# Multi-objective Building Design Optimization under Operational Uncertainties Using the NSGA II Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Prescriptive building codes set strict performance limits for each building component;
- The trade-off compliance path is similar to a prescriptive approach, but it allows for some substitution between code components;
- Point system compliance involves scoring for meeting certain specific requirements accompanied by incentives for achieving levels of over-compliance.
- Simulated performance compliance relies on simulation tools to simulate energy performance for proposed buildings by comparing their energy performance to a reference benchmark building. It is estimated that between 20% and 50% of energy savings could be achieved by interventions in the building envelope, 20% and 60% for HVAC systems, and 20% and 50% for lighting [12,13].

## 2. Literature Review

## 3. Building Design Optimization

## 4. Optimization under Uncertainty

## 5. Research Methodology

#### 5.1. NSGA II Evolutionary Algorithm

#### 5.2. Case Study

^{2}was modeled using the Energy Plus simulation program (Figure 6). The unit consists of two air-conditioned bedrooms and three naturally ventilated zones, including kitchen, living room, and bathroom. Occupants operate the windows in both the bedrooms and allow natural ventilation whenever outdoor weather conditions were suitable. Specific details about the residential unit are listed in Table 1.

## 6. Results

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Wikipedia Global South. Available online: https://en.wikipedia.org/wiki/Global_South (accessed on 3 April 2020).
- Confederation of Indian Industry. Building a Low-Carbon Indian Economy; Confederation of Indian Industry: New Delhi, India, 2012; Volume 66, pp. 37–39. [Google Scholar]
- Yu, S.; Northwest, P.; Evans, M.; Northwest, P. Indias R & D for Energy Efficient Buildings: Insights for U.S. Cooperation with India; U.S. Department of Energy: Washington, DC, USA, 2015. [Google Scholar]
- Bano, F.; Kamal, M.A. Examining the Role of Building Envelope for Energy Efficiency in Office Buildings in India. Arch. Res.
**2016**, 6, 107–115. [Google Scholar] - Mckinsey. Building India Accelerating Infrastructure Projects. Dataquest
**2009**, 22, 16. [Google Scholar] - Wikipedia Köppen Climate Classification. Available online: https://en.wikipedia.org/wiki/Köppen_climate_classification (accessed on 9 April 2020).
- Sadie, C. Building Energy Codes: Policy Overview and Good Practices; The Clean Energy Ministerial: Paris, France, 2015. [Google Scholar]
- Yu, S.; Eom, J.; Evans, M.; Clarke, L. A long-term, integrated impact assessment of alternative building energy code scenarios in China. Energy Policy
**2014**, 67, 626–639. [Google Scholar] [CrossRef] - Yu, S.; Tan, Q.; Evans, M.; Kyle, P.; Vu, L.; Patel, P.L. Improving building energy efficiency in India: State-level analysis of building energy efficiency policies. Energy Policy
**2017**, 110, 331–341. [Google Scholar] [CrossRef] - McKinsey. Environmental and Energy Sustainability: An Approach for India; McKinsey: New Delhi, India, 2009; pp. 1–90. [Google Scholar]
- Evans, M.; Roshchanka, V.; Graham, P. An international survey of building energy codes and their implementation. J. Clean. Prod.
**2017**, 158, 382–389. [Google Scholar] [CrossRef] - Harish, V.S.K.V.; Kumar, A. A review on modeling and simulation of building energy systems. Renew. Sustain. Energy Rev.
**2016**, 56, 1272–1292. [Google Scholar] [CrossRef] - Kelso, J.D. 2011 Buildings Energy Data Book; Institute for Energy and Environmental Research: Takoma Park, MD, USA, 2012. [Google Scholar]
- Rouleau, J.; Ramallo-González, A.P.; Gosselin, L.; Blanchet, P.; Natarajan, S. A unified probabilistic model for predicting occupancy, domestic hot water use and electricity use in residential buildings. Energy Build.
