# Estimating Heating Load in Residential Buildings Using Multi-Verse Optimizer, Self-Organizing Self-Adaptive, and Vortex Search Neural-Evolutionary Techniques

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Established Database

## 3. Methodology

#### 3.1. Multilayer Perceptron

#### 3.2. Multi-Verse Optimizer (MVO)

_{i}and ub

_{i}are the lower and upper bounds of the jth element,${r}_{2}$;${r}_{3}$;${r}_{4}$ are randomly generated numbers drawn from the interval of [0, 1], ${x}_{i}^{j}$ represents the jth parameter in ith individual, and ${x}_{rouletteWheel}^{j}$. does the roulette wheel selection mechanism to pick the jth element of a solution.

#### 3.3. Self-Organizing and Self-Adaptive (SOSA)

#### 3.4. Vortex Search Algorithm (VSA)

## 4. Results and Discussion

#### 4.1. Accuracy Indicators

^{2}) required to compute the compatibility between the measured and predicted HLs:

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

#### 4.2. Combining the MLP with Hybrid Optimizers

^{2}for three methods of MVO, SOSA, and VSA is (0.977 and 0.978), (0.885 and 0.895), and (0.974 and 0.975) for testing and training phases, respectively. Also, in the case of RMSE, MVO, SOSA, and VSA have the value of (0.117 and 0.110), (0.255 and 0.239), and (0.124 and 0.112) in the training and testing phases, respectively. These results show that the lowest value of RMSE and the highest value of R

^{2}are related to the MVO technique, indicating the best performance of MVO-MLP. According to R

^{2}and RMSE values (Table 1, Table 2, Table 3 and Table 4), the second technique for predicting HL and CL is VSA-MLP, and the last is SOSA-MLP.

#### 4.3. Prediction Results

^{−5}and 0.12416], respectively. The preceding section indicates that the RMSE values are 0.3540, 8.8064, and 0.2887. In addition, the estimated MAEs of the three models (0.08499, 0.19662, and 0.088861) demonstrate a small degree of training error. Moreover, the computed R2 values indicate that greater than 93% of the objective and output HLs are consistent.

#### 4.4. Efficiency Comparison

^{2}are chosen as the most exact HL predictors, considering the learning and prediction stages. Table 4 displays the accuracy standards that must be satisfied to attain this objective. As demonstrated, the MLP constructed utilizing the MVO’s weights and biases provide the most accurate knowledge of the HL and predicting it. The VSA appears as the second possible optimizer after the MVO. This study’s MVO and VSA algorithms appear to outperform previously proposed models in the training and testing phases. For example, six different MLP network’s hybrids (for instance, based on other hybrid techniques, such as whale optimization algorithm (WOA) [94], ABC [95], PSO [96], the salp swarm algorithm (SSA) [97], wind-driven optimization (WDO) [98], the spotted hyena optimization (SHO) [99], the imperialist competitive algorithm (ICA) [100], GOA [101], the genetic algorithm (GA) [102], and GWO [103]) were utilized to estimate the HL by using the same dataset. This suggests that the objective of developing more effective HL assessment tools has been met.

#### 4.5. Discussion

^{2}or RMSE, as those were the hybrid techniques that we employed in the current study.

## 5. Conclusions

^{2}was 0.978, 0.895, and 0.977 demonstrating that the developed models were successful and had minimal prediction error. The most powerful model was the MVO-MLP, followed by the VSA-MLP and the SOSA-MLP. The MVO-MLP methodology was presented for use in real-world situations, but potential ideas for future projects were also presented in light of the shortcomings of the research, such as data enhancement and future selection, optimizing building characteristics using the model, and comparing the model to improved time-saving methods.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Box plot of used dataset variations with the heating load. (

