A three-phase search approach with dynamic population size for solving the maximally diverse grouping problem

The maximally diverse grouping problem (MDGP) aims to assign a given set of elements into a number of groups with size restrictions for the sake of maximizing the sum of diversity in these groups. MDGP is an NP-hard combinatorial optimization problem, possessing widespread application and practical importance. This paper introduces a novel hybrid algorithm, called a three-phase search approach with dynamic population size (TPSDP), for solving the problem. The proposed algorithm devises the search process into three phases with distinct functions which are iterated: (1) an undirected perturbation phase to improve the population diversity, (2) a restructure phase using a distinctive crossover operator to increase the information interaction among solutions, and (3) a directed perturbation phase to discover the adjacent local optima around current solutions. TPSDP also combines a dynamic population size strategy to reserve limited computing resources for potential solutions. The results of experiments and the Friedman test show that the overall performance of the proposed TPSDP is highly competitive with or better than previous state-of-the-art MDGP algorithms on 500 instances taken from five popular benchmark sets. Furthermore, an additional experiment of parameter analysis and a discussion of critical ingredients are presented. The source code of TPSDP is provided at https://toyamaailab.github.io/sourcedata.html.