# Surrogate Models for Efficient Multi-Objective Optimization of Building Performance

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## Abstract

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## 1. Introduction

- Tackling portability issues by deploying the developed SM for a widely used BPS tool and a common BPO problem.
- Significantly improving the required computational time to use BPS and BPO.
- Providing SM that are easier to grasp than the respective BPS inputs and do not require as much knowledge and expertise.
- Providing workflows capable of addressing the current limitations regarding the use of BPS tools and BPO.

## 2. Materials and Methods

#### 2.1. Baseline Optimization

#### 2.2. Surrogate Model

#### 2.3. Hyperparameter Tuning

## 3. Results and Discussion

#### 3.1. Results

#### 3.2. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BPS | Building Performance Simulation |

BPO | Building Performance Optimization |

MOO | Multi-Objective Optimization |

AD | Algorithm Design |

ADA | Algorithm Design and Analysis |

SM | Surrogate Models |

CNN | Convolutional Neural Network |

EA | Evolutionary Algorithms |

PSO | Particle Swarm Optimization |

NSGAII | Non-Dominated Sorting Genetic Algorithm II |

IBEA | Indicator-Based Genetic Algorithm |

SMPSO | Speed-Constrained Multi-Objective PSO |

OMOPSO | MOPSO Algorithm |

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**Figure 4.**NSGAII non-dominated solutions for 10,000 iterations—the most expensive solution is represented in red.

Simulation Setting | Value |
---|---|

Period | 1 year |

Timestep | 1 timestep per hour |

Program and schedules | Midrise apartment |

Window-to-wall ratio | 0.2 |

Outputs | Zone Ideal Load Supply Air Total Heating Energy (J) |

Zone Ideal Load Supply Air Total Cooling Energy (J) |

Construction Type | Total Area ${\mathbf{m}}^{2}$ | x | Cost [€/m${}^{2}$] | Materials | ||
---|---|---|---|---|---|---|

Walls | 8699.94 | 0 | 20 | Plaster—2 cm | ||

Bored brick—11 cm | ||||||

Air gap—6 cm | ||||||

Bored brick—11 cm | ||||||

Stucco—1.5 cm | ||||||

1 | 25 | Plaster—2 cm | ||||

Bored brick—15 cm | ||||||

Air gap—6 cm | ||||||

Bored brick—11 cm | ||||||

Stucco—1.5 cm | ||||||

2 | 35 | Plaster—2 cm | ||||

Bored brick—11 cm | ||||||

Air gap—6 cm | ||||||

XPS—4 cm | ||||||

Bored brick—11 cm | ||||||

Stucco—1.5 cm | ||||||

Interior floors | 9327.27 | 0 | 10 | Wood panels—12 cm | ||

Stucco—1.5 cm | ||||||

1 | 25 | Ceramics—1 cm | ||||

Screed—8 cm | ||||||

Lightweight slab—15 cm | ||||||

Stucco—1.5 cm | ||||||

2 | 30 | Ceramics—1 cm | ||||

Screed—8 cm | ||||||

Concrete slab—15 cm | ||||||

Stucco—1.5 cm | ||||||

Roofs | 1216.67 | 0 | 20 | Screed—8 cm | ||

Waterproofing—0.2 cm | ||||||

Screed—8 cm | ||||||

Lightweight slab—15 cm | ||||||

Stucco—1.5 cm | ||||||

1 | 30 | Screed—8 cm | ||||

Waterproofing—0.2 cm | ||||||

XPS—4 cm | ||||||

Screed—8 cm | ||||||

Lightweight slab—15 cm | ||||||

Stucco—1.5 cm | ||||||

2 | 35 | Screed—8 cm | ||||

Waterproofing—0.2 cm | ||||||

XPS—4 cm | ||||||

Screed—8 cm | ||||||

Concrete slab—15 cm | ||||||

Stucco—1.5 cm | ||||||

$\mathbf{U}[\mathbf{W}/{\mathbf{m}}^{\mathbf{2}}\mathbf{K}]$ | ${\mathbf{\tau}}_{\mathbf{sol}}$ | ${\mathbf{\tau}}_{\mathbf{vis}}$ | ||||

