Optimal multiplicative generalized linear search plan for a discrete random walker (Q896731)

Summary: This paper formulates a search model that gives the optimal search plan for the problem of finding a discrete random walk target in minimum time. The target moves through one of \(n\)-disjoint real lines in \(\mathbb R^n\): we have \(n\)-searchers starting the searching process for the target from any point rather than the origin. We find the conditions that make the expected value of the first meeting time between one of the searchers and the target finite. Furthermore, we show the existence of the optimal search plan that minimizes the expected value of the first meeting time and find it. The effectiveness of this model is illustrated using numerical example.