A searcher and target move among a finite set of cells C = 1, 2, …,N in discrete time. At the beginning of each time period, one cell is searched. If the target is in the selected cell j, it is detected with probability qj. If the target is not in the cell searched, it cannot be detected during the current time period. After each search, a target in cell j moves to cell k with probability pjk. The target transition matrix, P = [pjk] is known to the searcher. The searcher's path is constrained in that if the searcher is currently in cell j, the next search cell must be selected from a set of neighboring cells Cj. The object of the search is to minimize the probability of not detecting the target in T searches.
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.
A search is conducted for a target moving in discrete time among a finite number of cells according to a known Markov process. The searcher must choose one cell in which to search in each time period. The set of cells available for search depends upon the cell chosen in the last time period. The problem is to find a search path, i.e., a sequence of search cells, that either maximizes the probability of detection or minimizes the mean number of time periods required for detection. The search problem is modelled as a partially observable Markov decision process and several approximate solutions procedures are proposed. © 1995 John Wiley & Sons, Inc.
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 threesearcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% ofother heuristic solution times. 0 1996 John Wiley & Sons, Inc. The constrained-path, moving-target search problem [ 6 , 15, 161 has the following characteristics: 0 A single searcher and target move among a finite set of cells in discrete time. 0 The searcher and target occupy only one cell each time period. 0 Each time period, the searcher moves from its current cell to one of a specified 0 The target moves among cells according to a specified stochastic process. 0 If the target occupies the searched cell, the random search formula determines the probability of detection-otherwise the detection probability is zero. 0 The target's probability distribution is Bayesian updated for nondetection each time period. set of accessible cells.The objective of the search is to find a feasible search path that maximizes the probability of detecting the target in T time periods. The main contributions of this article center around extending the constrained-path, moving-target search problem to consider multiple searchers explicitly. As this article demonstrates, exact procedures developed to effectively solve single-searcher versions of this
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