In this paper, we apply multi-objective evolutionary computation to the synthesis of real-time, embedded, heterogeneous, multiprocessor systems (briefly, Multiprocessor Systems-on-Chip or MP-SoCs). Our approach simultaneously explores the architecture, the mapping and the scheduling of the system, by using multi-objective evolution. In particular, we considered three approaches: a multi-objective genetic algorithm, multi-objective Simulated Annealing, and multi-objective Tabu Search. The algorithms search for optimal architectures, in terms of processing elements (processors and hardware accelerators) and communication infrastructure, and for the best mappings and schedules of multi-rate real-time applications given objectives such as: system area, hard and soft dead-lines violations, dimensions of memory buffers. We formalize the problem, describe our flow and compare the three algorithms, dis- cussing which one performs better with respect to different classes of applications.