In this work, we study the optimal scheduling problem for embedded control systems. Given a number of numerical computation tasks that must be executed on an embedded computer, the goal is to find a periodic schedule that minimizes the error of the implementation with respect to the ideal system. In this paper, we pose two open problems: the decidability of the optimal scheduling problem for timed-triggered controllers (OSTTC) and the time complexity of the corresponding bounded version of the problem. We conjecture that the former is undecidable and that the latter is NP-Complete. In view of the previous conjectures, we present a Genetic Algorithm (GA) for the OSTTC problem. Initial experimental results of GA-OSTTC are very promising when compared to random search and exhaustive bounded search.