Time and Space Partitioning (TSP) introduces the concept of partitions that allow application isolation. Applications can be assigned to partitions according to various objective functions or constraints related to safety, security, schedulability or energy requirements. Some of these objective functions may be conflicting, i.e. an improvement of one objective leads to a decrease of another. For example, improving the safety by active redundancy of a system may impact its schedulability. In this paper, we investigate the conflicting aspect between schedulability and security (confidentiality and integrity) in TSP real-time systems. We formulate 3 design space exploration algorithms with a meta-heuristic called Pareto Archived Evolutionary Strategy (PAES). These algorithms are implemented into Cheddar, a schedulability analysis tool. We investigate the effect of different architecture implementations to bring confidentiality and integrity in TSP systems. Our experiments reveal that the security architecture implementation alternatives offer opportunities for good trade-offs between schedulability and security. We also establish that our proposed mutation algorithms are adapted to large-scale problems. Comparison with the exact method for small size test-case shows that the proposed approach converges towards the Pareto front, missing only one non dominated solution.