Recommender systems enable companies to generate meaningful recommendations to users for items or products that might interest them. Stochastic Gradient Descent Matrix Factorization (SGD-MF) is one of the most popular model-based recommender systems. Fractional Adaptive Stochastic Gradient Descent matrix factorization (FASGD-MF) is a subset of SGD-MF-based models that apply fractional calculus in an adaptive way. There are some hyperparameters in these models that impact the quality of the recommender system. However, searching the hyperparameter space to find the best configuration using an exhaustive search is often a time-consuming task. This paper employs a genetic algorithm as a search metaheuristic to tackle this problem. The proposed method is designed based on non-uniform mutation and whole arithmetic crossover. The results indicate that optimizing hyperparameters by the proposed method not only adjusts the values of hyperparameters automatically but also can improve the quality of SGD-MF-based models. Implementing the proposed genetic algorithm on two datasets (MovieLens 100K and MovieLens 1M) verifies the assertion about the performance.