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Grey Wolf Optimizer (GWO) is a popular and effective nature-inspired, swarm intelligence based metaheuristic optimization algorithm which imitates the hunting process of a wolf pack in the nature. It has been widely used to solve both theoretical and real life engineering optimization problems. Even though metaheuristics have many advantages such as requiring no derivative information of the problem at hand, simplicity, and flexibility, they also have some drawbacks like trapping local optima, and premature convergence. They should have a proper balance between diversification (exploration) and intensification (exploitation). In this study, inclusion of a simple operator, namely "parasitism", is proposed to improve the performance of GWO by means of exploration. Parasitism is a phase within Symbiotic Organisms Search (SOS) algorithm. The performances of 2 modified versions are compared with the original GWO, using 13 test beds. Results indicate that inclusion of parasitism phase into the original version has produced better results on the parameters of the algorithm.