AirCROP: Airline Crew Pairing Optimizer for Complex Flight Networks Involving Multiple Crew Bases Billion-Plus Variables

03/09/2020 ∙ by Divyam Aggarwal, et al. ∙ universiteit leiden IIT Roorkee 0

Airline scheduling poses some of the most challenging problems in the entire Operations Research (OR) domain. In that, crew scheduling (CS) constitutes one of the most important and challenging planning activities. Notably, the crew operating cost is the second-largest component of an airline's total operating cost (after the fuel cost). Hence, its optimization promises enormous benefits, and even marginal improvements may translate to annual savings worth millions of dollars for an airline. However, CS is a combination of complex combinatorial optimization problems (with NP-hard computational complexity), namely crew pairing and crew assignment, which are solved sequentially. Here, crew pairing optimization aims at generating a set of flight sequences (each called a crew pairing) to cover a finite set of flight legs from an airline's timetable at minimum cost, while satisfying several legality constraints linked to the federations' safety rules, airline-specific regulations, labor laws, etc. Subsequently, crew assignment aims at assigning crew members to these optimal crew pairings. This research focuses on the critically fundamental step of CS, in that, a crew pairing optimization problem (CPOP) is formulated, and an optimization framework to solve the posed CPOP has been proposed. The distinctive contribution of this research relates to its tackling of a large-scale complex flight network for an airline (leading to more than a billion legal pairings/variables), and validation of the results by the research consortium's Industrial partner, GE Aviation.

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1 Airline Crew Pairing Optimization: Its challenges

Airline scheduling poses some of the most challenging problems in the entire Operations Research (OR) domain. In that, crew scheduling (CS) constitutes one of the most important and challenging planning activities. Notably, the crew operating cost is the second-largest component of an airline’s total operating cost (after the fuel cost). Hence, its optimization promises enormous benefits, and even marginal improvements may translate to annual savings worth millions of dollars for an airline. However, CS is a combination of complex combinatorial optimization problems (with NP-hard computational complexity), namely crew pairing and crew assignment, which are solved sequentially. Here, crew pairing optimization aims at generating a set of flight sequences (each called a crew pairing) to cover a finite set of flight legs from an airline’s timetable at minimum cost, while satisfying several legality constraints linked to the federations’ safety rules, airline-specific regulations, labor laws, etc. Subsequently, crew assignment aims at assigning crew members to these optimal crew pairings. This research focuses on the critically fundamental step of CS, in that, a crew pairing optimization problem (CPOP) is formulated, and an optimization framework to solve the posed CPOP has been proposed. The distinctive contribution of this research relates to its tackling of a large-scale complex flight network for an airline (leading to more than a billion legal pairings/variables), and validation of the results by the research consortium’s Industrial partner, GE Aviation.

2 Related Work

This research assumes significance owing to the unprecedented scale and complexity of the underlying problem. Notably, airline CPOP has received significant attention from the OR society, resulting which numerous optimization frameworks have been developed, and either published or commercialized as black-box software. The available literature could be categorized in terms of small-scale and large scale CPOPs. In the former case, where enumeration of all legal pairings is computationally viable, the most widely adopted optimization class of techniques are Genetic Algorithms

(GA) which which are population-based randomized search heuristics [

1, 2, 3, 4]. However, these GA-based approaches become obsolete when tested for large-scale CPOPs [2, 4]. In the latter case, where enumeration of all legal pairings is computationally challenging, Column Generation (CG) is the most widely adopted technique, since it allows for guided exploration of search space based on the corresponding gain in the objective function(s). In that, only the pairings promising objective improvement are generated. However, as the scale of the problem grows, the exact CG implementation becomes intractable. This justifies the heuristic implementations of CG for medium and large-scale CPOPs [5, 6]. Despite this progress, the much prevalent complex flight networks, incorporating multiple hub-and-spoke subnetworks and/or multiple crew bases, largely remain unaddressed. In that, the number of potential crew pairings (optimization variables) grow exponentially with the number of flights on account of not only its departure from a point-to-point network; multiplicity of hubs as opposed to a single hub; but also the multiplicity of crew bases. Hence, the practical utility of the existing solutions is limited, and all the more questionable considering that air traffic is expected to grow double in 20 years with a 3.5% compound annual growth rate [7].

3 Proposed Optimization Framework

The merit of this work lies in its attempt to overcome the existent research/utility gap by way of its addressal of a complex flight network through a customizable optimization framework, named as , tested and validated on real-world data, endorsing its higher technology readiness levels (TRL 8-9: System Test, Launch & Operations [8]). The research consortium’s Industrial sponsor, GE Aviation, has provided this real-world data set (from the US airlines’ flight network) for the testing and validation of the

. It is structured around the integration of deterministic optimization methodologies and airline-domain-knowledge-based heuristics. It is usable for optimizing airlines’ crew pairing costs, even for their large and complex flight networks (characterized by the presence of multiple hub-and-spoke subnetworks and/or multiple crew bases). It leverages the recent advancements in mathematical programming techniques (particularly, Column Generation, CG, and Mixed-Integer Linear Programming, MILP) along with enhanced data-handling capabilities and computational speeds. Furthermore, it is open to modifications, a freedom not generally available with commercial software. In doing so, it offers an opportunity for airlines to adapt and improvise the existing modules based on their domain knowledge or demand-base. Its higher-level block diagram is presented in figure 1.

