The Use of Uncertainty in a Simultaneous Search

Shannon's measure of uncertainty (entropy) is used to plan a simultaneous search for the extreme of a unimodal function of one variable. A general expression is developed to express the expected uncertainty about the location of the extreme of the function after the N-point function has been evaluated at H points. The optimum locations of these H evaluations are then found by choosing them so as to minimize the expected uncertainty. The method requires that the user assign values to the probability that the extremum lies at each of the N locations. In so doing it enables him to develop a search policy that reflects his prior partial knowledge about the location of the extremum. It is shown that the entropy policy is identical to the min-max policy for the special case of equal initial probabilities.