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 a n-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 Hahn et 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.