$ possible children from two crossover parents. The parameters of this version of GP module are setup almost the same as the standard one for comparison reasons. Therefore, the exact population sizes, set of operators, maximum depth, and fitness functions, and sampling methods have been adopted for this version.

#### 3.3. Experiments Setup

#### 3.3.1. Training and Testing Dataset

#### 3.3.2. Experiments

- A standard version of GP comprises the crossover operator with advanced versions of and mutation operators described in Section 2.1. This version is implemented in the GPLearn framework as described in Section 2.1.1.

#### 3.3.3. Evaluation Metrics

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

GSR | Global Solar Radiation |

LSTM | Long-Short Term Memory |

RNN | Recurrent Neural Network |

SR | Solar Radiation |

GP | Genetic Programming |

ANN | Artificial Neural Network |

SVM | Support Vector Machines |

RF | Random Forest |

DT | Decision Tree |

RT | Regression Tree |

RMSE | Root Mean Square Error |

ARIMA | Autoregressive Integrated Moving Average |

MLR | Multilinear Regression |

BDT | Bagged Decision Tree |

BDTs | Bagging Decision Techniques |

SVR | Support Vector Regressors |

MP | Memetic Programming |

LGP | Linear Genetic programming |

MGGP | Multi-Gene Genetic Programming |

Tpanel | Panel’s Temperature |

NOCT | Nominal Operating Cell Temperature |

NMOT | Nominal Module Operating Temperature |

GEP | Gene Expression Programming |

SA | Simulated Annealing |

BPTT | Back-Propagation Through Time |

GA | Genetic Algorithm |

KNN | K-Nearest Neighbors |

MAE | Mean Absolute Error |

MBE | Mean Bias Error |

MAPE | Mean Absolute Percentage Error |

r | Correlation Coefficient $\mathrm{r}$ |

${r}^{2}$ | Coefficient of Determination |

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**Figure 2.**The crossover of two individuals to produce two new ones (Offsprings) for the next generation.

**Figure 3.**Advanced mutation operators implemented in GPLearn. (

**a**) Sub-tree mutation, (

**b**) Hoist mutation, and (

**c**) Point mutation.

**Figure 5.**The general structure of an LSTM unit with one input sign vector ${X}_{t}$ and one output ${h}_{t}$.

**Figure 8.**The GP-LSTM hybrid model for combining LSTM models. Each individual predictor receives the weather and the GSR data of the current and the k previous 15-min slots to predict the GSR for the next 15-min slot.

**Figure 9.**Binary tree that represents the fittest individual in the last population of the standard GP evolutionary computation, and that represents the best combination formula that we have adopted in the hybrid GP_LSTM model, where x

_{1}= LSTM_1, x

_{2}= LSTM_2, x

_{3}= LSTM_3, x

_{4}= LSTM_4, and x

_{5}= LSTM_5.

**Figure 10.**The daily average prediction error of GSR of the simple average combiner, the best stacking model MLP, and standard GP combiner during March 2021.

Authors | Base Learners | Ensemble Type | Combiner Meta-Model |
---|---|---|---|

Al-Hajj et al. [4] | RNNs + SVRs | Parallel stacking | MLPs |

Linares-Rodriguez et al. [17] | ANNs | Parallel structure | Simple averaging |

Ahmed et al. [18] | DTs + RF Regressors + Lasso Regressors | Parallel with probabilistic combination | Normal distribution methods for probabilistic forecasts |

Guo et al. [19] | ANNs, Linear Regression + RF | Parallel structure—weighted sum | Linear weighted sum |

Yeboah et al. [20] | DT | Bagging technique | RF |

Pan et al. [21] | RF | Parallel staking | Weighted average with Ridge Regression |

Basaran et al. [22] | SVR, ANN, DT | Bagging technique | Boosting–Bagging |

Abuella et al. [23] | SVRs | Parallel structure—stacking | Random Forest RF |

**Table 2.**Results of individual models: underlined and bold scores indicate the best ones, and the best model is marked with ‘*’.

Model | RMSE | MAE | MBE | MAPE | ${\mathit{r}}^{2}$ | |
---|---|---|---|---|---|---|

Global model | LSTM_6 | 0.0666 | 0.0513 | −0.0352 | 123.50% | 0.9840 |

Individual models | LSTM_1 | 0.1112 | 0.0901 | −0.0446 | 325.17% | 0.9814 |

LSTM_2 | 0.0766 | 0.0608 | −0.0269 | 85.92% | 0.9696 | |

LSTM_3 * | 0.0272 | 0.0201 |
−0.0118 | 70.58% | 0.9977 | |

LSTM_4 | 0.0359 | 0.0287 | −0.0159 | 58.72% | 0.9939 | |

LSTM_5 | 0.0301 | 0.0235 | 0.0122 | 30.08% | 0.9957 |

**Table 3.**Results of combination models of type simple averaging, machine learning-based stacking, and GP. Underlined and bold scores indicate the best ones.

Model | RMSE | MAE | MBE | MAPE | ${\mathit{r}}^{2}$ | |
---|---|---|---|---|---|---|

Simple Averaging | LSTM_Avg | 0.0443 | 0.0349 | 0.0174 | 13.60% | 0.9942 |

Machine Learning Stacking Models | LSTM_RF | 0.0540 | 0.0352 | 0.0069 | 11.59% | 0.9848 |

LSTM_MLP | 0.0337 | 0.0262 | 0.0024 | 11.25% | 0.9959 | |

LSTM_SVR | 0.0625 | 0.0540 | −0.0236 | 15.08% | 0.9914 | |

LSTM_KNN | 0.0506 | 0.0382 | 0.0093 | 12.86% | 0.9904 | |

GP | LSTM_GP (Standard) | 0.0238 | 0.0173 | 0.0033 | 8.41% | 0.9976 |

LSTM_MP (GP + Local Search) | 0.0233 | 0.0177 |
−
0.0018 | 30.14% | 0. 9969 |

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**MDPI and ACS Style**

Al-Hajj, R.; Assi, A.; Fouad, M.; Mabrouk, E. A Hybrid LSTM-Based Genetic Programming Approach for Short-Term Prediction of Global Solar Radiation Using Weather Data. *Processes* **2021**, *9*, 1187.
https://doi.org/10.3390/pr9071187

**AMA Style**

Al-Hajj R, Assi A, Fouad M, Mabrouk E. A Hybrid LSTM-Based Genetic Programming Approach for Short-Term Prediction of Global Solar Radiation Using Weather Data. *Processes*. 2021; 9(7):1187.
https://doi.org/10.3390/pr9071187

**Chicago/Turabian Style**

Al-Hajj, Rami, Ali Assi, Mohamad Fouad, and Emad Mabrouk. 2021. "A Hybrid LSTM-Based Genetic Programming Approach for Short-Term Prediction of Global Solar Radiation Using Weather Data" *Processes* 9, no. 7: 1187.
https://doi.org/10.3390/pr9071187