**2019**, 202. [Google Scholar] [CrossRef] - India’s Construction Industry Regains Growth Momentum; Construction Week Online, India. 2019. Available online: https://www.constructionweekonline.in/business/9399-indias-construction-industry-regains-growth-momentum (accessed on 23 February 2020).
- Tulsyan, A.; Dhaka, S.; Mathur, J.; Yadav, J.V. Potential of energy savings through implementation of Energy Conservation Building Code in Jaipur city, India. Energy Build.
**2013**, 58, 123–130. [Google Scholar] [CrossRef] - Dhaka, S.; Mathur, J.; Garg, V. Combined effect of energy efficiency measures and thermal adaptation on air conditioned building in warm climatic conditions of India. Energy Build.
**2012**, 55, 351–360. [Google Scholar] [CrossRef] - Ramesh, T.; Prakash, R.; Shukla, K.K. Life cycle approach in evaluating energy performance of residential buildings in Indian context. Energy Build.
**2012**, 54, 259–265. [Google Scholar] [CrossRef] - Ramesh, T.; Prakash, R.; Shukla, K.K. Life cycle energy analysis of a residential building with different envelopes and climates in Indian context. Appl. Energy
**2012**, 89, 193–202. [Google Scholar] [CrossRef] - Nguyen, A.T.; Reiter, S.; Rigo, P. A review on simulation-based optimization methods applied to building performance analysis. Appl. Energy
**2014**, 113, 1043–1058. [Google Scholar] [CrossRef] - Wang, W.; Zmeureanu, R.; Rivard, H. Applying multi-objective genetic algorithms in green building design optimization. Build. Environ.
**2005**, 40, 1512–1525. [Google Scholar] [CrossRef] - Delgarm, N.; Sajadi, B.; Delgarm, S. Multi-objective optimization of building energy performance and indoor thermal comfort: A new method using artificial bee colony (ABC). Energy Build.
**2016**, 131, 42–53. [Google Scholar] [CrossRef] - Delgarm, N.; Sajadi, B.; Kowsary, F.; Delgarm, S. Multi-objective optimization of the building energy performance: A simulation-based approach by means of particle swarm optimization (PSO). Appl. Energy
**2016**, 170, 293–303. [Google Scholar] [CrossRef] - Hamdy, M.; Nguyen, A.T.; Hensen, J.L.M. A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems. Energy Build.
**2016**, 121, 57–71. [Google Scholar] [CrossRef] [Green Version] - Christensen, C.; Anderson, R.; Horowitz, S.; Courtney, A.; Spencer, J. BEoptTM Software for Building Energy Optimization: Features and Capabilities. 2006. Available online: https://www.nrel.gov/docs/fy06osti/39929.pdf (accessed on 23 February 2020).
- Emanuelenaboni, E.; MacCarini, A.; Korolija, I.; Zhang, Y. Comparison of conventional, parametric and evolutionary optimization approaches for the architectural design of nearly zero energy buildings. In Proceedings of the 13th Conference of International Building Performance Simulation Association, Chambéry, France, 26–28 August 2013; pp. 2559–2566. [Google Scholar]
- Wetter, M. GenOpt
^{®}User Manual v3.1.1; Simulation Research Group: Berkeley, CA, USA, 2016; pp. 1998–2016. [Google Scholar] - Palonen, M.; Hamdy, M.; Hasan, A. MOBO A New Software for Multi-Objective Building Performance Optimization. In Proceedings of the 13th Conference of International Building Performance Simulation Association, Chambéry, France, 26–28 August 2013; pp. 2567–2574. [Google Scholar]
- Li, K.; Pan, L.; Xue, W.; Jiang, H.; Mao, H. Multi-Objective Optimization for Energy Performance Improvement of Residential Buildings: A Comparative Study. Energies
