# Evaluation of Urban Green Building Design Schemes to Achieve Sustainability Based on the Projection Pursuit Model Optimized by the Atomic Orbital Search

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## Abstract

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## 1. Introduction

## 2. Related Research

## 3. The Evaluation Index System of Green Building Design Schemes

#### 3.1. Analysis of the Evaluation Factors

#### 3.2. Evaluation Index System

#### 3.3. Definition and Data Acquisition Methods of Secondary Indicators

## 4. The Proposed Evaluation Model of Green Building Design Schemes

#### 4.1. Data Collection and Preprocessing

#### 4.2. Building the PPM for the Evaluation of Green Building Design Schemes

#### 4.3. Title

#### 4.4. Developing a Mathematical Evaluation Model via the Interpolation Method

#### 4.5. The Implementation of the Proposed Model

## 5. Case Study

#### 5.1. Engineering Background

#### 5.2. Data Collection and Preprocessing

#### 5.3. Building the PPM for the Evaluation of Green Building Design Schemes

#### 5.4. Developing a Mathematical Evaluation Model via the Interpolation Method

## 6. Discussion

#### 6.1. Computational Performance of Different Optimization Algorithms

#### 6.2. Computational Performance of Different Evaluation Methods

#### 6.3. Impact of the Evaluation Index System on the Evaluation Results

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Primary Indicator | Secondary Indicator | Type | Refs |
---|---|---|---|

${X}_{1}$: Economic Index | ${X}_{11}$: Project cost | Cost | [5] |

${X}_{12}$: Incremental NPV of investment | Benefit | [5,6] | |

${X}_{13}$: Incremental payback period | Cost | [6,25] | |

${X}_{2}$: Resource Utilization Index | ${X}_{21}$: Rate of land use | Benefit | [26,27,28] |

${X}_{22}$: Energy consumption of the air conditioning system | Cost | [29,30] | |

${X}_{23}$: Energy consumption of the lighting system | Cost | [31] | |

${X}_{24}$: Utilization rate of reclaimed water | Benefit | [32,33] | |

${X}_{25}$: Utilization rate of rainwater | Benefit | [32,34] | |

${X}_{26}$: Utilization rate of new wall materials | Benefit | [35,36] | |

${X}_{27}$: Recovery rate of construction waste | Benefit | [37,38,39] | |

${X}_{3}$: Environmental Impact Index | ${X}_{31}$: Indoor sunshine | Benefit | [40,41] |

${X}_{32}$: Ratio of the window area to the indoor area | Benefit | [42,43] | |

${X}_{33}$: Effect of sound insulation and noise reduction | Benefit | [44,45] | |

${X}_{4}$: Technical Management Index | ${X}_{41}$: Technical difficulty of construction | Benefit | [46,47] |

${X}_{42}$: Reduction of the construction period | Benefit | [48,49] | |

${X}_{43}$: Difficulty of project management organization | Benefit | [50,51,52] | |

${X}_{5}$: Social Impact Index | ${X}_{51}$: Ratio of the energy consumption of the building area to the GDP | Cost | [53,54] |

${X}_{52}$: Coordination between architectural modeling and regional planning | Benefit | [55] | |

${X}_{53}$: Effect of protecting the human environment | Benefit | [55] |

Secondary Indicator | Unit | I | II | III | IV |
---|---|---|---|---|---|

${X}_{11}$ | Million CNY | [100, 200] | [75, 100) | [50, 75) | [0, 50) |

${X}_{12}$ | Million CNY | [0, 5) | [5, 10) | [10, 20) | [20, 50] |

${X}_{13}$ | Year | [20, 50] | [10, 20) | [5, 10) | [0, 5) |

${X}_{21}$ | % | [75, 100] | [50, 75) | [25, 50) | [0, 25) |

${X}_{22}$ | $\mathrm{kWh}/{\mathrm{m}}^{2}$ | [65, 85] | [45, 65) | [25, 45) | [0, 25) |

${X}_{23}$ | $\mathrm{W}/{\mathrm{m}}^{2}$ | [8, 10] | [5, 8) | [3, 5) | [0, 3) |

