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Optimal assigning jobs to resources is an important problem in grid computing. Now grid scheduling policies are mostly traditional heuristic algorithms for scheduling n independent tasks on m processors in early finishing time. However grids have developed to wide area, heterogeneous and non autonomous environments, business objective also became crucial for the success of the scheduling. Therefore base on a grid scheduling model with business parameters, we designed an evolutionary scheduling algorithm. The algorithm capability and performance were demonstrated by simulations. Furthermore a predictive resource mechanism was brought out to improve scheduling efficiency. At last we presented implementation scenario of our algorithm with predictive resource optimization in wide area open grid.