# Multi-Objective 3D Airspace Sectorization Problem Using NSGA-II with Prior Knowledge and External Archive

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## Abstract

**:**

## 1. Introduction

- (1)
- Under the realistic constraints of operation and safety, a multi-objective framework is proposed to optimize 3D airspace sectorization in terms of intra-sector workload balance and the minimum total inter-sector workload.
- (2)
- To improve solution diversity and model efficiency, an initial population strategy with prior knowledge and an external archive mechanism are introduced into NSGA-II.
- (3)
- An in-depth experimental analysis of actual operational data in the Singapore regional airspace is carried out from qualitative and quantitative perspectives, and the effectiveness of the airspace sectorization scheme is confirmed.

## 2. Related Works

## 3. Multi-Objective Framework for 3D Airspace Sectorization

#### 3.1. Flight Clustering as Prior Knowledge

#### 3.2. Sector Generation Based on Voronoi Diagrams

#### 3.3. Workloads Evaluation Using Dynamic Density

#### 3.4. Sector Optimization Based on NSGA-II with Advanced Strategy and Mechanism

#### 3.4.1. Problem Definitions: Objectives and Constraints

#### 3.4.2. Algorithm Designs: NSGA-II with Prior Knowledge and External Archive

## 4. Empirical Analysis: A Case Study of Singapore Regional Airspace

#### 4.1. Experimental Setup

#### 4.1.1. Data Preparation

#### 4.1.2. Implementation Details

#### 4.2. Results and Discussions

#### 4.2.1. Analysis of the Pareto Front

#### 4.2.2. Performance Comparison of Different Algorithms

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Fuzzy clustering results of flight position data at 11:30 UTC on 1 December 2019 (Singapore regional airspace).

**Figure 8.**Airspace sectorization results for area one (i.e., solutions of [0.128, 44], [0.082, 45], and [0.064, 46] in Run 1). (

**a**) Results in 3D view; (

**b**) results in 2D view; (

**c**) intra-sector and inter-sector workloads for each solution.

**Figure 9.**Airspace sectorization results for area two (i.e., solutions of [0.0034, 56], [0.0032, 57], and [0.0019, 58] in Runs 1, 5, and 3, respectively). (

**a**) Results in 3D view; (

**b**) results in 2D view; (

**c**) intra-sector and inter-sector workloads for each solution.

Factors of Dynamic Density | |||||||||
---|---|---|---|---|---|---|---|---|---|

HC | SC | AC | MD5 | MD10 | CP25 | CP40 | CP70 | TD | |

Weight | 2.40 | 2.45 | 2.94 | 2.45 | 1.83 | 4.00 | 3.00 | 2.11 | 1.00 |

Methods | Evaluation Indicators | ||
---|---|---|---|

NS | SP | HV | |

NSGA-II | 11 | 0.12 | 0.51 |

NSGA-II-ea | 27 | 0.06 | 0.52 |

NSGA-II-pk | 11 | 0.09 | 0.59 |

Proposed method | 27 | 0.06 | 0.61 |

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**MDPI and ACS Style**

Zhang, W.; Hu, M.; Yin, J.; Li, H.; Du, J.
Multi-Objective 3D Airspace Sectorization Problem Using NSGA-II with Prior Knowledge and External Archive. *Aerospace* **2023**, *10*, 216.
https://doi.org/10.3390/aerospace10030216

**AMA Style**

Zhang W, Hu M, Yin J, Li H, Du J.
Multi-Objective 3D Airspace Sectorization Problem Using NSGA-II with Prior Knowledge and External Archive. *Aerospace*. 2023; 10(3):216.
https://doi.org/10.3390/aerospace10030216

**Chicago/Turabian Style**

Zhang, Weining, Minghua Hu, Jianan Yin, Haobin Li, and Jinghan Du.
2023. "Multi-Objective 3D Airspace Sectorization Problem Using NSGA-II with Prior Knowledge and External Archive" *Aerospace* 10, no. 3: 216.
https://doi.org/10.3390/aerospace10030216