~ In this paper we investigate a new algorithm for solving the optimal task assignment problem. The assignment is based on Stone's [11] "throughput" metric with the optimality criteria being the total cost for execution and interprocess communication.Two approaches studied are a new approach based on genetic algorithms and A*, a well known tree search algorithm for solving the same problem. We use the algorithm execution time as a performance criteria for the two algorithms. It is shown that the genetic algorithm techniques are more favorable than A* for larger search spaces while for smaller search spaces A* is preferred.