Multi-strategy multi-modal multi-objective evolutionary algorithm using macro and micro archive sets

In multi-modal multi-objective optimization problems (MMOPs), more than one decision vector is mapped to the same objective vector. The loss of the optimal decision vector is a huge challenge, which result in the loss of population diversity. To effectively tackle this issue and preserve population diversity, it is imperative to fully leverage both macro and micro perspectives. The macro perspective is based on subpopulations divided by centroids, whereas the micro is based on individuals with higher priorities. Therefore, a multi-strategy multi-modal multi-objective evolutionary algorithm using macro and micro archive set (MMMEA) is proposed. Among them, the macro archive set (MAA) uses the centroid truncation strategy, which controls the global of the algorithm through the centroid. This strategy can ensure the diversity of the population. The micro archive set (MIA) uses a priority truncation strategy based on the perspective of individuals to filter the population information by priority. Different individuals in the population have dissimilar properties at various times, so the emphasis of generating offspring is also distinct. For this reason, the multistage multi-strategy method is proposed to generate offspring based on different individual information. With the purpose of verifying the feasibility of the algorithm, MMMEA is compared with seven advanced multi-modal multi-objective optimization algorithms (MMOEAs) on 28 test problems. The experimental results show that MMMEA can effectively solve multi-modal multi-objective optimization problems. MMMEA is competitive on most of the test problems.