Large-scale flight frequency optimization with global convergence in the US domestic air passenger markets

The US domestic air passenger transportation is one of the largest markets worldwide. Optimally allocating flights to the US domestic airways (i.e., air routes) is essential in maximizing the revenue of airlines and many research works have been proposed to improve their market shares/profits. Most proposed methods, however, suffer from a lack of scalability; even state-of-the-art methods demonstrate their performance with only tens of routes. To address this shortcoming, we propose a novel unified framework to integrate the market share prediction model and the frequency optimization module, which significantly improves the scalability of the entire framework. By design, our proposed prediction model is concave w.r.t. flight frequency and its gradients are Lipschitz continuous. Exploiting these two properties allows us to use an alternating direction method of multipliers (ADMM)-based optimization technique, which quickly solves a large-scale frequency optimization problem with guaranteed global convergence. Our proposed method is able to solve a problem whose search space size is O(n⁷⁰⁰) (vs. O(n³⁰) in existing works).