# Synthesizing Multi-Layer Perceptron Network with Ant Lion Biogeography-Based Dragonfly Algorithm Evolutionary Strategy Invasive Weed and League Champion Optimization Hybrid Algorithms in Predicting Heating Load in Residential Buildings

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## Abstract

**:**

## 1. Introduction

## 2. Data Provision and Analysis

## 3. Methodology

#### 3.1. Artificial Neural Network

#### 3.2. Swarm-Based Metaheuristic Ideas

#### 3.3. Hybridization Process and Sensitivity Analysis

## 4. Results and Discussion

#### 4.1. Statistical Accuracy Assessment

^{2}) are used. These criteria are applied to the data belonging to the training and testing groups to demonstrate the qualities of learning and prediction, respectively. Assuming G as the total number of samples, and J

_{i observed,}and J

_{i predicted}as the real and forecasted HL values, Equations (6)–(8) formulate the RMSE, MAE, and R

^{2}.

_{observed}denotes the mean of J

_{i observed}values.

#### 4.2. Training Results

^{2}are 0.9539, 0.9596, 0.9222, 0.9357, 0.9547, and 0.9386.

#### 4.3. Validation Results

^{2}s (0.9406, 0.9516, 0.9340, 0.9318, 0.9431, and 0.9400) reflect higher than 93% accuracy for all models. In this phase, the errors range between −5.5792 and 6.9349, −5.6311 and 6.3000, −9.3137 and 6.8288, −7.0282 and 7.0647, −6.2505 and 5.8823, and −8.2384 and 6.1992, respectively.

#### 4.4. Score-Based Comparison and Time Efficiency

^{2}obtained for the training and testing phases. In this section, the comparison between the performance of the used predictors is carried out to determine the most reliable one. For this purpose, by taking into consideration all three accuracy criteria, a ranking system is developed. In this way, a score is calculated for each criterion based on the relative performance of the proposed model. The summation of these scores gives an overall score (OS) to rank the models. Table 2 gives the scores assigned to each model.

#### 4.5. Presenting the HL Predictive Equation

_{BBO-MLP}= 0.9076 × Z1 + 0.0050 × Z2 − 0.3986 × Z3 − 0.4754 × Z4 − 0.2692 × Z5 + 0.0283

#### 4.6. Further Discussion and Future Works

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The distribution of the heating load (HL) versus environmental factors: (

**a**) relative compactness, (

**b**) overall height, (

**c**) surface area, (

**d**) orientation, (

**e**) wall area, (

**f**) glazing area, (

**g**) roof area, and (

**h**) glazing area distribution.

**Figure 4.**The sensitivity analysis accomplished for determining the best population size of the (

**a**) ant lion optimization (ALO)-MLP, (

**b**) biogeography-based optimization (BBO)-MLP, (

**c**) dragonfly algorithm (DA)-MLP, (

**d**) evolutionary strategy (ES)-MLP, (

**e**) invasive weed optimization (IWO)-MLP, and (

**f**) league champion optimization (LCA)-MLP.

**Figure 5.**The training errors calculated for the (

**a**) ALO-MLP, (

**b**) BBO-MLP, (

**c**) DA-MLP, (

**d**) ES-MLP, (

**e**) IWO-MLP, and (

**f**) LCA-MLP prediction.

**Figure 6.**The R

^{2}results calculated in the testing phase of the (

**a**) ALO-MLP, (

**b**) BBO-MLP, (

**c**) DA-MLP, (

**d**) ES-MLP, (

**e**) IWO-MLP, and (

**f**) LCA-MLP models.

Ensemble Models | Network Results | |||||
---|---|---|---|---|---|---|

Training Phase | Testing Phase | |||||

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

ALO-MLP | 2.6054 | 2.0992 | 0.9539 | 2.7162 | 2.1865 | 0.9406 |

BBO-MLP | 2.5359 | 2.0846 | 0.9596 | 2.4807 | 1.8284 | 0.9516 |

DA-MLP | 3.4314 | 2.9402 | 0.9222 | 3.3998 | 2.8713 | 0.9340 |

ES-MLP | 2.7146 | 2.0848 | 0.9357 | 3.0958 | 2.5072 | 0.9318 |

IWO-MLP | 3.2506 | 2.8709 | 0.9547 | 3.3524 | 2.9702 | 0.9431 |

LCA-MLP | 3.8297 | 3.4091 | 0.9386 | 3.2954 | 2.7807 | 0.9400 |

Models | Scores | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Training | Testing | |||||||||

RMSE | MAE | R^{2} | Overall Score | Rank | RMSE | MAE | R^{2} | Overall Score | Rank | |

ALO-MLP | 5 | 4 | 4 | 13 | 2 | 5 | 5 | 4 | 14 | 2 |

BBO-MLP | 6 | 6 | 6 | 18 | 1 | 6 | 6 | 6 | 18 | 1 |

DA-MLP | 2 | 2 | 1 | 5 | 5 | 1 | 2 | 2 | 5 | 6 |

ES-MLP | 4 | 5 | 2 | 11 | 3 | 4 | 4 | 1 | 9 | 3 |

IWO-MLP | 3 | 3 | 5 | 11 | 3 | 2 | 1 | 5 | 8 | 5 |

LCA-MLP | 1 | 1 | 3 | 5 | 5 | 3 | 3 | 3 | 9 | 3 |

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**MDPI and ACS Style**

Moayedi, H.; Mosavi, A.
Synthesizing Multi-Layer Perceptron Network with Ant Lion Biogeography-Based Dragonfly Algorithm Evolutionary Strategy Invasive Weed and League Champion Optimization Hybrid Algorithms in Predicting Heating Load in Residential Buildings. *Sustainability* **2021**, *13*, 3198.
https://doi.org/10.3390/su13063198

**AMA Style**

Moayedi H, Mosavi A.
Synthesizing Multi-Layer Perceptron Network with Ant Lion Biogeography-Based Dragonfly Algorithm Evolutionary Strategy Invasive Weed and League Champion Optimization Hybrid Algorithms in Predicting Heating Load in Residential Buildings. *Sustainability*. 2021; 13(6):3198.
https://doi.org/10.3390/su13063198

**Chicago/Turabian Style**

Moayedi, Hossein, and Amir Mosavi.
2021. "Synthesizing Multi-Layer Perceptron Network with Ant Lion Biogeography-Based Dragonfly Algorithm Evolutionary Strategy Invasive Weed and League Champion Optimization Hybrid Algorithms in Predicting Heating Load in Residential Buildings" *Sustainability* 13, no. 6: 3198.
https://doi.org/10.3390/su13063198