Moving target search or the game of cops and robbers has been given much attention during the last two decades. It is known that optimal solutions, given an-cop-win graph, are computable in polynomial time in the size of the input graph. However, a first practical polytime algorithm was only given recently by Hahnet al. . All other known approaches are learning and anytime algorithms that try to approximate the optimal solution. In this work we present four algorithms: an adaptation of Two-Agent IDA*, Proof-Number Search, alpha-beta, and Reverse Minimax A*, a new algorithm. We show how these techniques can be applied to compute optimal moving target search solutions and give benchmarks on their performance for the one cop one robber problem.