${X}_{24}$ | % | [0, 10) | [10, 20) | [20, 30) | [30, 50] |

${X}_{25}$ | % | [0, 10) | [10, 20) | [20, 30) | [30, 50] |

${X}_{26}$ | % | [0, 5) | [5, 10) | [10, 20) | [20, 30] |

${X}_{27}$ | % | [0, 10) | [10, 20) | [20, 30) | [30, 50] |

${X}_{31}$ | - | [0, 5) | [5, 10) | [10, 15) | [15, 20] |

${X}_{32}$ | % | [0, 25) | [25, 50) | [50, 75) | [75, 100] |

${X}_{41}$ | - | Difficult [0, 25) | Simple [25, 50) | Very simple [50, 75) | Simplest [75, 100] |

${X}_{42}$ | % | [0, 10) | [10, 15) | [15, 20) | [20, 30] |

${X}_{43}$ | - | Difficult [0, 25) | Simple [25, 50) | Very simple [50, 75) | Simplest [75, 100] |

${X}_{51}$ | Ton of standard coal/ten thousand CNY | [1, 1.5] | [0.75, 1) | [0.5, 0.75) | [0, 0.5) |

${X}_{52}$ | - | Average [0, 25) | Harmonious [25, 50) | Very harmonious [50, 75) | Most harmonious [75, 100] |

${X}_{53}$ | - | Partially effective [0, 25) | Effective [25, 50) | Very effective [50, 75) | Most effective [75, 100] |

Secondary Indicator | Original Data | Normalized Data | Secondary Indicator | Original Data | Normalized Data |
---|---|---|---|---|---|

${X}_{11}$ | 128 | 0.640 | ${X}_{31}$ | 8 | 0.400 |

${X}_{12}$ | 7.25 | 0.145 | ${X}_{32}$ | 30.43 | 0.304 |

${X}_{13}$ | 9.33 | 0.187 | ${X}_{33}$ | 45.5 | 0.455 |

${X}_{21}$ | 70 | 0.700 | ${X}_{41}$ | 72 | 0.720 |

${X}_{22}$ | 57.5 | 0.676 | ${X}_{42}$ | 12 | 0.400 |

${X}_{23}$ | 4.12 | 0.412 | ${X}_{43}$ | 65 | 0.650 |

${X}_{24}$ | 18.76 | 0.375 | ${X}_{51}$ | 0.661 | 0.441 |

${X}_{25}$ | 12.57 | 0.251 | ${X}_{52}$ | 45 | 0.450 |

${X}_{26}$ | 28.02 | 0.934 | ${X}_{53}$ | 55.5 | 0.555 |

${X}_{27}$ | 13.47 | 0.269 | - | - | - |

Typical Technology | I | II | III | IV | Score |
---|---|---|---|---|---|

Difficult [0, 25) | Simple [25, 50) | Very Simple [50, 75) | Simplest [75, 100] | ||

${X}_{41}^{1}$ | The supporting system is very complicated, construction amount is very large. | Supporting system is complex, construction amount is large. | Supporting system is simple, construction amount is general. | The supporting system is very simple, construction amount is small. | 30 |

${X}_{41}^{2}$ | Concrete pouring and curing are very difficult, quality is difficult to control. | Concrete pouring and curing are difficult, quality is difficult to control. | Concrete pouring and curing are not difficult, quality is easy to control. | Concrete pouring and curing are easy, there are almost no quality problems. | 75 |

${X}_{41}^{3}$ | Many kinds of steel bars and complicated connections. | Many kinds of steel bars, connections are not too complicated. | A few kinds of steel bars, connections are simple | Few kinds of steel bars, connections are very simple. | 85 |

${X}_{41}^{4}$ | The template system is too large and the security risk is high. | The template system is huge and the security risk is high. | The template system is simple and the security risks are controllable. | The template is very simple and the security risks are completely controllable. | 75 |

${X}_{41}^{5}$ | The construction is very difficult, quality is very difficult to control. | The construction is difficult, quality is difficult to control. | The construction is simple, quality is simple to control. | The construction is very simple, quality is very simple to control. | 60 |

