Skip to main content
Log in

Bounding the optimum for the problem of scheduling the photographs of an Agile Earth Observing Satellite

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

The problem of managing an Agile Earth Observing Satellite consists of selecting and scheduling a subset of photographs among a set of candidate ones that satisfy imperative constraints and maximize a gain function. We propose a tabu search algorithm to solve this NP-hard problem. This one is formulated as a constrained optimization problem and involves stereoscopic and time window visibility constraints; and a convex evaluation function that increases its hardness. To obtain a wide-ranging and an efficient exploration of the search space, we sample it by consistent and saturated configurations. Our algorithm is also hybridized with a systematic search that uses partial enumerations. To increase the solution quality, we introduce and solve a secondary problem; the minimization of the sum of the transition durations between the acquisitions. Upper bounds are also calculated by a dynamic programming algorithm on a relaxed problem. The obtained results show the efficiency of our approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Benoist, T., Rottembourg, B.: Upper bounds of the maximal revenue of an Earth observation satellite. 4OR: Q. J. Oper. Res. 2(3), 235 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bensana, E., Agnèse, G.V.J., Bataille, N., Blumstein, D.: Exact and approximate methods for the daily management of an Earth observation satellite. In: Proceeding of the 4th International Symposium od Space Mission Operations and Ground Data Systems (spaceOps–96) (1996)

  3. Bensana, E., Lemaître, M., Verfaillie, G.: Earth observation satellite management. Constraints: Int. J. 4(3), 293–299 (1999)

    Article  MATH  Google Scholar 

  4. Cordeau, J., Laporte, G., Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows. J. Oper. Res. Soc. 59, 928–936 (2001)

    Article  Google Scholar 

  5. Desrochers, M., Desrosiers, J., Solomon, M.: A new optimization algorithm for the vehicle routing problem with time window. Oper. Res. 40, 342–354 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Desrochers, M., Soumis, F.: A generalized permanent labelling algorithm or the shortest path problem with time windows. INFOR 26, 191–212 (1988)

    MATH  Google Scholar 

  7. Fleurent, C., Ferland, J.A.: Genetic and hybrid algorithms for graph coloring. Ann. Oper. Res. 63, 437–461 (1996)

    Article  MATH  Google Scholar 

  8. Gabrel, V.: Improved linear programming bounds via column generation for daily scheduling of Earth observation satellite. Technical report, LIPN (1999)

  9. Gabrel, V., Moulet, A., Murat, C., Paschos, V.T.: A new model and derived algorithms for the satellite shot planning problem using graph theory concepts. Ann. Oper. Res. 69, 115–134 (1997)

    Article  MATH  Google Scholar 

  10. Glover, F., Laguna, M.: Tabu Search. Kluwer, Amsterdam (1997)

    MATH  Google Scholar 

  11. Hall, N., Magazine, M.: Maximizing the value of a space mission. Eur. J. Oper. Res. 78, 224–241 (1994)

    Article  MATH  Google Scholar 

  12. Harrison, S.A., Price, M.E.: Task scheduling for satellite based imagery. In Proceedings of the 18th Workshop of UK Planning and Scheduling Special Interest Group, pp. 64–78 (1999)

  13. Houck, D., Picard, J., Queyranne, M., Vemuganti, R.: The travelling salesman problem as a constrained shortest path problem: theory and computational experience. Oper. Res. 17(2–3), 93–109 (1980)

    MATH  MathSciNet  Google Scholar 

  14. Kohl, N., Madsen, O.B.G.: An optimization algorithm for the vehicle routing problem with time windows based on Lagrangean relaxation. Oper. Res. 45, 395–406 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lemaître, M., Verfaillie, G., Jouhaud, F., Lachiver, J.M., Bataille, N.: Selecting and scheduling observations of agile satellites. Aerosp. Sci. Technol. 6(5), 367–381 (2002)

    Article  Google Scholar 

  16. Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Comput. J. 44, 2245–2269 (1965)

    MATH  Google Scholar 

  17. ROADEF’2003 Challenge: Booklet of Abstracts. ROADEF society, France (2003)

  18. Schiex, T., Fargier, F., Verfaillie, G.: Valued constrained satisfaction problems: hard and easy problems. In Proceedings of IJCAI’95, 14th International Joint Conference on Artificial Intelligence pp. 631–639 (1995)

  19. Vasquez, M., Habet, D., Dupont, A.: Neighborhood design by consistency checking. In the Proceedings of the First International Workshop on Heuristics (IWH’02), vol. 4, pp. 19–27 (2002)

  20. Vasquez, M., Hao, J.K.: A logic-constrained knapsack formulation and a tabu algorithm for the daily photograph scheduling of an Earth observation satellite. J. Comput. Optim. Appl. 20(2), 137–157 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  21. Vasquez, M., Hao, J.K.: Upper bounds for the SPOT5 daily photograph scheduling problem. J. Comb. Optim. 7, 87–103 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wolf, W., Sorensen, S.: Three scheduling algorithms applied to the Earth observing systems domain. Manag. Sci. 46(1), 146–168 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Djamal Habet.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Habet, D., Vasquez, M. & Vimont, Y. Bounding the optimum for the problem of scheduling the photographs of an Agile Earth Observing Satellite. Comput Optim Appl 47, 307–333 (2010). https://doi.org/10.1007/s10589-008-9220-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-008-9220-7

Keywords

Navigation