The Optimal Search For A Markovian Target Which Moves Among Finite Number Of Cells

The optimal search problem includes two categories, respectively for stationary target search problem and moving target search problem. Up to now, the stationary target search problem has made abundant achievements of theory and application, relatively speaking, the study of moving target search problem is relatively lagging behind. At present, the research of moving target search problem are mainly focused on search algorithm design and application, and lack of rigorous mathematical definition and theoretical proof in search of many specific problems. This paper researches on the optimal search strategy for a Markovian target which moves among finite number of cells from the angle of the theory of probability. Mathematically and strict proof for a complete description of these problems are presented.The paper is divided into two parts, on the first part, on the basis of the detailed introduction and analysis of existing theoretical achievements about moving target search problem, when the markovian target moves between two cells, and when there is or not an overlook probability, we have presented the mathematical definition of effective strategy and the optimal strategy, determined the existence of effective strategies, calculated the expectations of the number of looks of the effective strategy, given the expression of the minimum search number of looks, and presented the method of determination of Pollock strategy. On the second part is about when the markovian target moves between n(greater than2) cells, we deduced some of the necessary conditions for the optimal search using bayes’ theorem.