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To exploit the power of modern heterogeneous multiprocessor embedded platforms on partitioned applications, the designer usually needs to efficiently map and schedule all the tasks and the communications of the application, respecting the constraints imposed by the target architecture. Since the problem is heavily constrained, common methods used to explore such design space usually fail, obtaining low-quality solutions. In this paper, we propose an ant colony optimization (ACO) heuristic that, given a model of the target architecture and the application, efficiently executes both scheduling and mapping to optimize the application performance. We compare our approach with several other heuristics, including simulated annealing, tabu search, and genetic algorithms, on the performance to reach the optimum value and on the potential to explore the design space. We show that our approach obtains better results than other heuristics by at least 16% on average, despite an overhead in execution time. Finally, we validate the approach by scheduling and mapping a JPEG encoder on a realistic target architecture.