Skip to main content
Springer Nature Link
Log in

An information theoretic based integer linear programming approach for the discrete search path planning problem

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Discrete search path planning is known to be a NP-hard problem, and problem-solving methods proposed so far rely on heuristics with no way to reasonably estimate solution quality for practical size problems. Departing from traditional nonlinear model formulations, a novel information theoretic based approach using integer linear programming (ILP) is proposed to optimally solve the discrete open-loop centralized search path planning problem with anticipated feedback, involving a team of homogeneous agents. The approach takes advantage of objective function separability and conditional probability independence of observations to efficiently minimize expected system entropy. A network representation is exploited to simplify modeling, reduce constraint specification and speed-up problem-solving. The novelty of the approach consists in capturing false-alarm observations explicitly while proposing an original and efficient way to linearize the underlying non-linear expected entropy function required to properly represent target location uncertainty, making for the first time practical problems tractable. The proposed ILP formulation rapidly yields near-optimal solutions for realistic problems while providing for the first time, a robust lower bound through Lagrangian relaxation. Long planning problem horizon may be dynamically adapted by periodically solving new problem instances incorporating actual observation outcomes from previous episodes over receding horizons. Computational results clearly show the value of the approach in comparison to a myopic heuristic over various problem instances.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Agmon, N., et al.: The giving tree: constructing trees for efficient offline and online multi-robot coverage. Ann. Math. Artif. Intell. 52, 109–142 (2008)

    Article  MathSciNet  Google Scholar 

  2. Benkoski, S., Monticino, M., Weisinger, J.: A survey of the search theory literature. Naval Res. Logist. 38, 469–494 (1991)

    Article  MATH  Google Scholar 

  3. Chung, T.: On probabilistic search decisions under searcher motion constraints. In: Workshop on Algorithmic Foundation of Robotics VIII, Guanajuato, Mexico, pp. 501–516 (2009)

  4. Choo, C., Smith, J., Nasrabadi, N.: An efficient terrain acquisition algorithm for a mobile robot. In: Proceedings of IEEE International Conference on Robotics and Automation, Sacramento, CA, pp. 306–311 (1991)

  5. Cover, T., Thomas, J.: Elements of Information Theory, 2nd edn. Wiley, New York (2006)

    MATH  Google Scholar 

  6. Finn, A., et al.: Design challenges for an autonomous cooperative of UAVs. In: Proceedings of the International Conference on Information, Decision and Control, pp. 160–169 (2007)

  7. Flint, F.E., Fernandez-Gaucherand, E., Polycarpou, M.: Efficient Bayesian methods for updating and storing uncertain search information for UAV’s. In: Proceedings of 43rd IEEE Conference on Decision and Control, pp. 1093–1098 (2004)

  8. Hohzaki, R., Iida, K.: Optimal search plan for a moving target when a search path is given. Math. Jpn. 41(1), 175–184 (1995)

    MATH  MathSciNet  Google Scholar 

  9. Hollinger, G.A.: Search in the physical world. CMU-RI-TR-10-20, Robotics Institute. Ph.D. thesis, Carnegie Mellon University (2010)

  10. Hollinger, G.A., Singh, S.: GSST: anytime guaranteed search with spanning trees. Auton. Robots 29(1), 99–118 (2010)

    Article  Google Scholar 

  11. IBM ILOG CPLEX Optimization Studio Academic Research Edition Fix Pack 12.2.0.2. http://www-01.ibm.com/support/docview.wss?uid=swg24028951

  12. Jin, Y., Liao, Y., Minai, A., Polycarpou, M.: Balancing search and target response in cooperative unmanned aerial vehicle (UAV) teams. IEEE Trans. Syst. Man Cybern. Part B 36(3), 571–587 (2006)

    Article  Google Scholar 

  13. Latombe, J.-C.: Robot Motion Planning, ser. International Series in Engineering and Computer Science; Robotics: Vision, Manipulation and Sensors, vol. 124. Kluwer Academic Publishers, Boston (1991)

    Google Scholar 

  14. Lau, H.: Optimal search in structured environments. Ph.D. thesis, University of Technology, Sydney (2007)

  15. Lau, H., Dissanayake, G.: Probabilistic search for a moving target in an indoor environment. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3393–3398 (2006)

  16. Lau, H., Dissanayake, G.: Optimal search for multiple targets in a built environment. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Alberta, Canada, pp. 228–233 (2005)

  17. Martins, G.: A new branch-and-bound procedure for computing optimal search paths. Master’s thesis. Naval Postgraduate School (1993)

  18. Mathews, G., Durrant-Whyte, H.: Scalable decentralised control for multi-platform reconnaissance and information gathering tasks. In: 9th International Conference on Information Fusion, pp. 1–8 (2006)

  19. Rekleitis, I., et al.: Efficient Boustrophedon multi-robot coverage: an algorithmic approach. Ann. Math. Artif. Intell. 52, 109–142 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  20. Sankaranarayanan, A., Masuda, I.: Sensor based terrain acquisition: a new, hierarchical algorithm and a basic theory. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Raleigh, pp. 1515–1523 (1992)

  21. Svennebring, J., Koenig, S.: Building terrain-covering ant robots: a feasibility study. Auton. Robots 16(3), 313–332 (2004)

    Article  Google Scholar 

  22. Stone, L.: What’s happened in search theory since the 1975 Lanchester prize? Oper. Res. 37(3), 501–506 (1989)

    Article  MathSciNet  Google Scholar 

  23. Vincent, P., Rubin, I.: A framework and analysis for cooperative search using UAV swarms. In: ACM Symposium on Applied Computing, pp. 79–86 (2004)

  24. Wagner, W., et al.: Distributed covering by ant-robots using evaporating traces. IEEE Trans. Robot. Autom. 15(5), 918–933 (1999)

    Article  Google Scholar 

  25. Washburn, A.R.: Branch and bound methods for a search problem. Naval Res. Logist. 45, 243–257 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  26. Wong, S., MacDonald, B.: A topological coverage algorithm for mobile robots. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, pp. 1685–1690 (2003)

  27. Yang, S., Luo, C., Neural, A.: Network approach to complete coverage path planning. IEEE Trans. Syst. Man Cybern. B Cybern. 34(1), 718–724 (2004)

    Article  Google Scholar 

  28. Yang, Y., Minai, A., Polycarpou, M.: Evidential map building approaches for multi-UAV cooperative search. In: Proceedings of the American Control Conference, pp. 116–121 (2005)

Download references

Author information

Authors and Affiliations

  1. DRDC Valcartier, Quebec City, Canada

    Jean Berger

  2. T-OptLogic Inc., Quebec City, Canada

    Nassirou Lo

  3. DRDC CORA, Ottawa, Canada

    Abdeslem Boukhtouta

  4. UQAM, TELUQ, Quebec City, Canada

    Martin Noel

Authors
  1. Jean Berger
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Nassirou Lo
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Abdeslem Boukhtouta
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Martin Noel
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jean Berger.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berger, J., Lo, N., Boukhtouta, A. et al. An information theoretic based integer linear programming approach for the discrete search path planning problem. Optim Lett 9, 1585–1607 (2015). https://doi.org/10.1007/s11590-015-0874-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-015-0874-7

Keywords