${X}_{41}^{6}$ | Waterproof and pipe network structures are very complex. | Waterproof and pipe network structures are complex. | Waterproof and pipe network structures are simple. | Waterproof and pipe network structures are very simple. | 20 |

${X}_{41}^{7}$ | Many kinds of steel members, and the connection is very complicated. | Many kinds of steel members, and the connection is complicated. | A few kinds of steel members, and the connection is simple. | Few kinds of steel members, and the connection is very simple. | 25 |

${X}_{41}^{8}$ | Too many high-altitude hoisting operations. | High-altitude hoisting operations. | High-altitude hoisting operations. | Few high-altitude hoisting operations. | 45 |

${X}_{41}^{9}$ | Building information modeling (BIM) is not applied. | BIM technology is initially applied. | BIM technology is acceptably applied. | BIM technology is deeply applied. | 80 |

Iteration (n) | Fitness (n − 1) | Fitness (n) | Fitness (n)–Fitness (n − 1) | Result |
---|---|---|---|---|

126 | 59.23787871 | 59.23787871 | 0 < 0.00001 | Continue |

127 | 59.23787871 | 59.23800214 | 0.00012343 > 0.0001 | Continue |

128 | 59.23800214 | 59.23800214 | 0 < 0.0001 | Continue |

1000 | 59.23800214 | 59.23800214 | 0 < 0.0001 | Stop |

Secondary Indicator | Corresponding Element | Weight | Ranking | Secondary Indicator | Corresponding Element | Weight | Ranking |
---|---|---|---|---|---|---|---|

${X}_{11}$ | 0.2610 | 0.0681 | 6 | ${X}_{31}$ | 0.1747 | 0.0305 | 17 |

${X}_{12}$ | 0.3207 | 0.1029 | 1 | ${X}_{32}$ | 0.2764 | 0.0764 | 3 |

${X}_{13}$ | 0.2175 | 0.0473 | 11 | ${X}_{33}$ | 0.1713 | 0.0293 | 18 |

${X}_{21}$ | 0.2138 | 0.0457 | 12 | ${X}_{41}$ | 0.2652 | 0.0703 | 5 |

${X}_{22}$ | 0.2800 | 0.0784 | 2 | ${X}_{42}$ | 0.2204 | 0.0486 | 9 |

${X}_{23}$ | 0.2702 | 0.0730 | 4 | ${X}_{43}$ | 0.2411 | 0.0581 | 7 |

${X}_{24}$ | 0.1372 | 0.0188 | 19 | ${X}_{51}$ | 0.1931 | 0.0373 | 15 |

${X}_{25}$ | 0.2346 | 0.0550 | 8 | ${X}_{52}$ | 0.1990 | 0.0396 | 14 |

${X}_{26}$ | 0.1778 | 0.0316 | 16 | ${X}_{53}$ | 0.2034 | 0.0414 | 13 |

${X}_{27}$ | 0.2181 | 0.0476 | 10 | - | - | - | - |

Computational Performance | AOS | PSO | GA | |
---|---|---|---|---|

Computation speed | Best result | 107th | 132th | 174th |

Average result | 131.54th | 197.39th | 284.08th | |

Worst result | 154th | 274th | 402th | |

Stability | Variance of the fitness | 0.0000074 | 0.0000684 | 0.0001974 |

Variance of maximum projection value | 0.0000120 | 0.0000769 | 0.0001026 | |

Variance of optimal projection vector | 0.0000032 | 0.0000107 | 0.0000184 |

Secondary Indicator | Group 1 | Group 2 | Group 3 | Group 4 | ||||
---|---|---|---|---|---|---|---|---|

Weights | Rankings | Weights | Rankings | Weights | Rankings | Weights | Rankings | |

