# A TLBO-Tuned Neural Processor for Predicting Heating Load in Residential Buildings

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Provision

#### 2.2. Methodology

## 3. Results and Discussion

#### 3.1. Accuracy Indicators

^{2}) that is used to calculate the compatibility between the measured and forecasted HLs:

_{iobserved}and S

_{ipredicted}, give the measured and forecasted HLs, respectively. Further, U signifies the number of records, and $\overline{S}$

_{observed}is the average of the observed HLs.

#### 3.2. Incorporated MLP with Optimizers

_{TLBO-MLP}= 0.303606 × K1 − 0.311304 × K2 − 0.276431 × K3 + 0.137188 × K4 + 0.689859 × K5 − 0.265206 × K6 + 0.831238

#### 3.3. Prediction Results

^{2}indicate a consistency of more than 93% of target and output HLs.

^{2}s (0.9438, 0.9373, 0.9556, and 0.9610) give a high accuracy in predicting the HL.

#### 3.4. Efficiency Comparison

^{2}are selected as the most accurate predictors of the HL. To this end, Table 1 presents all obtained accuracy criteria. As shown, without any discrepancy, the MLP made by the weights and biases from the TLBO presents the most reliable understanding of the HL and also the most accurate prediction of this parameter. Subsequently, the SCE emerges as the second promising optimizer, followed by the FA and OIO.

#### 3.5. Discussion

- (a)
- With an upcoming construction project, the suggested models can give an accurate early measurement of the required thermal load with respect to the dimensions and building characteristics. The models would effectively assist engineers and owners in providing suitable HVAC systems.
- (b)
- Another form of early-stage assistance would be the proper design of the building itself and tuning the architecture through input parameters (i.e., RA, RC, GA, WA, OH, SA, OR, and GAD) in reconstruction projects. In this sense, it is also possible to investigate the effect of each input parameter separately to achieve an understanding of the thermal load behavior. Figure 9 shows the behavior of the HL with an increase in RC. As shown, the trend is not regular and easy to predict; however, it is nicely predicted by the TLBO-MLP. Hence, this algorithm can give reliable approximations for real-world buildings, too.

## 4. Conclusions

- According to the sensitivity analysis carried out, the best complexities of the FA-MLP, OIO-MLP, SCE-MLP, and TLBO-MLP ensembles result for the swarm sizes of 50, 200, 50, and 300, respectively.
- Compared to other algorithms, the optimum configuration of the TLBO needed considerably higher computation time for optimizing the MLP.
- Considering the accuracy evaluation (the MEAs of 1.6821, 1.9568, 1.5466, and 1.4626), all four ensembles attained a good perception of the relationship between the HL and influential parameters.
- In the testing phase, the calculated error values of 1.7979, 1.9278, 1.6077, and 1.5804 indicated a low prediction error and the success of the implemented models.
- By comparison, the TLBO-MLP came up to be the strongest model, followed by SCE-MLP, FA-MLP, and OIO-MLP.
- The TLBO and SCE surpassed several other optimizers, including those used in the literature.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

HVAC | heating, ventilating, and air conditioning |

ANN | artificial neural network |

MLP | multi-layer perceptron |

CL | cooling load |

HL | heating load |

PSO | particle swarm optimization |

ABC | artificial bee colony |

GWO | gray wolf optimization |

GOA | grasshopper optimization algorithm |

FA | firefly algorithm |

OIO | optics inspired optimization |

SCE | shuffled complex evolution |

TLBO | teaching–learning-based optimization |

RA | roof area |

RC | relative compactness |

GA | glazing area |

WA | wall area |

OH | overall height |

SA | surface area |

OR | orientation |

GAD | glazing area distribution |

RMSE | root mean square error |

MAE | mean absolute error |

R^{2} | coefficient of determination |

ICA | imperialist competitive algorithm |

WDO | wind-driven optimization |

WOA | whale optimization algorithm |

SHO | spotted hyena optimization |

SSA | salp swarm algorithm |

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**Figure 1.**Box plot of the dataset: (

**a**) RC, (

**b**) SA, (

**c**) WA, (

**d**) RA, (

**e**) OH, (

**f**) OR, (

**g**) GA, (

**h**) GAD, and (

**i**) HL.

**Figure 4.**The convergence curves belonging to the FA-MLP, OIO-MLP, SCE-MLP, and TLBO-MLP executed with populations of 50, 200, 50, and 300, respectively.

