On the Optimal Search for a Randomly Moving Target

Abstract

The problem involved in the search for a randomly moving target is considered in the case where the probability density function of the location of the target satisfies an equation of type (1). The searching effort is expressed in terms of a time-dependent search density function, and a necessary condition for the optimality of the search density function is derived. In the case of a stationary target this condition becomes the familiar one of Koopman [4]. Since most applications would involve the solution of a partial differential equation of parabolic type with appropriate initial and boundary conditions, the application of the optimality condition is difficult. Obviously a special numerical technique needs to be introduced, a task which we shall not attempt in the present paper.