**2017**, 10, 245. [Google Scholar] [CrossRef] [Green Version] - Xu, D.; Qu, M.; Hang, Y.; Zhao, F. Multi-objective optimal design of a solar absorption cooling and heating system under life-cycle uncertainties. Sustain. Energy Technol. Assessments
**2015**, 11, 92–105. [Google Scholar] [CrossRef] - Zhang, S.; Huang, P.; Sun, Y. A multi-criterion renewable energy system design optimization for net zero energy buildings under uncertainties. Energy
**2016**, 94, 654–665. [Google Scholar] [CrossRef] - Hopfe, C.J.; Emmerich, M.T.M.; Marijt, R.; Hensen, J. Robust multi-criteria design optimisation in building design. In Proceedings of the 1st IBPSA-England Conference Building Simulation and Optimization, Loughborough, UK, 10–11 September 2012; pp. 19–26. [Google Scholar]
- Ramallo-gonzález, A.P.; Blight, T.S.; Coley, D.A. New optimisation methodology to uncover robust low energy designs that accounts for occupant behaviour or other unknowns. J. Build. Eng.
**2015**, 2, 59–68. [Google Scholar] [CrossRef] [Green Version] - Jacob, D.; Burhenne, S.; Florita, A.; Henze, G. Optimizing building energy simulation models in the face of uncertainty. In Proceedings of the Fourth National Conference of IBPSA-USA, New York, NY, USA, 11–13 August 2010; pp. 11–13. [Google Scholar]
- Yu, Z.; Chen, J.; Sun, Y.; Zhang, G. A GA-based system sizing method for net-zero energy buildings considering multi-criteria performance requirements under parameter uncertainties. Energy Build.
**2016**, 129, 524–534. [Google Scholar] [CrossRef] - Lu, Y.; Wang, S.; Yan, C.; Huang, Z. Robust optimal design of renewable energy system in nearly/net zero energy buildings under uncertainties. Appl. Energy
**2017**, 187, 62–71. [Google Scholar] [CrossRef] - Hoes, P.; Trcka, M.; Hensen, J.L.M.; Bonnema, B.H. Optimizing building designs using a robustness indicator with respect to user behavior. In Proceedings of the 12th Conference of International Building Performance Simulation Association, Sydney, Australia, 14–16 November 2011; pp. 14–16. [Google Scholar]
- EnergyPlus EnergyPlus Essentials - EnergyPlus v9.1.0 Documentation. 2019. Available online: https://bigladdersoftware.com/epx/docs/9-1/essentials/title.html (accessed on 9 April 2020).
- Wikipedia Genetic Algorithm. Available online: https://en.wikipedia.org/wiki/Genetic_algorithm (accessed on 2 April 2020).
- Deb, K. NSGA II paper by Kalyanmoy Deb. IEEE Trans. Evol. Comput.
**2002**, 6, 182–197. [Google Scholar] [CrossRef] [Green Version] - Wikipedia Mutation (Genetic Algorithm)- Wikipedia. Available online: https://en.wikipedia.org/wiki/Mutation_(genetic_algorithm) (accessed on 2 April 2020).
- Wikipedia Crossover (Genetic Algorithm)- Wikipedia. Available online: https://en.wikipedia.org/wiki/Crossover_(genetic_algorithm) (accessed on 2 April 2020).
- Vasinton, S.; Raslan, R. Multi Objective Optimisation for the Minimisation of Life Cycle Carbon Footprint and Life Cycle Cost Using NSGA II: A Refurbished High-Rise Residential Building Case Study by Simona Vasinton; IBPSA: Las Cruces, NM, USA, 2015; p. 2. [Google Scholar]
- Penna, P.; Prada, A.; Cappelletti, F.; Gasparella, A. Multi-objectives optimization of Energy Efficiency Measures in existing buildings. Energy Build.
**2015**, 95, 57–69. [Google Scholar] [CrossRef] - Buso, T.; Valentina, F.; Anderson, R.K.; Corganti, S.P. Occupant behaviour and robustness of building design. Build. Environ.
**2015**, 94, 694–703. [Google Scholar] [CrossRef] - Glazer, J.; Gard, P.E. Using Python and Eppy for a Large National Simulation Study; IBPSA: Las Cruces, NM, USA, 2016; pp. 230–237. [Google Scholar]

