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Grid computing system is different from conventional distributed computing systems by its focus on large-scale resource sharing and open architecture for services. The global grid technologies and the Globus toolkit in particular, are evolving toward an open grid service architecture with which a grid system provides an extensible infrastructure so that various organizations can offer their own services and integrate their resources. Hence, this paper aims at solving the problem of optimally allocating resource on the grid to maximize the grid service reliability. Based on resource allocation in grid computing, we develop an optimization model and a quantum chromosomes genetic algorithm (QCGA) to effectively solve it. Simulation experiment is given to show the modeling procedures and efficiency of the QCGA.