A new prediction strategy for dynamic multi-objective optimization using Gaussian Mixture Model

Dynamic multi-objective optimization problems (DMOPs), in which the environments change over time, have attracted many researchers’ attention in recent years. Since the Pareto set (PS) or the Pareto front (PF) can change over time, how to track the movement of the PS or PF is a challenging problem in DMOPs. Over the past few years, lots of methods have been proposed, and the prediction based strategy has been considered the most effective way to track the new PS. However, the performance of most existing prediction strategies depends greatly on the quantity and quality of the historical information and will deteriorate due to non-linear changes, leading to poor results. In this paper, we propose a new prediction method, named MOEA/D-GMM, which incorporates the Gaussian Mixture Model (GMM) into the MOEA/D framework for the prediction of the new PS when changes occur. Since GMM is a powerful non-linear model to accurately fit various data distributions, it can effectively generate solutions with better quality according to the distributions. In the proposed algorithm, a change type detection strategy is first designed to estimate an approximate PS according to different change types. Then, GMM is employed to make a more accurate prediction by training it with the approximate PS. To overcome the shortcoming of a lack of training solutions for GMM, the Empirical Cumulative Distribution Function (ECDF) method is used to resample more training solutions before GMM training. Experimental results on various benchmark test problems and a classical real-world problem show that, compared with some state-of-the-art dynamic optimization algorithms, MOEA/D-GMM outperforms others in most cases.