On Learning Combinatorial Patterns to Assist Large-Scale Airline Crew Pairing Optimization

Divyam Aggarwal, Yash Kumar Singh, Dhish Kumar Saxena

Airline Crew Pairing Optimization (CPO) aims at generating a set of \textit{legal flight sequences} (\textit{crew pairings}), to cover an airline's flight schedule, at minimum cost. It is usually performed using \textit{Column Generation} (CG), a mathematical programming technique for guided search-space exploration. CG exploits the interdependencies between the current and the preceding CG-iteration for generating new variables (pairings) during the optimization-search. However, with the unprecedented scale and complexity of the emergent flight networks, it has become imperative to \textit{learn} higher-order interdependencies among the flight-connection graphs, and utilize those to enhance the efficacy of the CPO. In first of its kind and what marks a significant departure from the state-of-the-art, this paper proposes a novel adaptation of the Variational Graph Auto-Encoder for \textit{learning} plausible combinatorial patterns among the flight-connection data obtained through the search-space exploration by an Airline Crew Pairing Optimizer, \textit{AirCROP} (developed by the authors and validated by the research consortium's industrial sponsor, \textit{GE Aviation}). The resulting flight-connection predictions are combined \textit{on-the-fly} using a novel heuristic to generate new pairings for the optimizer. The utility of the proposed approach is demonstrated on large-scale (over 4200 flights), real-world, \textit{complex} flight-networks of US-based airlines, characterized by multiple hub-and-spoke subnetworks and several crew bases.

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