With the eruption of communication technology and its supportive protocols, the field of testing of timed-IUT (Implementation Under Test with time constraints) was quick to follow. New and extended test generation methods using timed automata were in the need. Many papers were written on a broad range of timed automata testing. Few papers, however, dealt with generation of state identification sequences problems. Those who did, keyed their algorithms towards transformation of a timed-IUT into a regular, untimed IUT; thus, avoiding the need of redefining well known generation algorithms. This method, however, only functions if we search for optimal sequences w.r.t. their lengths. Optimality w.r.t. execution time was not considered in this context. In this paper we present a search algorithm for the direct generation of timed homing sequences optimal w.r.t. to execution time. This is accomplished by expanding and modifying the search tree used in previous algorithms such that it contains the capability of satisfying our goal. The solution found is proven to be optimal with respect to execution time. A comparison with other related algorithms is presented.