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Avionic systems are integrating more and more functions to cope with the increasing number of features on modern aircrafts. These systems are subject to many requirements that have to be considered during their design. Time and Space Partitioning (TSP), which consists of isolating applications within partitions, is a well-known means to assign avionic applications to computing units according to security, schedulability, and safety constraints. Multicore execution platforms are becoming popular in avionic systems. In this paper, we propose to investigate the partitioning of avionic applications over such execution platforms while considering schedulability, security, and safety constraints. We propose a design space exploration approach using a multi-objective meta-heuristic, that provides trade-offs between schedulability and security while considering safety and multicore platforms with different numbers of cores. We illustrate how this meta-heuristic can investigate key parameters such as hardware shared resource overhead.