Solution of the Retiring Search Problem

Abstract

The well-known variational principle of the optimal distribution of search effort is applied to the case where the sought-for target has been located momentarily but the search cannot begin until a time T o later, during which interval the target may or may not move. The optimal search path, called the retiring search curve,, is a spiral starting at the point of original location, with the relationship between r and or L, the length of path, given by a differential equation derived from the variational principle. This equation is solved for a range of values of the parameters of greatest practical interest. The results are tabulated and also displayed in graphical form for use in practice. General conclusions emerge, of considerable practical value in searches of this kind.