**Figure 5.**The errors of training data in (

**a**) FA-MLP, (

**b**) OIO-MLP, (

**c**) SCE-MLP, and (

**d**) TLBO-MLP models.

**Figure 7.**Measured testing CLs vs. prediction of (

**a**) FA-MLP, (

**b**) OIO-MLP, (

**c**) SCE-MLP, and (

**d**) TLBO-MLP.

**Figure 8.**The execution time for the used hybrids (on a 64-bit system at 2.5 GHz and 6 gigabytes main memory).

Study | Models | Network Results | |||||
---|---|---|---|---|---|---|---|

Training | Testing | ||||||

RMSE | MAE | R^{2} | RMSE | MAE | R^{2} | ||

This study | FA-MLP | 2.3838 | 1.6821 | 0.9426 | 2.5456 | 1.7979 | 0.9438 |

OIO-MLP | 2.6256 | 1.9568 | 0.9304 | 2.7099 | 1.9278 | 0.9373 | |

SCE-MLP | 2.1448 | 1.5466 | 0.9536 | 2.2774 | 1.6077 | 0.9556 | |

TLBO-MLP | 1.9817 | 1.4626 | 0.9604 | 2.1103 | 1.5804 | 0.9610 | |

[49] | ABC-MLP | 2.9855 | 2.1197 | 0.9120 | 2.6159 | 1.9111 | 0.9349 |

PSO-MLP | 2.9736 | 2.1479 | 0.9126 | 2.5693 | 1.8630 | 0.9370 | |

[78] | GA-MLP | 2.9986 | 2.1797 | 0.8711 | 2.8878 | 2.0622 | 0.9076 |

ICA-MLP | 2.8050 | 2.0068 | 0.8816 | 2.7819 | 2.0089 | 0.9115 | |

[79] | WDO-MLP | 2.5896 | 1.7944 | 0.9344 | 2.8312 | 1.9863 | 0.9213 |

WOA-MLP | 2.6998 | 1.9702 | 0.9287 | 2.9213 | 2.1921 | 0.9154 | |

SHO-MLP | 4.2283 | 3.2232 | 0.8337 | 4.1501 | 3.1092 | 0.8385 | |

SSA-MLP | 2.4321 | 1.6737 | 0.9421 | 2.7527 | 1.9178 | 0.9248 | |

[51] | GOA-MLP | 2.3715 | 1.6934 | 0.9432 | 2.4459 | 1.7373 | 0.9486 |

GWO-MLP | 2.2959 | 1.6475 | 0.9468 | 2.2899 | 1.6514 | 0.9551 |

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Almutairi, K.; Algarni, S.; Alqahtani, T.; Moayedi, H.; Mosavi, A.
A TLBO-Tuned Neural Processor for Predicting Heating Load in Residential Buildings. *Sustainability* **2022**, *14*, 5924.
https://doi.org/10.3390/su14105924

**AMA Style**

Almutairi K, Algarni S, Alqahtani T, Moayedi H, Mosavi A.
A TLBO-Tuned Neural Processor for Predicting Heating Load in Residential Buildings. *Sustainability*. 2022; 14(10):5924.
https://doi.org/10.3390/su14105924

**Chicago/Turabian Style**

Almutairi, Khalid, Salem Algarni, Talal Alqahtani, Hossein Moayedi, and Amir Mosavi.
2022. "A TLBO-Tuned Neural Processor for Predicting Heating Load in Residential Buildings" *Sustainability* 14, no. 10: 5924.
https://doi.org/10.3390/su14105924