In complex network analyses, mainly in social networks, the detection of communities is an important source of information for revealing an internal organization of nodes. On the other hand, if the network reveals a leadership structure, it is possible to understand the mechanisms of information dissemination on it. The detection of leaders and communities is a big challenge depending on the complexity level of the network. In the literature, there are some metaheuristic algorithms for detecting leaders and communities based on pattern recognition on the graph associated with the network. In this paper, we developed a random graph system to generate a synthetic network instance with leader and community structures that define a ground truth. We compare this ground truth to determine the performance of the algorithms LCDA 1 and LCDA 2 for detecting leaders and communities. The results corroborate that the benchmarking system would help in selecting useful configurations for practical applications.

The maximum diversity problem (MDP) aims to select a subset with a predetermined number of elements from a given set, maximizing the diversity among them. This NP-hard problem requires efficient algorithms that can generate high-quality solutions within reasonable computational time. In this study, we propose a novel approach that combines the biased random-key genetic algorithm (BRKGA) with local search to tackle the MDP. Our computational study utilizes a comprehensive set of MDPLib instances, and demonstrates the superior average performance of our proposed algorithm compared to existing literature results. The MDP has a wide range of practical applications, including biology, ecology, and management. We provide future research directions for improving the algorithm’s performance and exploring its applicability in real-world scenarios.