# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 1 Introduction  
With the rapid development of the aviation industry and the development strategy of regional economic integration, heightened requirements have emerged regarding the operational efficiency and optimization of regional aviation networks. Single-airport operation resources are limited and often face the phenomenon of limited airport slot resources, leading to supply and demand imbalances. A multi-airport system consists of geographically close airports. Optimizing airport slots from this system perspective allows for the sharing of terminal airspace resources. These resources include airspace capacity assets such as departure/arrival fixtures. This approach maximizes airspace capacity use and reduces underutilization. It also diverts airport slots between system airports to improve operational efficiency, consequently enhancing the quality of air transportation services. This study focuses on the concept of multi-airport systems. Currently, interactions among airports in these systems increase congestion and delays. Such a system can be configured through airport slot optimization. This approach enhances the interactionsbetween airports and optimizes shared resources. It also decouples resources to reduce flight delays and prevent potential air traffic congestion. A significant discrepancy persists between theoretical research on flight slot allocation and operational practices in the international aviation domain. China, the United States, and Europe predominantly adopt the airport slot guidelines published by the International Air Transport Association as their operational standard [1; 2]. Their methodologies largely focus on individual airport capacity parameters (i.e., slot coordination parameters), neglecting to address the issue from a multi-airport systems perspective that incorporates crucial factors such as interconnected capacity coupling and shared airspace constraints [3]. While pioneering initiatives exist in theoretical frameworks, demonstrating sound conceptual approaches, they have yet to yield substantial contributions concerning the optimization of coupled capacity within multi-airport systems or the enhancement of broader air route network efficiency. The integrated economic situation has evolved rapidly in the last decade. For this reason, researchers have argued that airport slot deviation at a single airport is affected by the regional economy and neighboring airports. Additionally, more studies have focused on analysis and optimization from a multi-airport system perspective. Researchers believe that capacity is an important basis for the optimization and deviation of multi-airport system airport slots--which is the core focus of this study--and most studies consider the demand and restrictions based on the announced capacity as a definite value [4]. On this basis, centering on the capacity research dimension, some studies consider the demand and constraints from the flight transit time [5], the time interval before and after flights [6], the arrival/departure capacity constraints, and the traffic flow constraints [7]. Airport slot optimization involves a large number of research objectives. It also involves a large number of influencing factors. Due to this complexity, model development for multi-airport systems presents heightened complexity. Therefore, some studies have explored the establishment of algorithmic solutions for such models. Multi-airport system airport slot optimization models generally rely on integer linear programming [8; 9] while for the more complex model structure of multi-airport systems, most researchers have relied on heuristic algorithms [10], nondominated sequential genetic algorithms [11], asymptotic binary heuristic methods [12], simulated annealing algorithm [13], k-means clustering algorithm [12], and multi-objective particle swarm algorithm [14].