There are few studies in the literature to address the multi-objective multi-label feature selection for the classification of video data using evolutionary algorithms. Selecting the most appropriate subset of features is a significant problem while maintaining/improving the accuracy of the prediction results. This study proposes a framework of parallel multi-objective Non-dominated Sorting Genetic Algorithms (NSGA-II) for exploring a Pareto set of non-dominated solutions. The subsets of non-dominated features are extracted and validated by multi-label classification techniques, Binary Relevance (BR), Classifier Chains (CC), Pruned Sets (PS), and Random k-Labelset (RAkEL). Base classifiers such as Support Vector Machines (SVM), J48-Decision Tree (J48), and Logistic Regression (LR) are performed in the classification phase of the algorithms. Comprehensive experiments are carried out with local feature descriptors extracted from two multi-label data sets, the well-known MIR-Flickr dataset and a Wireless Multimedia Sensor (WMS) dataset that we have generated from our video recordings. The prediction accuracy levels are improved by 6.36% and 25.7% for the MIR-Flickr and WMS datasets respectively while the number of features is significantly reduced. The results verify that the algorithms presented in this new framework outperform the state-of-the-art algorithms.