${X}_{11}$ | 0.0522 | 9 | 0.0580 | 9 | 0.0193 | 16 | 0.0407 | 11 |

${X}_{12}$ | 0.0821 | 3 | 0.1100 | 1 | 0.0852 | 3 | 0.1222 | 2 |

${X}_{13}$ | 0.0431 | 13 | 0.0854 | 4 | 0.0338 | 13 | 0.0832 | 4 |

${X}_{21}$ | 0.0364 | 16 | 0.0530 | 11 | 0.0449 | 11 | 0.0317 | 13 |

${X}_{22}$ | 0.0919 | 1 | 0.1040 | 2 | 0.1080 | 1 | 0.1279 | 1 |

${X}_{23}$ | 0.0372 | 14 | 0.0547 | 10 | 0.0470 | 10 | 0.0925 | 3 |

${X}_{24}$ | 0.0541 | 8 | 0.0505 | 12 | 0.0285 | 15 | 0.0342 | 12 |

${X}_{25}$ | 0.0899 | 2 | 0.0643 | 6 | 0.0323 | 14 | 0.0279 | 15 |

${X}_{26}$ | 0.0745 | 4 | 0.0324 | 13 | 0.0562 | 9 | 0.0311 | 14 |

${X}_{27}$ | 0.0665 | 6 | 0.0706 | 5 | 0.0870 | 2 | 0.0228 | 17 |

${X}_{31}$ | 0.0498 | 10 | 0.0992 | 3 | 0.0625 | 8 | 0.0448 | 9 |

${X}_{32}$ | 0.0659 | 7 | 0.0151 | 17 | 0.0175 | 17 | 0.0200 | 18 |

${X}_{33}$ | 0.0258 | 18 | 0.0180 | 15 | 0.0705 | 7 | 0.0439 | 10 |

${X}_{41}$ | 0.0445 | 12 | 0.0588 | 8 | 0.0375 | 12 | 0.0574 | 7 |

${X}_{42}$ | 0.0671 | 5 | 0.0592 | 7 | 0.0754 | 6 | 0.0276 | 16 |

${X}_{43}$ | 0.0490 | 11 | 0.0173 | 16 | 0.0794 | 5 | 0.0158 | 19 |

${X}_{51}$ | 0.0283 | 17 | 0.0261 | 14 | 0.0817 | 4 | 0.0597 | 6 |

${X}_{52}$ | 0.0367 | 15 | 0.0133 | 18 | 0.0167 | 19 | 0.0686 | 5 |

${X}_{53}$ | 0.0049 | 19 | 0.0100 | 19 | 0.0168 | 18 | 0.0480 | 8 |

Deleted Indicators | Optimum Projection Value | Evaluation Grade | The Minimum Index Set or Not? |
---|---|---|---|

${X}_{24}$ | 3.471 | 2.104 | No |

${X}_{24}$, ${X}_{31}$ | 3.832 | 2.433 | No |

${X}_{24}$, ${X}_{31}$, ${X}_{33}$ | 4.541 | 2.680 | No |

${X}_{24}$, ${X}_{31}$, ${X}_{33}$, ${X}_{51}$ | 5.048 | 3.157 | Yes |

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**MDPI and ACS Style**

Liu, G.; Zhao, T.; Yan, H.; Wu, H.; Wang, F.
Evaluation of Urban Green Building Design Schemes to Achieve Sustainability Based on the Projection Pursuit Model Optimized by the Atomic Orbital Search. *Sustainability* **2022**, *14*, 11007.
https://doi.org/10.3390/su141711007

**AMA Style**

Liu G, Zhao T, Yan H, Wu H, Wang F.
Evaluation of Urban Green Building Design Schemes to Achieve Sustainability Based on the Projection Pursuit Model Optimized by the Atomic Orbital Search. *Sustainability*. 2022; 14(17):11007.
https://doi.org/10.3390/su141711007

**Chicago/Turabian Style**

Liu, Genbao, Tengfei Zhao, Hong Yan, Han Wu, and Fuming Wang.
2022. "Evaluation of Urban Green Building Design Schemes to Achieve Sustainability Based on the Projection Pursuit Model Optimized by the Atomic Orbital Search" *Sustainability* 14, no. 17: 11007.
https://doi.org/10.3390/su141711007