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

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.

[1]  T. P. Dinh,et al.  Convex analysis approach to d.c. programming: Theory, Algorithm and Applications , 1997 .

[2]  J. R. Weisinger,et al.  A survey of the search theory literature , 1991 .

[3]  Marco Scarsini,et al.  Search for an immobile hider on a stochastic network , 2020, Eur. J. Oper. Res..

[4]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[5]  Steve Alpern.  Search for an immobile Hider in a known subset of a network , 2019, Theor. Comput. Sci..

[6]  George L. Nemhauser,et al.  The Traveling Salesman Problem: A Survey , 1968, Oper. Res..

[7]  S. Gal.  Search Games with Mobile and Immobile Hider , 1979 .

[8]  Le Thi Hoai An,et al.  A Based-DC Programming Approach for Planning a Multisensor Multizone Search for a Moving Target , 2015, MCO.

[9]  Lawrence D. Stone.  Necessary and Sufficient Conditions for Optimal Search Plans for Moving Targets , 1979, Math. Oper. Res..

[10]  Bruce L. Golden,et al.  Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey , 2018, Networks.

[11]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[12]  Scott Shorey Brown,et al.  Optimal Search for a Moving Target in Discrete Time and Space , 1980, Oper. Res..

[13]  Le Thi Hoai An,et al.  A DC programming approach for planning a multisensor multizone search for a target , 2014, Comput. Oper. Res..

[14]  J. Willard,et al.  Simultaneous Area Search and Task Assignment for a Team of Cooperative Agents , 2003 .

[15]  Frédéric Dambreville,et al.  A hierarchical approach for planning a multisensor multizone search for a moving target , 2009, Comput. Oper. Res..

[16]  Ryusuke Hohzaki,et al.  SEARCH GAMES : LITERATURE AND SURVEY , 2016 .

[17]  B. O. Koopman.  Search and Screening: General Principles and Historical Applications , 1980 .

[18]  Gigliola Vaglini,et al.  Enhancing biologically inspired swarm behavior: Metaheuristics to foster the optimization of UAVs coordination in target search , 2019, Comput. Oper. Res..

[19]  Jacques de Guenin.  Optimum Distribution of Effort: An Extension of the Koopman Basic Theory , 1961 .

[20]  Gonzalo Pajares,et al.  Multi-UAV target search using decentralized gradient-based negotiation with expected observation , 2014, Inf. Sci..

[21]  James M. Dobbie,et al.  A Survey of Search Theory , 1968, Oper. Res..

[22]  François-Alex Bourque.  Solving the moving target search problem using indistinguishable searchers , 2019, Eur. J. Oper. Res..

[23]  Tüze Kuyucu,et al.  Superadditive effect of multi-robot coordination in the exploration of unknown environments via stigmergy , 2015, Neurocomputing.

[24]  P. Hudson.  Search Games , 1982 .

[25]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[26]  Ryusuke Hohzaki,et al.  A CONCAVE MAXIMIZATION PROBLEM WITH DOUBLE LAYERS OF CONSTRAINTS ON THE TOTAL AMOUNT OF RESOURCES , 2000 .

[27]  P. B. Sujit,et al.  Search Strategies for Multiple UAV Search and Destroy Missions , 2011, J. Intell. Robotic Syst..

[28]  Joarder Kamruzzaman,et al.  Search and tracking algorithms for swarms of robots: A survey , 2016, Robotics Auton. Syst..