# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 4 Algorithm  
The objective of airport slot optimization for a multi-airport system is to determine the optimal airport slot allocation scheme by building a multiple-objective optimization model to minimize slot deviations with optimal fairness and aeronautical fairness of airports in the multi-airport system under airspace capacity coupling. In this study, the NSGA-II algorithm (Non-dominated Sorting Genetic Algorithm II) is used to solve the model. The algorithm process is shown in Algorithm 1. Non-dominated sorting is a mechanism that partitions solutions within a population into distinct hierarchical levels (termed fronts) based on their mutual dominance relations. The Pareto front comprises the set of solutions that are not dominated by any other solution, representing the optimal trade-off solutions attainable for a multi-objective optimization problem [22]. The NSGA-II algorithm efficiently approximates the Pareto-optimal solution set for multi-objective problems by employing non-dominated sorting to stratify and select high-quality solutions (progressing towards the Pareto front) and utilizing crowding distance to maintain diversity within the solution set. ``` Input: The population size, the maximal generation number, the dataset Output: Non-dominated solution set of slot displacement, airport fairness, airline fairness \(



Beijing's multi-airport system comprises three Level 3 airports (airports where capacity providers have not developed sufficient infrastructure, or where governments have imposed conditions that make it impossible to meet demand [1]), 19 approach control sectors, and 17 corridors. Within this structure, 11 approach control sectors manage traffic for more than one airport. The terminal area handles over 3000 flights daily, making it a congested terminal area featuring highly shared airspace with coupled airspace units. In the southwestern and eastern portions of the terminal area, in particular, air traffic controllers rely heavily on radar vectoring during actual operations to mitigate potential conflicts. Moreover, unscientific historical flight schedule planning has resulted in significant temporal imbalances between capacity and traffic demand within the current operation. These imbalances further propagate flight delays. Therefore, there is a pressing need to optimize the temporal and spatial distributions and to allocate resources effectively for the shared corridors and coupled sectors within this terminal area. This study utilizes operational data from a representative day in the schedule of each airport in the 2023 summer and autumn seasons. The capacity parameters are the schedule coordination parameters, corridor capacity, and minimum transit time published by the Civil Aviation Administration of China. The maximum acceptable slot deviation for airlines is 30 min. ### Scene Setting

Taking the multi-airport system airport slot as the main data, and based on the existing model, three experimental scenarios were formulated for system analysis. It should be noted that scenario 1 does not involve solving the equation and only serves as a benchmark for simulation verification. **Scenario 1 (Baseline):**: _No optimization is applied; the original timetable is used as a reference._

Figure 4: Structure of Beijing’s multi-airport system. (The red box represents the airport name, and the green circle represents the corridor entrance name. The dark green sectors are shared by multiple airports. The light green sectors are used by each airport for takeoff or landing). **Scenario 2 (Single-airport task):**: _The base timetable of each of the three airports is optimized using a single-airport optimization model with the objective of minimizing slot deviation.