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Planning a multi-sensors search for a moving target considering traveling costs

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  • Delavernhe, Florian
  • Jaillet, Patrick
  • Rossi, André
  • Sevaux, Marc

Abstract

This paper addresses the optimization problem of managing the research efforts of a set of sensors in order to minimize the probability of non-detection of a target. A novel formulation of the problem taking into account the traveling costs between the searched areas is proposed; it is more realistic and extends some previous problems addressed in the literature. A greedy heuristic algorithm is devised, it builds a solution gradually, using a linear approximation of the objective function refined at each step. The heuristic algorithm is complemented by a lower bound based on a piecewise linear approximation of the objective function with a parametric error, and extended to the case where the target is moving. Finally, a set of numerical experiments is performed to analyze and evaluate the proposed contributions.

Suggested Citation

  • Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    • Handle: RePEc:eee:ejores:v:292:y:2021:i:2:p:469-482
    DOI: 10.1016/j.ejor.2020.11.012
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    References listed on IDEAS

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    1. James M. Dobbie, 1968. "A Survey of Search Theory," Operations Research, INFORMS, vol. 16(3), pages 525-537, June.
    2. Bourque, François-Alex, 2019. "Solving the moving target search problem using indistinguishable searchers," European Journal of Operational Research, Elsevier, vol. 275(1), pages 45-52.
    3. Jacques de Guenin, 1961. "Optimum Distribution of Effort: An Extension of the Koopman Basic Theory," Operations Research, INFORMS, vol. 9(1), pages 1-7, February.
    4. M. Bellmore & G. L. Nemhauser, 1968. "The Traveling Salesman Problem: A Survey," Operations Research, INFORMS, vol. 16(3), pages 538-558, June.
    5. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    6. Scott Shorey Brown, 1980. "Optimal Search for a Moving Target in Discrete Time and Space," Operations Research, INFORMS, vol. 28(6), pages 1275-1289, December.
    7. Garrec, Tristan & Scarsini, Marco, 2020. "Search for an immobile hider on a stochastic network," European Journal of Operational Research, Elsevier, vol. 283(2), pages 783-794.
    8. Lawrence D. Stone, 1979. "Necessary and Sufficient Conditions for Optimal Search Plans for Moving Targets," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 431-440, November.
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