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The LSVN (limitation of the scope of visited nodes) problem is defined, which is caused by the scope limitation of visited nodes in Grid environment. It is found that at least one third nodes in grid are not visited. Problems caused by LSVN such as network bottleneck and service delay are studied. This paper proposes three strategies based on historical information to solve the LSVN problem and promote grid utilization. Simulation shows that all the strategies efficiently expand the scope of visited nodes and improve the grid utilization by two or three times.