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The dissertation consists of six chapters. In the first chapter, we present basic notions and relevant results in the area of grid scheduling. We understand that the current approaches of GA have little weaknesses when it was used in grid scheduling. This inspires us to study the method of MGA (modified genetic algorithm) to solve grid-scheduling problems. Consequently, in the second and the third chapter, we introduce mathematical model of grid scheduling and give a detailed MGA method by using the "pattern theory" and "building block hypothesis" technologies. This modified method can decrease the randomicity of the current GA. In the fourth chapter, we use the MGA method to study grid-scheduling problems and find a necessary and sufficient design method. In the latter chapters, we analyze the laboratory result to show that the modified algorithm has better characteristics than the standard GA when it was used in task scheduling.