Entropy determined hybrid two-stage multi-objective evolutionary algorithm combining locally linear embedding

For some probabilistic model-based multi-objective evolutionary algorithms (MOEAs), the probability model established may not accurate enough due to the lack of effective distribution information in the early evolutionary stage. To improve this problem, a novel hybrid multi-objective optimization algorithm is proposed in this paper. Specifically, traditional crossover and mutation operation are used in the early evolutionary stage to explore the promising search areas. Moreover, the locally linear embedding (LLE) with low neighbor parameter approach is involved to enhance the exploitation ability of the proposed algorithm. In addition, an entropy-based criterion is introduced to judge whether certain regularity is presented in population's distribution. The probabilistic model-based approach will be used to reproduce new offspring if some certain regularity is presented. The hybrid two-stage multi-objective evolutionary algorithm proposed in this paper is called entropy determined hybrid two-stage multi-objective evolutionary algorithm combining locally linear embedding (EHMOEA_LLE). To verify the performance of EHMOEA_LLE, several test problems used widely are employed to conduct the comparison experiments with two state-of-the-art multi-objective evolutionary algorithms NSGA-II and RM-MEDA. The simulation results show that the entropy-based criterion is effective and the proposed algorithm is better optimization performance.