HMOEDA_LLE: A hybrid multi-objective estimation of distribution algorithm combining locally linear embedding

Based on the regularity that: the Pareto set of a continuous m-objectives problem is a piecewise continuous (m-1)-dimensional manifold, a novel hybrid multi-objective optimization algorithm is proposed in this paper. In the early evolutionary stage, traditional crossover and mutation operations are used to produce offspring, in addition, the locally linear embedding (LLE) with small neighbor parameter approach is introduced to learn the local geometry of the manifold. When certain regularity in population´s distribution is detected, new offspring are sampled from the probability models created by the statistical distribution information. An entropy-based criterion is imported to determine the switching time of the two different phases of evolutionary search. The proposed hybrid multi-objective estimation of distribution algorithm combining locally linear embedding (HMOEDA_LLE) adopts several widely used test problems to conduct the comparison experiments with two state-of-the-art multi-objective evolutionary algorithms NSGA-II and RM-MEDA. The simulated results show the effectiveness of the entropy-based criterion and the proposed algorithm has better optimization performance.