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Full-mission simulators (FMSs) are considered the most critical simulation tool belonging to the flight simulator family. FMSs include a faithful reproduction of fighter aircraft. They are used by armed forces for design, training, and investigation purposes. Due to the criticality of their timing constraints and the high computation cost of the whole simulation, FMSs need to run in a high-performance computing system. Heterogeneous distributed systems are among the leading computing platforms and can guarantee a significant increase in performance by providing a large number of parallel powerful execution resources. One of the most persistent challenges raised by these platforms is the difficulty of finding an optimal mapping of n tasks on m processing elements. The mapping problem is considered a variant of the quadratic assignment problem, in which an exhaustive search cannot be performed. The mapping problem is an NP-hard problem and solving it requires the use of meta-heuristics, and it becomes more challenging when one has to optimize more than one objective with respect to the timing constraints. Multi-objective evolutionary algorithms have proven their efficiency when tackling this problem. Most of the existent works deal with the task mapping by considering either a single objective or homogeneous architectures. Therefore, the main contribution of this paper is a framework based on the modeldriven design paradigm allowing us to map a set of intercommunicating real-time tasks making up the FMS model onto the heterogeneous distributed multi-processor system model. We propose a multi-objective approach based on the well-known optimization algorithm ''Non-dominated Sorting Genetic Algorithm-II'' satisfying the tight timing constraints of the simulation and minimizing makespan, communication cost, and memory consumption simultaneously.