Feature selection and hyper-parameters optimization (tuning) are two of the most important and challenging tasks in machine learning. To achieve satisfying performance, every machine learning model has to be adjusted for a specific problem, as the efficient universal approach does not exist. In addition, most of the data sets contain irrelevant and redundant features that can even have a negative influence on the model’s performance. Machine learning can be applied almost everywhere; however, due to the high risks involved with the growing number of malicious, phishing websites on the world wide web, feature selection and tuning are in this research addressed for this particular problem. Notwithstanding that many metaheuristics have been devised for both feature selection and machine learning tuning challenges, there is still much space for improvements. Therefore, the research exhibited in this manuscript tries to improve phishing website detection by tuning extreme learning model that utilizes the most relevant subset of phishing websites data sets features. To accomplish this goal, a novel diversity-oriented social network search algorithm has been developed and incorporated into a two-level cooperative framework. The proposed algorithm has been compared to six other cutting-edge metaheuristics algorithms, that were also implemented in the framework and tested under the same experimental conditions. All metaheuristics have been employed in level 1 of the devised framework to perform the feature selection task. The best-obtained subset of features has then been used as the input to the framework level 2, where all algorithms perform tuning of extreme learning machine. Tuning is referring to the number of neurons in the hidden layers and weights and biases initialization. For evaluation purposes, three phishing websites data sets of different sizes and the number of classes, retrieved from UCI and Kaggle repositories, were employed and all methods are compared in terms of classification error, separately for layers 1 and 2 over several independent runs, and detailed metrics of the final outcomes (output of layer 2), including precision, recall, f1 score, receiver operating characteristics and precision–recall area under the curves. Furthermore, an additional experiment is also conducted, where only layer 2 of the proposed framework is used, to establish metaheuristics performance for extreme machine learning tuning with all features, which represents a large-scale NP-hard global optimization challenge. Finally, according to the results of statistical tests, final research findings suggest that the proposed diversity-oriented social network search metaheuristics on average obtains better achievements than competitors for both challenges and all data sets. Finally, the SHapley Additive exPlanations analysis of the best-performing model was applied to determine the most influential features.