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Optimization of a simplified Fleet Assignment Problem with metaheuristics: Simulated Annealing and GRASP

  • Danuta Sosnowska
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 42)

Abstract

The Fleet Assignment Problem consists of assigning aircrafts to flights, taking into consideration operational constraints of the airline company. This paper presents heuristics based on simulated annealing and GRASP for solving a simplified version of the Fleet Assignment Problem. The application of heuristics is essential as the space of feasible solutions grows exponentially with the size of the fleet and the number of flights. It allows to quickly find near-optimal results, by exploring only small part of the space of solutions.

A sequence of flight legs assigned to an aircraft is called a rotation cycle. Both methods presented are based on the operation of swapping parts of rotation cycles between two randomly selected aircrafts.

In simulated annealing the exchange is directed by a so called cooling schedule converging to 0 in either an exponential, logarithmic or asymptotic rate, while the number of iterations grows. A solution which gives a better cost is always accepted, other solutions are accepted only with some probability depending on the cooling schedule.

In GRASP, only exchanges leading to a better result are permitted and every fixed number of swaps the solution is rearranged, i.e. the potentially best part of the assignment is conserved and the rest is reattributed randomly.

The problem is tested on real data of a medium size airline company (about 20 aircrafts and 3000 flights), for a period of one month. The experimental results show that simulated annealing gives solutions with slightly lower cost than the GRASP algorithm.

Keywords

GRASP simulated annealing fleet assignment. 

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References

  1. [1]
    Jeph Abara. (1989), “Applying integer linear programming to the fleet assignment problem”, Interfaces, vol. 19, pp 20–28.CrossRefGoogle Scholar
  2. [2]
    Abdullah A. Al-Haimy. (1984) “Development of a Mathematical Model for Airline Fleet Planning”, Proceedings of the XXIV AGIFORS Symposium.Google Scholar
  3. [3]
    Zonghao Gu, Ellis Johnson, George Nemhauser and Yinhua Wang. (1994) “Some properties of the fleet assignment problem”, Operations Research Letters, vol. 15, pp 59–71.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    R. Subramanian et al. (1994) “Coldstart: Fleet Assignement at Delta Airlines”, Interfaces, vol. 24, no 1, pp 104–120.CrossRefGoogle Scholar
  5. [5]
    Lloyd Clarke, Ellis Johnson, George Nemhauser and Zhongxi Zhu. (1995) “The Aircraft Rotation Problem”Google Scholar
  6. [6]
    Thomas A. Feo, Mauricio G.C. Resende. (1995) “Greedy Randomized Adaptive Search Procedures”, Journal of Global Optimization, vol 6, pp 109–133.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Hani El Sakkout. (1996) “Modelling and Solving Fleet Assignment in a Flexible Environment”, Proceedings of the Second International Conference on the Practical Application of Constraint Technology (PACT 96), pp 27–39.Google Scholar
  8. [8]
    Cynthia Barnhart et al. (1997) “Flight String Models for Aircraft Fleeting and Routing”, Proceedings of the AGIFORS Symposium.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Danuta Sosnowska
    • 1
  1. 1.CUIGeneva UniversityGenève 4Switzerland

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