**a**) Relative compactness (RC), (

**b**) surface area, (

**c**) wall area, (

**d**) roof area, (

**e**) overall height, (

**f**) orientation, (

**g**) glazing area, (

**h**) glazing area distribution, with the heating load.

**Figure 4.**The accuracy of the best-fit proposed model for the (

**a**) MVO-MLP training dataset, (

**b**) MVO-MLP testing dataset, (

**c**) SOSA-MLP training dataset, (

**d**) SOSA-MLP testing dataset, (

**e**) VSA-MLP training dataset, and (

**f**) VSA-MLP testing dataset.

**Figure 5.**The error analysis for the best-fit proposed model for the (

**a**) MVO-MLP training dataset, (

**b**) MVO-MLP testing dataset, (

**c**) SOSA-MLP training dataset, (

**d**) SOSA-MLP testing dataset, (

**e**) VSA-MLP training dataset, and (

**f**) VSA-MLP testing dataset.

Population Size | Network Result | Scoring | Total Score | RANK | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Train | Test | Train | Test | |||||||

R² | RMSE | R² | RMSE | R² | RMSE | R² | RMSE | |||

50 | 0.962 | 0.149 | 0.964 | 0.143 | 1 | 1 | 1 | 1 | 4 | 10 |

100 | 0.972 | 0.130 | 0.974 | 0.120 | 5 | 5 | 4 | 5 | 19 | 6 |

150 | 0.972 | 0.129 | 0.975 | 0.117 | 6 | 6 | 6 | 7 | 25 | 5 |

200 | 0.971 | 0.132 | 0.975 | 0.119 | 3 | 3 | 5 | 6 | 17 | 7 |

250 | 0.973 | 0.127 | 0.976 | 0.115 | 8 | 8 | 7 | 8 | 31 | 3 |

300 | 0.977 | 0.117 | 0.978 | 0.110 | 9 | 9 | 9 | 10 | 37 | 1 |

350 | 0.971 | 0.130 | 0.973 | 0.123 | 4 | 4 | 3 | 4 | 15 | 8 |

400 | 0.967 | 0.140 | 0.966 | 0.137 | 2 | 2 | 2 | 2 | 8 | 9 |

450 | 0.978 | 0.113 | 0.980 | 0.127 | 10 | 10 | 10 | 3 | 33 | 2 |

500 | 0.973 | 0.127 | 0.976 | 0.115 | 7 | 7 | 8 | 9 | 31 | 3 |

Population Size | Network Result | Scoring | Total Score | RANK | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Train | Test | Train | Test | |||||||

R² | RMSE | R² | RMSE | R² | RMSE | R² | RMSE | |||

50 | 0.810 | 0.343 | 0.806 | 0.355 | 2 | 2 | 2 | 2 | 8 | 9 |

100 | 0.776 | 0.378 | 0.781 | 0.384 | 1 | 1 | 1 | 1 | 4 | 10 |

150 | 0.874 | 0.289 | 0.893 | 0.274 | 6 | 7 | 6 | 7 | 26 | 4 |

200 | 0.889 | 0.289 | 0.894 | 0.278 | 10 | 6 | 7 | 6 | 29 | 3 |

250 | 0.881 | 0.307 | 0.898 | 0.302 | 7 | 4 | 9 | 5 | 25 | 5 |

300 | 0.871 | 0.278 | 0.836 | 0.304 | 4 | 9 | 4 | 4 | 21 | 7 |

350 | 0.832 | 0.327 | 0.807 | 0.342 | 3 | 3 | 3 | 3 | 12 | 8 |

400 | 0.884 | 0.285 | 0.899 | 0.270 | 8 | 8 | 10 | 8 | 34 | 2 |

450 | 0.871 | 0.293 | 0.880 | 0.255 | 5 | 5 | 5 | 9 | 24 | 6 |

500 | 0.885 | 0.255 | 0.895 | 0.239 | 9 | 10 | 8 | 10 | 37 | 1 |

Population Size | Network Result | Scoring | Total Score | RANK | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Train | Test | Train | Test | |||||||

