  What is the most efficient search strategy for the random located target
sites subject to the physical and biological constraints? Previous results
suggested the L\'evy flight is the best option to characterize this optimal
problem, however, which ignores the understanding and learning abilities of the
searcher agents. In the paper we propose the Continuous Time Random Walk (CTRW)
optimal search framework and find the optimum for both of search length's and
waiting time's distributions. Based on fractional calculus technique, we
further derive its master equation to show the mechanism of such complex
fractional dynamics. Numerous simulations are provided to illustrate the
non-destructive and destructive cases.
