An Optimal Search Problem
Wallace E. Franck · SIAM Review · 1965
Suppose a searcher is at a given point on a line and wishes to locate an object which is known to be somewhere on the line. Suppose further that there is a probabilistic law which governs the location of the object on the line. The searcher can only locate the object by traveling to the point where it is. He desires to formulate a search plan which will minimize the average distance traveled before locating the object. The only initial choice he has is as to which direction to go. Then he must decide how far to go before turning around and searching in the other direction. The decision about how far to go before turning around presents itself over and over until the object is located.