Evolutionary Direction Learning With Multivariate Gaussian Probabilistic Model for Multiobjective Optimization

In recent years, utilizing data from the evolutionary process of multiobjective evolutionary algorithms (MOEAs) to learn knowledge and guide evolutionary search has become a popular research topic. However, existing knowledge learning (KL) frameworks often suffer from the low quality of collected datasets and the inefficiency of model construction, which significantly limits their effectiveness. To address this issue, this paper proposes a novel evolutionary direction learning (EDL) framework, which aims to learn the evolutionary direction (ED) knowledge for each objective to enhance the population generation of MOEAs. The proposed EDL incorporates an effective data collection method based on objective improvement to generate high-quality datasets, based on which a multivariate Gaussian probabilistic model is employed to learn ED knowledge for each objective through a data fusion modeling approach. Besides, a knowledge assignment method is designed to select the most suitable ED knowledge to guide the evolution of solutions. Experimental results on both synthetic and real-world problems demonstrate that the proposed EDL framework can accelerate the convergence of MOEAs and significantly improve their performance. A comparison of the proposed EDL with three state-of-the-art KL frameworks indicates that EDL is a highly competitive learning framework, achieving superior performance with larger datasets and impressive efficiency.