Route Optimization for Multiple Searchers

We consider a discrete time-and-space route-optimization problem, across a finite time horizon, in which multiple searchers seek to detect one or more probabilistically moving targets. The paper formulates a novel convex mixed-integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and targetand location-dependent search effectiveness. We present two solution approaches, one based on the cutting-plane method and the other on linearization. These approaches result in the first practical, exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting-plane approach solves many realistically sized problem instances in few minutes, while existing branch-and-bound algorithms fail. A specialized cut improves solution times by 50% in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution times with one or two orders of magnitude. The solution times for the cutting-plane approach tend to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers. Subject Classifications: Military operations research, search and surveillance, route planning, mixed-integer nonlinear programming. Area of review: Military and Homeland Security. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 04 SEP 2009 2. REPORT TYPE 3. DATES COVERED 00-00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Route Optimization for Multiple Searchers 5a. CONTRACT NUMBER