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This work presents a Genetic Algorithm (GA) based optimization technique, called GA-ParFnt, to find the Pareto frontier for optimizing data transfer versus job execution time in grids. As the performance of a generic GA is not suitable to find such Pareto relationship, several modifications are applied to it so that it can efficiently discover such relationship. The frontier curve representing this relationship is then matched against performance of several scheduling techniques - for both data intensive and computationally intensive applications -to measure their overall performances. Results show that several of these algorithms are far from the Pareto front despite their claims of being efficient in optimizing their targeted objectives. Results also provide invaluable insights into this formidable problem and should aid in the design of future schedulers.