On the optimal search problem
On the optimal search problem
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关于最优搜索问题
DOI：
10.1137/1007106
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发表时间：
1965
期刊：
影响因子：
--
通讯作者：
W. Franck
中科院分区：
文献类型：
--
作者：
W. Franck
介绍。一个粒子位于由一个随机变量y的值所给定的实线上的一点上。我们希望以这样一种方式来搜索该粒子，使其在定位该物体之前所走过的平均距离最小。我们假设搜索器从原点开始，并且期望以1的概率找到目标。本文将从以下几个方面探讨这一问题。首先，存在一些关于解是否存在的问题。得到了Y的分布函数存在解的充分必要条件，并给出了一个违反这些条件且不存在解的例子。证明了一个定理，使我们对最小序列的性质有了一些认识。对两个相当简单的分布函数进行了求解，并提出了一般情况下近似解的数值方法。
Introduction. A particle is located on the real line at a pointgiven by the value of a random variable, Y. It is desired to search for the particle in such a way as to minimize the average distance traveled before locating the object. We assume that the searcher starts at the origin and that it is desired to locate the object with probability one.This paper will deal with the following aspects of theproblem. First of all, there issome question as to the existence ofa solution. Necessary and sufficient conditions on the distribution function of Y are obtained for the existence of a solution, and an example is given in which the conditions are violated and no solution exists. A theorem is proved which gives some insight into the nature of the minimal sequence. The problem is solved for two rather simple distribution functions and a numerical method is advanced for approximating the solution in thegeneral case.