Biased Random-Key Genetic Algorithm with Local Search Applied to the Maximum Diversity Problem

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.