# Multi-Objective Optimisation of Urban Form: A Framework for Selecting the Optimal Solution

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Selection Strategy

#### 2.2. Selection Stage 1

#### 2.2.1. Clustering the Pareto Front

#### 2.2.2. Fittest Solutions (Outliers)

#### 2.2.3. Global Compromise

#### 2.2.4. Equal Fitness for All Functions

#### 2.3. Selection Stage 1

## 3. Case Study

#### 3.1. The Design Problem

#### 3.1.1. Elevating the Flow of the City

#### 3.1.2. Spatial Distribution of Public Space

#### 3.1.3. Ecology and Spatial Qualities of the City

#### 3.2. Experiment Setup

#### 3.2.1. Spatial Distribution of Public Space

#### 3.2.2. Fitness Functions

#### 3.2.3. Algorithm Settings

## 4. Results

#### 4.1. Algorithm Results

#### 4.2. Selection

#### 4.2.1. Selection Stage 1

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#### 4.2.2. Selection Stage 2

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Example of clustering solutions along the pareto front. The ‘representative’ solution is the closest one to the cluster centre (represented in the figure by ‘x’).

**Figure 4.**Example of the ‘global compromise’ solution. This solution is the closest (Euclidean) solution to the ‘Utopia’ solution.

**Figure 5.**Example of the solution with the most equal weights among the fitness ranks; i.e., the solution with the least trade-offs between fitness functions. This solution may not be located on the pareto front.

**Figure 8.**Step-by-step process for the phenotype’s construction; each step presents the chromosome applied and the morphological impact of its application.

**Figure 9.**The relationship between the fitness functions and chromosomes defining the design problem.

**Figure 10.**Fitness Function 1: Solar gain calculation on the different morphological characteristics of the superblock.

**Figure 11.**Fitness Function 2: Length and distribution of the spatial interventions throughout the superblock.

**Figure 12.**Fitness Function 3: Calculation of the volumetric mass of the spatial interventions throughout the superblock.

**Figure 13.**Fitness Function 4: Calculation of the volumetric mass of the larger towers, in this case the primary structural supports for the spatial interventions.

**Figure 14.**The results of the evolutionary algorithm. Each fitness function was analysed separately across four key metrics (from

**left**to

**right**): standard deviation, fitness values, standard deviation trendline, and mean value trendline.

**Figure 15.**The hierarchical clustering of the pareto front solutions with a K-value of 20, presented through the objective space and dendrogram. As the problem comprised of four fitness functions, it is difficult to read the cluster distribution in the objective space (which is 3-dimensional). In this case the dendrogram provides a clearer understanding of the relationship between solutions, both within and between clusters.

**Figure 17.**The fittest solution for each fitness function (outliers) alongside each solution’s respective diamond chart.

**Figure 18.**The ‘global compromise’ solution (solution closest to the ‘Utopia’ point) alongside its diamond chart.

**Figure 19.**The solution with equal weighting for all fitness functions. Although this solution minimises trade-offs between fitness functions, its performance is significantly poor when compared to the other selected solutions.

**Figure 20.**The results of each solution and its applied phenotypic indicator. The solutions above a specific threshold are highlighted as the top-performing solutions.

**Figure 21.**The phenotypes of the selected three solutions from Figure 20.

Simulation Size | Algorithm Settings | ||
---|---|---|---|

Generation Size | 50 | Mutation Rate | 1/n (n = no. of var.) |

Generation Count | 100 | Crossover Probability | 0.9 |

Population Size | 5000 | Mutation Distribution Index | 20 |

No. of Chromosome | 13 | Crossover Distribution Index | 20 |

No. of Variables | 88,445 | Runtime | 17:46:48 |

**Table 2.**Each solution carried forward from the first stage of selection was evaluated according to the phenotypic indicators and weights listed below.

Phenotypic Indicator | Vector Direction | Weighting |
---|---|---|

Urban FSI (w/o morphological interventions) | Positive | 0.25 |

Urban FSI (w/morphological interventions) | Positive | 0.5 |

Surface to volume ratio (w/o morphological interventions) | Positive | 0.25 |

Surface to volume ratio (w/morphological interventions) | Positive | 0.5 |

Surface Coverage Ratio | Target: 35% | 0.25 |

Average Height | Target: 20 Floors | 0.25 |

Open Space Ratio | Target: 60% | 0.5 |

Mid-Level Private Spatial Units Volume | Positive | 0.25 |

Mid-Level Semi-Private Spatial Units Volume | Positive | 0.25 |

Mid-Level Walking Length | Positive | 0.25 |

High Level Private Spatial Units Volume | Positive | 0.25 |

High Level Semi-Private Spatial Units Volume | Positive | 0.25 |

High Level Walking Length | Positive | 0.25 |

Urban Access | Negative | 0.75 |

Local Open Space | Positive | 1.00 |

Low-rise Building Volume | Positive | 0.25 |

High-rise Building Volume | Negative | 0.25 |

Length of Skyways | Positive | 0.75 |

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Showkatbakhsh, M.; Makki, M. Multi-Objective Optimisation of Urban Form: A Framework for Selecting the Optimal Solution. *Buildings* **2022**, *12*, 1473.
https://doi.org/10.3390/buildings12091473

**AMA Style**

Showkatbakhsh M, Makki M. Multi-Objective Optimisation of Urban Form: A Framework for Selecting the Optimal Solution. *Buildings*. 2022; 12(9):1473.
https://doi.org/10.3390/buildings12091473

**Chicago/Turabian Style**

Showkatbakhsh, Milad, and Mohammed Makki. 2022. "Multi-Objective Optimisation of Urban Form: A Framework for Selecting the Optimal Solution" *Buildings* 12, no. 9: 1473.
https://doi.org/10.3390/buildings12091473