A Novel Column Generation Heuristic for Airline Crew Pairing Optimization with Large-scale Complex Flight Networks

arXiv (Cornell University)

Abstract

Crew Pairing Optimization (CPO) is critical for an airlines' business viability, given that the crew operating cost is second only to the fuel cost. CPO aims at generating a set of flight sequences (crew pairings) to cover all scheduled flights, at minimum cost, while satisfying several legality constraints. The state-of-the-art heavily relies on relaxing the underlying Integer Programming Problem into a Linear Programming Problem, which in turn is solved through the Column Generation (CG) technique. However, with the alarmingly expanding airlines' operations, CPO is marred by the curse of dimensionality, rendering the exact CG-implementations obsolete, and necessitating the heuristic-based CG-implementations. Yet, in literature, the much prevalent large-scale complex flight networks involving multiple { crew bases and/or hub-and-spoke sub-networks, largely remain uninvestigated. This paper proposes a novel CG heuristic, which has enabled the in-house development of an Airline Crew Pairing Optimizer (AirCROP). The efficacy of the heuristic/AirCROP has been tested on real-world, large-scale, complex network instances with over 4,200 flights, 15 crew bases, and multiple hub-and-spoke sub-networks (resulting in billion-plus possible pairings). Notably, this paper has a dedicated focus on the proposed CG heuristic (not the entire AirCROP framework) based on balancing random exploration of pairings; exploitation of domain knowledge (on optimal solution features); and utilization of the past computational & search effort through archiving. Though this paper has an airline context, the proposed CG heuristic may find wider applications across different domains, by serving as a template on how to utilize domain knowledge to better tackle combinatorial optimization problems.

Authors 4

1. Divyam Aggarwal

   Indian Institute of Technology Roorkee

   Affiliation as printed

   Department of Mechanical & Industrial Engineering (MIED) , Indian Institute of Technology Roorkee , Roorkee , Uttarakhand - 247667 , India

2. Dhish Kumar Saxena

   Indian Institute of Technology Roorkee

   Affiliation as printed

   East Block , MIED , IIT Roorkee , Roorkee , Uttarakhand - 247667 , India;

3. Thomas Bäck Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science (LIACS) , Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , the Nether- lands

4. Michael Emmerich Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science (LIACS) , Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , the Nether- lands