# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 1 Introduction
This study focuses on nine types of constraints, including coupling capacity, congestion fairness of airports, and uncertainty of capacity-flow matching, to comprehensively analyze and optimize the allocation of airport slots in a multi-airport system. This study investigates the airport slot co-optimization problem for multi-airport systems, incorporating China's civil aviation slot management rules. Based on the coupled impact of airspace capacity, a capacity model is developed while interpreting the characteristics of China's 24 h slot coordination. Focusing on slot deviations, a multi-objective slot optimization model is established, incorporating factors such as system-wide fairness and the levels of congestion contributed by airlines. Finally, using actual flight data, the model is solved using the NSGA-II algorithm. Its efficiency is validated through comparison with a single-airport optimization model, and the superiority of its results is verified using the AirTOP (V2.3.29B54) simulation software. This provides a theoretical and technological support foundation for promoting the construction and coordinated operation of multi-airport systems. This study makes three major contributions to the research field:  
(1) By introducing the probabilistic competitiveness of shared resources, it embodies capacity operation coupling among multiple airports within the multi-airport system and realizes the decoupling of the multi-airport system's spatial-temporal resources. In this study, we optimize the capacity use of the airport itself by fully considering airport slot uncertainty and imposing corridor mouth constraints. The airport coupling relationship is mainly embodied in the multi-airport capacity constraint relationship, describing the constraints and interrelationships relating to each airport's capacity, airport group capacity, corridor port capacity, and airport parking position group capacity, etc., in order to study the synergistic optimization of airport slots. (2) It considers the fairness of airport slot optimization of the multi-airport system. This study stands at the level of the airport and airline operation and integrates the fairness of operation indices, allowing us to measure not only the number of slots of airline companies in the coordinated airports as a basis but also the fairness of airlines based on the contribution of flight congestion, combining the amount of slot deviation for each airport within the multi-airport system to assess the fairness of airports. (3) It includes flexible compatibility with China's 24 h slot coordination parameters and its slot firebreak. In China's airport slot management, 24 h coordination parameters are set for each airport, with slot firebreaks introduced at specific times to mitigate potential scheduled delays. In this study, based on the fixed slot firebreak, we further introduce a constraint on the capacity-flow ratio during a peak-valley cycle to accommodate the demand uncertainty. The subsequent sections of this paper are organized as follows. Section 2 delineates the characteristic parameters of the multi-airport system capacity, encompassing system-wide capacity metrics and 24 h slot coordination parameters. Section 3 presents the proposed slot co-optimization model for multi-airport systems, founded on airspace capacity coupling. Section 4 details the solution algorithm developed for this model. Section 5 details the model evaluation, first analyzing the results and subsequently performing empirical validation using the AirTOp simulation software. Finally, Section 6 concludes the key innovations of this research and discusses prospective directions for future applications.