Figure 1: Higher-level block diagram of

accepts a finite set of an airline’s flight schedule, its pairing-costing rules and pairing-legality constraints as input; and outputs a set of legal pairings, covering the given set of flights at minimal cost. As shown in figure 1, the proposed framework is based on multiple modules which are elaborated here. The novelty of AirCROP lies not just in the design of its building modules, namely Legal Crew Pairing Generation, Initial Feasible Solution Generation, and Optimization Engine; but critically in how these modules interact. In that:

  1. Legal Crew Pairing Generation [9]:

    • Enumeration of all possible legal crew pairings from a given set of flights while satisfying a given set of pairing-legality constraints

    • Efficient constraint-satisfaction methodology by prioritizing the order in which a given set of pairing-legality constraints have to be satisfied

    • Time-efficient execution of this module using parallelization on multiple cores of a single processor, exploiting the multiple crew base characteristic of the input flight data set

  2. Initial Feasible Solution Generation [10]:

    • Developed a computationally- and time-efficient initialization heuristic to generate an Initial Feasible Solution (IFS; a manageable set of legal pairings covering all given flights) for large-scale CPOPs

    • Utilizes a divide-and-cover strategy to decompose the given flight schedule into smaller flight subsets, and an Integer Programming (IP) technique to select pairings, constituting a minimal-cost solution for each decomposed flight subset

    • It is ensured that the generated IFS has a balance between its characteristics, namely cost and degrees of search-freedom, such that it favors an exploratory search in the subsequent module, Optimization Engine.

    • Generated IFS serves as input to the subsequent module, Optimization Engine.

  3. Optimization Engine:
    It involves recombination of input pairing set with new pairings promising lower-cost solution with full-flight coverage. It is implemented using the following submodules:

    1. Submodule I- Optimization in continuous domain:

      • Developed an iterative optimization approach to search for a full-coverage, lower-cost, linearly-relaxed solution (fractions of pairings are used to make up the full-coverage solution) which utilizes existing/novel OR techniques in a computationally- and time-efficient manner

      • In each of its iterations, need-base new legal pairings are generated using a domain-specific novel CG heuristic which attempts to maintain a balance between exploration (new pairings being generated from randomly-selected flights) and exploitation (new pairings being generated using domain-knowledge and flight-connection information of the previous iteration’s solution).

      • In addition to this, another CG strategy has been implemented which has improved the performance of drastically. In that:

        • An archive dictionary is being maintained in which legal pairings being generated in each iteration of Submodule I are updated (items of this dictionary are unique flight-pairs)

        • In each iteration of Submodule I, a set of critical flight-pairs are identified (using the iteration’s dual solution) and for each of these selected flight-pairs, a finite number of pairings are selected randomly from the archived dictionary. These pairings are added back to the LP-solution of the iteration.

    2. Submodule II- Optimization in integer domain:
      A full-coverage, lower-cost integer solution (full pairings are used to make up the full-coverage solution) is ensured through repetitive interactions between MILP technique (using available solvers) and Submodule I. Each of these interactions are referred to as a Re-optimization Loop.

Acknowledgments

This research is an outcome of an Indo-Dutch joint research project, supported by the Ministry of Electronics & Information Technology (MEITY), India [grant 13(4)/2015-CC&BT]; Netherlands Scientific Research Organization (NWO), Netherlands; and General Electric (GE) Aviation. The authors would like to thank GE Aviation team members: Saaju Paulose (Senior Manager), Arioli Arumugam (Senior Director- Data & Analytics), and Alla Rajesh (Senior Staff Data & Analytics Scientist) for their invaluable support in successfully completing this research work.

References

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  2. Zeren, B. & Özkol, İ. (2012) An improved genetic algorithm for crew pairing optimization. Journal of Intelligent Learning Systems and Applications 4, 70.

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    Computers & Industrial Engineering 115, 389–406.

  4. Aggarwal, D., Saxena, D.K., Bäck, T. & Emmerich, M. (July, 2019) Real-World Airline Crew Pairing Optimization: Customized Genetic Algorithm versus Column Generation Method. EADAL Report Number 2019001.

  5. Vance, P.H., Barnhart, C., Gelman, E., Johnson, E.L., Krishna, A., Mahidhara, D., Nemhauser, G.L. & Rebello, R. (1997) A heuristic branch-and-price approach for the airline crew pairing problem. Technical Report LEC-97-06, Georgia Institute of Technology, Atlanta.

  6. Zeren, B. & Özkol, İ. (2016) A novel column generation strategy for large scale airline crew pairing problems. Expert Systems with Applications 55, 133–144.

  7. Marisa, G. (Oct., 2018) Air Travel Projected To Double In 20 Years, But Protectionism Poses Threat. Forbes, URL [Online, accessed 8 March, 2020].

  8. Mihaly, H. (2017) From NASA to EU: the evolution of the TRL scale in Public Sector Innovation. The Innovation Journal, 22: 1–23, archived from the original (PDF) on October 11, 2017, URL.

  9. Aggarwal, D., Saxena, D.K., Emmerich, M. & Paulose, S. (2018) On large-scale airline crew pairing generation. In 2018 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 593–600.

  10. Aggarwal, D., Saxena, D.K., Bäck, T. & Emmerich, M. (2019) Customized Initialization for Large-Scale Airline Crew Pairing Optimization Problems. Abstract presented at 2nd National Conference on Multidisciplinary Design, Analysis, and Optimization (NCMDAO) held in Bengaluru, India in March 2019.