**Figure 1.**Köppen [6] climate classification for the Global South. We define the Global South as developing economies broadly located in tropical locations. Note that the type B climates (i.e., dry climates) on the map not only covers large land areas but also locations with high population density (e.g., large parts of India and Africa). The Köppen system is used for global climate classification based on local temperature and precipitation data. Under this, five main climate types include A (tropical), B (dry), C (temperate), D (continental), and E (polar) type. Additional subscripts, such as sh, fb, sc, etc., are added for further climate sub-classification.

**Figure 2.**Coupling between a building simulation program and an optimization algorithm (adopted after modification from [20]).

**Figure 3.**Control diagram displaying the different steps involved during the implementation of the non-dominated sorting genetic (NSGA II) algorithm (adopted after modification from [40]).

**Figure 4.**Robustness plot for a Pareto solution (adopted after modification from [37]).

**Figure 10.**Robustness plot displaying the relative standard deviation (RSD) values for the six Pareto solutions. The narrow ranges for the two axes were chosen intentionally to illustrate small variations between individual Pareto solutions.

Building Component | Description |
---|---|

Total floor area | 70 ${\mathrm{m}}^{2}$ |

Building roof | 100 mm RCC roof with a 50 mm earth-based weatherproofing tiles |

External Walls | 225 mm burnt brick core with 12.5 mm plaster on both sides |

Window to wall ratio | 30% |

Glazing type | 6 mm clear glass SHGC = 0.8 |

Natural ventilation setpoint | 22 °C |

Air conditioner setpoint | 24 °C |

Building lighting load | 5 W/${\mathrm{m}}^{2}$ |

Bedroom appliance load | 4 W/${\mathrm{m}}^{2}$ |

Living room appliance load | 10 W/${\mathrm{m}}^{2}$ |

Sno | Design Feature | Possible Options |
---|---|---|

${\mathrm{X}\text{}}_{1}$ | Window to wall ratio (%) | [10,20,30,40,50,60] |

${\mathrm{X}\text{}}_{2}$ | Depth of overhang | [0.3,0.6,1] m |

${\mathrm{X}\text{}}_{3}$ | Window glazing type [SHGC] | Single (0.8), Double (0.5), Triple (0.3) |

${\mathrm{X}\text{}}_{4}$ | Wall thickness | 150 mm, 200 mm, 250 mm |

${\mathrm{X}\text{}}_{5}$ | Wall density | [1400,1800,2200] kg/${\mathrm{m}}^{3}$ |

${\mathrm{X}\text{}}_{6}$ | Wall solar absorptance | [0.3,0.5,0.9] |

${\mathrm{X}\text{}}_{7}$ | 1^{st} bedroom AC size | [1,1.5,2] tonnes |

${\mathrm{X}\text{}}_{8}$ | 2^{nd} bedroom AC size | [1,1.5,2] tonnes |

Input Parameter | Parameter value |
---|---|

Population Size | 50 |

Maximum Generations | 100 |

Crossover rate | 1 |

Mutation Rate | 0.2 |

Selection rate | 2 |

Solution | ${\mathbf{X}\text{}}_{1}$ | ${\mathbf{X}\text{}}_{2}$ | ${\mathbf{X}\text{}}_{3}$ | ${\mathbf{X}\text{}}_{4}$ | ${\mathbf{X}\text{}}_{5}$ | ${\mathbf{X}\text{}}_{6}$ | ${\mathbf{X}\text{}}_{7}$ | ${\mathbf{X}\text{}}_{8}$ | ${\mathbf{O}}_{1}$ | ${\mathbf{O}\text{}}_{2}$ |
---|---|---|---|---|---|---|---|---|---|---|

Solution 1 | 20 | 1 | 0.3 | 0.25 | 1800 | 0.3 | 2 | 2 | 94 | 7752 |

Solution 2 | 10 | 1 | 0.3 | 0.25 | 2200 | 0.3 | 2 | 2 | 100 | 7669 |

Solution 3 | 10 | 0.3 | 0.3 | 0.25 | 2200 | 0.3 | 2 | 2 | 97 | 7748 |

Solution 4 | 10 | 1 | 0.3 | 0.2 | 2200 | 0.3 | 2 | 2 | 100 | 7699 |

Solution 5 | 10 | 1 | 0.3 | 0.15 | 1800 | 0.3 | 2 | 2 | 99 | 7704 |

Solution 6 | 10 | 0.6 | 0.3 | 0.15 | 1800 | 0.3 | 2 | 2 | 99 | 7739 |

Serial | Name of Variable | Options |
---|---|---|

1 | Cooling setpoint | [20,24,28] °C |

2 | Lighting load | [2.5,5,7] W/${\mathrm{m}}^{2}$ |

3 | Daily h of AC operation | [6,10,14] h per day |

4 | Living room appliance load | [7.5,10,12.5] W/${\mathrm{m}}^{2}$ |

5 | Bedroom appliance load | [4,8] W/${\mathrm{m}}^{2}$ |

Solution | Cooling Setpoint Unmet H 1 (O1) | Total Energy Consumption 2 [kWh] (O2) | RSD1 | RSD2 | ||||
---|---|---|---|---|---|---|---|---|

