Optimal ambushing search for a moving target

This paper investigates a search problem for a moving target in which a searcher can anticipate the probabilities of routes selected by the target but does not have any time information about when the target transits the route. If the searcher had some time information, he could develop an efficient search plan by varying allocations of search effort based on time. Due to the lack of time information, the searcher must ambush the target by distributing search effort to places where the target is likely to pass. There are few papers that deal mathematically with this type of search problem with no time information. Employing the criterion of detection probability, we formulate the problem and obtain necessary and sufficient conditions for the optimal solution. By applying the conditions, we propose two methods for solving the problem. The convex programming problem can be easily solved numerically by some well-known methods, e.g. the gradient projection method or the multiplier method. By numerical comparison, it is verified that the proposed methods have the excellent performance in computational time. We also elucidate some properties of the optimal distribution of search effort by some numerical examples.