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This article presents six parallel multiobjective evolutionary algorithms applied to solve the scheduling problem in distributed heterogeneous computing and grid systems. The studied evolutionary algorithms follow an explicit multiobjective approach to tackle the simultaneous optimization of a system-related (i.e. makespan) and a user-related (i.e. flowtime) objectives. Parallel models of the proposed methods are developed in order to efficiently solve the problem. The experimental analysis demonstrates that the proposed evolutionary algorithms are able to efficiently compute accurate results when solving standard and new large problem instances. The best of the proposed methods outperforms both deterministic scheduling heuristics and single-objective evolutionary methods previously applied to the problem.