### G-2020-13

# Machine learning in airline crew pairing to construct initial clusters for dynamic constraint aggregation

## Yassine Yaakoubi, François Soumis, and Simon Lacoste-Julien

The crew pairing problem is generally modelled as a set partitioning problem where the flights have to be partitioned in pairings. A pairing is a sequence of flight legs separated by connection-time and rest-periods that starts and ends at the same base. This problem becomes difficult to solve when the number of flights increases because the number of feasible pairings (number of variables) grows exponentially. This paper introduces a new paradigm for solving this large combinatorial problem: "Machine Learning `\(\rightarrow\)`

Mathematical Programming". This paradigm uses Machine Learning to learn from solutions of similar instances to produce predictions on some parts of the solution of the new instance. This information feeds the Mathematical Programming optimizer that connects these parts of the solution by modifying them as needed, taking account of the exact cost function and the complex constraints. We show that the clusters produced by ML-based heuristics are better suited for crew pairing problems, resulting in an average reduction of solution cost between 6.8% and 8.52% and cost of global constraints between 69.79% and 78.11%, when compared to pairings obtained with a standard initial solution.

Published **February 2020**
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23 pages