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Task scheduling and resource allocation are the key rationale behind the computational grid. Distributed resource clusters usually work in different autonomous domains with their own access and security policies that have a great impact on the successful task execution across the domain boundaries. Heuristics and metaheuristics are the effective technologies for scheduling in grids due to their ability to deliver high quality solutions in reasonable time. In this paper, the authors develop a Hierarchic Genetic Scheduler (HGS-Sched) for improving the effectiveness of the single-population genetic-based schedulers in the dynamic grid environment.