R² | RMSE | R² | RMSE | R² | RMSE | R² | RMSE | |||

50 | 0.961 | 0.152 | 0.965 | 0.140 | 2 | 2 | 2 | 3 | 9 | 9 |

100 | 0.965 | 0.143 | 0.967 | 0.135 | 3 | 3 | 3 | 4 | 13 | 8 |

150 | 0.968 | 0.138 | 0.968 | 0.133 | 5 | 5 | 4 | 5 | 19 | 6 |

200 | 0.959 | 0.155 | 0.964 | 0.141 | 1 | 1 | 1 | 1 | 4 | 10 |

250 | 0.974 | 0.124 | 0.977 | 0.112 | 10 | 10 | 10 | 10 | 40 | 1 |

300 | 0.969 | 0.136 | 0.973 | 0.122 | 7 | 7 | 8 | 8 | 30 | 3 |

350 | 0.968 | 0.136 | 0.970 | 0.128 | 6 | 6 | 6 | 7 | 25 | 4 |

400 | 0.972 | 0.128 | 0.974 | 0.120 | 9 | 9 | 9 | 9 | 36 | 2 |

450 | 0.972 | 0.130 | 0.973 | 0.140 | 8 | 8 | 7 | 2 | 25 | 4 |

500 | 0.967 | 0.140 | 0.970 | 0.129 | 4 | 4 | 5 | 6 | 19 | 6 |

Swarm Size | Training Dataset | Testing Dataset | Scoring | Total Score | Rank | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | R2 | RMSE | R2 | Training | Testing | ||||||

MVOMLP | 300 | 0.977 | 0.117 | 0.978 | 0.11 | 3 | 3 | 3 | 3 | 12 | 1 |

SOSAMLP | 500 | 0.885 | 0.255 | 0.895 | 0.239 | 3 | 3 | 1 | 1 | 8 | 2 |

VSAMLP | 250 | 0.974 | 0.124 | 0.977 | 0.112 | 2 | 2 | 2 | 2 | 8 | 2 |

References | Article Title | Scope |
---|---|---|

Refs. [26,60] | Comprehensive preference learning and predicting heating load in residential buildings using machine learning techniques | Using traditional machine learning in predicting heating and cooling load |

Refs. [57,107] | Proposing a novel predicting technique using M5Rules-PSO and M5Rules-GA model in estimating CL and HL in residential building system | Estimating cooling and heating load via a novel predictive technique using M5Rules |

Ref. [108] | Predicting heating and cooling loads in residential buildings using two hybrid intelligent models | Hybrid intelligent models in predicting heating and cooling load |

Ref. [109] | Optimal modification of HVAC system performances in energy-efficient buildings using the integration of metaheuristic optimization and neural computing | Using neural networks and metaheuristic optimization in modifying HVAC systems |

Ref. [56] | Employing ABC and PSO techniques for optimizing a neural network in prediction of HL and CL of residential buildings | Using neural network algorithms in predicting cooling and heating load in residential green buildings |

Ref. [39] | A teaching-learning based optimization Neural Processor for Predicting HL in Residential Buildings | Predicting heating load using a novel neural network algorithm of TLBO |

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## Share and Cite

**MDPI and ACS Style**

Nejati, F.; Tahoori, N.; Sharifian, M.A.; Ghafari, A.; Nehdi, M.L.
Estimating Heating Load in Residential Buildings Using Multi-Verse Optimizer, Self-Organizing Self-Adaptive, and Vortex Search Neural-Evolutionary Techniques. *Buildings* **2022**, *12*, 1328.
https://doi.org/10.3390/buildings12091328

**AMA Style**

Nejati F, Tahoori N, Sharifian MA, Ghafari A, Nehdi ML.
Estimating Heating Load in Residential Buildings Using Multi-Verse Optimizer, Self-Organizing Self-Adaptive, and Vortex Search Neural-Evolutionary Techniques. *Buildings*. 2022; 12(9):1328.
https://doi.org/10.3390/buildings12091328

**Chicago/Turabian Style**

Nejati, Fatemeh, Nayer Tahoori, Mohammad Amin Sharifian, Alireza Ghafari, and Moncef L. Nehdi.
2022. "Estimating Heating Load in Residential Buildings Using Multi-Verse Optimizer, Self-Organizing Self-Adaptive, and Vortex Search Neural-Evolutionary Techniques" *Buildings* 12, no. 9: 1328.
https://doi.org/10.3390/buildings12091328