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Temporal logic models (TLM's) have been recently defined and used  for the synthesis of discrete event systems (DES) supervisors. A synthesis procedure was developed by exploring the system state space and by determining the reachable states from a given state. The supervisor selects acceptable paths in the reachability graph of the unsupervised system. In this paper another synthesis problem will be addressed: the optimization of a DES supervisor. A sequence of events which drive the system from a given initial state to a given final state is generated by minimizing a cost function index. Introducing definitions regarding measurement spaces and measurement functions it is shown that sufficient conditions are met for the design of the active supervisor. The optimization is then solved by applying the A∗ algorithm on the reachability graph with the specification restrictions. A heuristic function is considered to help the search. An example of read-write processes illustrates our results and the novelty of this approach.