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In order to solve the multi-objective optimal grid workflow scheduling problems with various QoS constraints, SPEA2+ is employed to optimize the scheduling performance. The paper proposes a multi-objective optimal grid workflow scheduling algorithm with QoS constraints, namely GWSA. The proposed algorithm, based on the rich-construct AGWL grid workflow model, considers five-dimensional QoS parameters, and sets the five-dimensional QoS parameters to five objective functions as well as the corresponding constraints for multi-objective optimization, and eventually generates a set of Pareto optimal solutions which satisify all the five constraints through simultaneously optimizing those QoS parameters. Compared with the grid workflow scheduling algorithm GWSB based on SPEA2, the experimental results indicate that mean values of each dimensional QoS parameter of the set of Pareto optimal solutions which are obtained by GWSA are slightly superior than those of GWSB by a typical grid workflow instance.