Crew Pairing Optimization aims at generating a set of flight sequences (crew pairings), covering all flights in an airline's flight schedule, at minimum cost, while satisfying several legality constraints. CPO is critically important for airlines' business viability, considering that the crew operating cost is their second-largest expense. It poses an NP-hard combinatorial optimization problem, to tackle which, the state-of-the-art relies on relaxing the underlying Integer Programming Problem (IPP) into a Linear Programming Problem (LPP), solving the latter through Column Generation (CG) technique, and integerization of the resulting LPP solution. However, with the growing scale and complexity of the flight networks (those with a large number of flights, multiple crew bases and/or multiple hub-and-spoke subnetworks), the utility of the conventional CG-practices has become questionable. This paper proposed an Airline Crew Pairing Optimization Framework, AirCROP, whose constitutive modules include the Legal Crew Pairing Generator, Initial Feasible Solution Generator, and an Optimization Engine built on heuristic-based CG-implementation. In this paper, besides the design of AirCROP's modules, insights into important questions related to how these modules interact, which the literature is otherwise silent on, have been shared. These relate to the sensitivity of AirCROP's performance towards: sources of variability over multiple runs for a given problem, initialization method, and termination parameters for LPP-solutioning and IPP-solutioning. The efficacy of the AirCROP has been demonstrated on real-world large-scale and complex flight networks (with over 4200 flights, 15 crew bases, and billion-plus pairings). It is hoped that with the emergence of such complex flight networks, this paper shall serve as an important milestone for affiliated research and applications.

中文翻译：

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具有多个机组基地和轴辐式子网的大型网络的航空公司机组配对优化框架

机组配对优化旨在生成一组航班序列（机组配对），以最低成本覆盖航空公司航班时刻表中的所有航班，同时满足若干合法性约束。考虑到机组人员运营成本是航空公司的第二大开支，CPO 对航空公司的业务生存能力至关重要。它提出了一个 NP-hard 组合优化问题，为了解决这个问题，最先进的技术依赖于将底层整数规划问题 (IPP) 放松为线性规划问题 (LPP)，通过列生成 (CG ) 技术，以及所得 LPP 解决方案的整数化。然而，随着飞行网络（具有大量航班、多个机组人员基地和/或多个中心辐射子网的网络）规模和复杂性不断增加，传统的 CG 实践的效用已经成为问题。本文提出了一种航空公司机组配对优化框架AirCROP，其构成模块包括合法机组配对生成器、初始可行解决方案生成器和基于启发式CG实现的优化引擎。在本文中，除了 AirCROP 模块的设计之外，还分享了对与这些模块如何交互相关的重要问题的见解，否则文献没有提及这些问题。这些与 AirCROP 性能对以下方面的敏感性有关：针对给定问题的多次运行的可变性来源、初始化方法以及 LPP 求解和 IPP 求解的终止参数。AirCROP 的功效已在现实世界的大规模复杂飞行网络（拥有 4200 多个航班、15 个机组人员和十亿多个配对）中得到证明。希望随着如此复杂的飞行网络的出现，本文将成为相关研究和应用的重要里程碑。