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The assignment of fixed priorities to tasks and messages in distributed real-time systems is known to be an NP-hard problem, and thus there is no optimal method to accomplish it in polynomial time. This fact makes it a suitable problem to be approached with generic search and optimization algorithms. In this paper we propose a genetic algorithm with a permutational solution encoding for the assignment of fixed priorities to tasks and messages in distributed real-time systems using a holistic approach. This paper shows that the genetic algorithm can find more and better schedulable priority assignments than HO PA, which is, as far as we know, one of the best methods for the fixed priority assignment in distributed real-time systems.