The computational grid provides the global computing infrastructure for users to access the services over a network. However, grid service providers charge users for the services based on their usage and QoS level specified. Therefore, in order to optimize the grid workflow execution, a robust multi-objective scheduling algorithm is needed considering economic cost along with execution performance. Generally, in multi-objective problems, simulations rely on running large number of evaluations to obtain the accurate results. However, algorithms that consider the preferences of decision maker, convergence to optimal tradeoff solutions is faster. Thus, in this chapter, the author proposed the preference-based guided search mechanism into MOEAs. To obtain solutions near the pre-specified regions of interest, the author has considered two MOEAs, namely R-NSGA-II and R-ε-MOEA. Further, to improve the diversity of solutions, a modified form called M-R-NSGA-II is used. Finally, the experimental settings and performance metrics are presented for the evaluation of the algorithms.