A research overview of manifold-learning-based multiobjective evolutionary algorithm

Abstract

Manifold learning algorithm can find out the low-dimensional smooth manifold embedded in high-dimensional data. So, in this paper, the manifold learning algorithm is introduced into multiobjective optimisation algorithm for multiobjective optimisation problems MOPs, and a manifold-learning-based multiobjective evolutionary algorithm ML-MOEA is proposed to overcome deficiency of the traditional evolutionary multi-objective optimisation algorithms EMOAs and model-based multi-objective optimisation algorithms MOEAs for reducing dimension of data and mining manifold in the decision space of MOPs, build accurate model, guide algorithm evolution and accelerate convergence. The steps of ML-MOEA is as follows: 1 randomly initialisation; 2 modelling via manifold learning algorithm; 3 extend and reproduction; 4 elite selection; 5 halt or go to step 2. Based on the framework of ML-MOEA, a ML-MOEA via self-organising maps ML-MOEA/SOM and a ML-MOEA via SOM locally linear embedding ML-MOEA/LLE is proposed, and comparison experiment of algorithm performance is done.