Optimal Search for Detecting a Hidden Object
Kenji Onaga · SIAM Journal on Applied Mathematics · 1971
This paper formulates and analyzes a search problem for finding a stationary object hidden in one of N specified regions with a priori probability $p_i ,\sum olimits_{i = 1}^N {p_i = 1} $. A searcher looks for the object by repeated searches and switches of regions. Before a search begins in a new region i, a certain time (called switch time $c_i $) is necessarily wasted. The probability of object detection in region i is related to the accumulated visit time x by a probability distribution function $Q_i (x)$. With minimality of the average time to object detection as the measure of policy goodness, we have obtained optimality conditions and improvement algorithms. More detailed properties are presented for special cases of restricted $Q(x)$ and zero switch times.