Performance Score | Mean | SD | Performance Score | Mean | SD | |||

Solution 1 | 94 | 76.56 | 26.10 | 7752 | 6787 | 2195 | 0.34 | 0.32 |

Solution 2 | 100 | 76.17 | 22.39 | 7669 | 6732 | 2105 | 0.29 | 0.31 |

Solution 3 | 97 | 77.34 | 22.61 | 7748 | 6807 | 2118 | 0.29 | 0.31 |

Solution 4 | 100 | 76.85 | 22.78 | 7699 | 6629 | 2093 | 0.30 | 0.32 |

Solution 5 | 99 | 78.90 | 26.12 | 7704 | 6675 | 2168 | 0.33 | 0.32 |

Solution 6 | 99 | 79.08 | 26.04 | 7739 | 6807 | 2185 | 0.33 | 0.32 |

Solution | Cooling Setpoint Unmet H (w1 = 0.25) | Total Energy Consumption [kWh] (w2 = 0.75) | Final Score ${\mathit{F}}_{\mathit{x}}$ | Final Rank | ||||
---|---|---|---|---|---|---|---|---|

Performance Score | Normalized Performance Score | RSD1 | Performance Score | Normalized Performance Score | RSD2 | |||

Solution 1 | 94 | 0.00 | 0.34 | 7752 | 1 | 0.32 | 1.97 | 4 |

Solution 2 | 100 | 1.00 | 0.29 | 7669 | 0 | 0.31 | 5.67 | 1 |

Solution 3 | 97 | 0.50 | 0.29 | 7748 | 0.95 | 0.31 | 1.72 | 6 |

Solution 4 | 100 | 1.00 | 0.30 | 7699 | 0.36 | 0.32 | 2.76 | 3 |

Solution 5 | 99 | 0.83 | 0.33 | 7704 | 0.42 | 0.32 | 2.83 | 2 |

Solution 6 | 99 | 0.83 | 0.33 | 7739 | 0.84 | 0.32 | 1.76 | 5 |

Solution | Cooling Setpoint Unmet H (w1 = 0.25) | Total Energy Consumption [kWh] (w2 = 0.75) | ||||
---|---|---|---|---|---|---|

Performance Score | Normalized Performance Score | Performance Score | Normalized Performance Score | Final Score ${\mathit{F}}_{\mathit{x}}$ | Final Rank | |

Solution 1 | 94 | 0.00 | 7752 | 1 | 4.00 | 1 |

Solution 2 | 100 | 1.00 | 7669 | 0 | 4.00 | 1 |

Solution 3 | 97 | 0.50 | 7748 | 0.95 | 2.76 | 3 |

Solution 4 | 100 | 1.00 | 7699 | 0.36 | 2.94 | 4 |

Solution 5 | 99 | 0.83 | 7704 | 0.42 | 3.20 | 2 |

Solution 6 | 99 | 0.83 | 7739 | 0.84 | 2.40 | 5 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chaturvedi, S.; Rajasekar, E.; Natarajan, S.
Multi-objective Building Design Optimization under Operational Uncertainties Using the NSGA II Algorithm. *Buildings* **2020**, *10*, 88.
https://doi.org/10.3390/buildings10050088

**AMA Style**

Chaturvedi S, Rajasekar E, Natarajan S.
Multi-objective Building Design Optimization under Operational Uncertainties Using the NSGA II Algorithm. *Buildings*. 2020; 10(5):88.
https://doi.org/10.3390/buildings10050088

**Chicago/Turabian Style**

Chaturvedi, Shobhit, Elangovan Rajasekar, and Sukumar Natarajan.
2020. "Multi-objective Building Design Optimization under Operational Uncertainties Using the NSGA II Algorithm" *Buildings* 10, no. 5: 88.
https://doi.org/10.3390/buildings10050088