Windows | 2174.98 | 0 | 50 | 2.69 | 0.75 | 0.80 |

1 | 80 | 1.70 | 0.38 | 0.70 | ||

2 | 100 | 1.25 | 0.20 | 0.70 |

**Table 3.**Optimum convolutional neural network structure and performance for surrogate model of Equation (2).

Layer (Type) | Filters | Kernel Size |
---|---|---|

Dense | 300 | 1 |

1D-Convolutional | 157 | 2 |

1D-Convolutional | 6 | 2 |

1D-Convolutional | 290 | 2 |

1D-Convolutional | 70 | 1 |

Dense | 1 | 1 |

R${}^{\mathbf{2}}$ score | 0.96 | |

RMSE (kWh/m${}^{\mathbf{2}}$) | 0.54 |

**Table 4.**Optimum convolutional neural network structure and performance for a surrogate model of Equation (3).

Layer (Type) | Filters | Kernel Size |
---|---|---|

Dense | 300 | 1 |

1D-Convolutional | 300 | 2 |

1D-Convolutional | 300 | 2 |

1D-Convolutional | 6 | 2 |

1D-Convolutional | 100 | 1 |

Dense | 1 | 1 |

R${}^{\mathbf{2}}$ score | 0.97 | |

RMSE (kWh/m${}^{\mathbf{2}}$) | 0.01 |

Algorithm | Iterations | Hyperparameters | Range |
---|---|---|---|

NSGAII | 500 | Population size ${P}_{s}$ | [30 .. 200] |

SBX crossover S | [0, 1] | ||

Polynomial mutation ${P}_{m}$ | [0, 1] | ||

IBEA | 500 | ${P}_{s}$ | [30 .. 200] |

S | [0, 1] | ||

${P}_{m}$ | [0, 1] | ||

SMPSO | 500 | Swarm size ${S}_{s}$ | [30 .. 200] |

Leader size ${L}_{s}$ | [30 .. 200] | ||

Max iterations i | [30 .. 200] | ||

S | [0, 1] | ||

${P}_{m}$ | [0, 1] | ||

OMOPSO | 500 | ${S}_{s}$ | [30 .. 200] |

${L}_{s}$ | [30 .. 200] | ||

i | [30 .. 200] | ||

S | [0, 1] | ||

${P}_{m}$ | [0, 1] | ||

Epsilon $\u03f5$ | [0.0001, 1] |

Hyperparameter | Value | Hypervolume | |
---|---|---|---|

NSGAII | ${P}_{s}$ | 30 | 0.53 |

S | 1 | ||

${P}_{m}$ | 0.59 | ||

IBEA | ${P}_{s}$ | 32 | 0.54 |

S | 0.66 | ||

${P}_{m}$ | 1 | ||

SMPSO | ${S}_{s}$ | 68 | 0.52 |

${L}_{s}$ | 59 | ||

i | 67 | ||

S | 0.43 | ||

${P}_{m}$ | 0.35 | ||

OMOPSO | ${S}_{s}$ | 30 | 0.52 |

${L}_{s}$ | 200 | ||

i | 200 | ||

S | 1 | ||

${P}_{m}$ | 0 | ||

$\u03f5$ | 0.001 |

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## Share and Cite

**MDPI and ACS Style**

Araújo, G.R.; Gomes, R.; Gomes, M.G.; Guedes, M.C.; Ferrão, P.
Surrogate Models for Efficient Multi-Objective Optimization of Building Performance. *Energies* **2023**, *16*, 4030.
https://doi.org/10.3390/en16104030

**AMA Style**

Araújo GR, Gomes R, Gomes MG, Guedes MC, Ferrão P.
Surrogate Models for Efficient Multi-Objective Optimization of Building Performance. *Energies*. 2023; 16(10):4030.
https://doi.org/10.3390/en16104030

**Chicago/Turabian Style**

Araújo, Gonçalo Roque, Ricardo Gomes, Maria Glória Gomes, Manuel Correia Guedes, and Paulo Ferrão.
2023. "Surrogate Models for Efficient Multi-Objective Optimization of Building Performance" *Energies* 16, no. 10: 4030.
https://doi.org/10.3390/en16104030