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Optimal tasks allocation is one of the most important problems in multiprocessing. Optimal assignment of tasks to a multiprocessor is an NP-hard problem in general cases, and precedence task graph makes it more complex. Many factors affect optimal tasks allocation. One of them is cache reload time in multiprocessor systems. These problems exist in real-time systems, too. Due to high sensitivity of `time' in real-time systems, scheduling with respect to time constraints becomes very important. This paper proposes a suboptimal scheduler for hard realtime heterogeneous multiprocessor systems considering time constraints and cache reload time simultaneously, using multiobjective genetic algorithm. In addition, it tries to propose a generalized method for real-time multiobjective scheduling in multiprocessor systems using genetic algorithms.