Using multiple searchers in constrained-path, moving-target search problems

Abstract

The search theory open literature has paid little, if any, attention to the multiple‐searcher, moving‐target search problem. We develop an optimal branch‐and‐bound procedure and six heuristics for solving constrained‐path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one‐, two‐, and three‐searcher test problem considered. For one‐ and two‐searcher problems, the same heuristic's solution time is less than that of other heuristics. For three‐searcher problems, a genetic algorithm implementation obtains the best‐known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.

Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times

“…The glimpse function may typically take the form of (Dell et al, 1996, Eagle andYee, 1990), with being a measure of search effectiveness for a given cell Any function however can be used. This probability is assumed to be independent of past searches.…”

“…Alternative formulations exist in literature for the OSP (Thomas and Eagle 1995;Washburn, 1995), but the above, similar to that used in Dell et al (1996), is chosen here to make clear the intended generalisation in Section 6.…”

“…From an implementation perspective, drastically quicker solution times can be obtained with minimal change by accepting suboptimal solutions in the branch and bound process (Washburn, 1995) or implementing a rolling horizon technique and computing individually shorter plans (Dell et al, 1996).…”

“…A search plan respecting searcher travel constraints is sought to maximise the probability of detection within a specified time frame. Much work has been done in the past on this path constrained or optimal searcher path problem (OSP) (Stewart, 1979;Eagle and Yee, 1990;Dell et al 1996;Hohzaki, 1997;Washburn 1998), for the specific case where the environment is discretised into a grid of identically-sized cells and a searcher can immediately search one cell after another in successive time periods. In contrast, a platform searching a built environment cannot move from one region to another without expending some travel time for each transition.…”

Exact Solution for Search-and-Rescue Path Planning

“…Occupancy belief are assumed to be independent of past search visits as reported in [24]- [26], [5] for the optimal searcher path problem. Accordingly, based on the completion of a projected visit in cell c during time interval t, the posterior probability of cell containment p c' t+1 for any cell c' is given by:…”