A New Prediction Strategy for Dynamic Multi-objective Optimization Using Diffusion Model

To solve dynamic multi-objective optimization problems (DMOPs), the optimization algorithms are required to track the movement of the Pareto set after the environmental changes effectively. Many prediction-based dynamic multi-objective evolutionary algorithms (DMOEAs) have been proposed to address this challenge by utilizing environmental information for population reinitialization. However, when environmental changes are complex, irregular, and severe, the solutions and information during the evolution process often contain noise, making it difficult for prediction-based DMOEAs to accurately predict and reinitialize the population. To address this issue, we propose a novel dynamic multi-objective evolutionary algorithm (DM-DMOEA) which uses a diffusion model based prediction strategy. In DM-DMOEA, to improve the prediction accuracy, the diffusion model is introduced to extract the relationships of high-quality solutions and reinitialize the population, and a PS estimation method is employed to integrate both historical and new environmental information, providing a set of high-quality solutions for diffusion model training. To speed up the response time, a variational autoencoder (VAE) is used to map the decision space to a latent space, which can reduce the diffusion model size and accelerate the diffusion process. To evaluate the effectiveness of the proposed DM-DMOEA on DMOPs, comprehensive experiments are conducted on several benchmarks and a practical problem. The results show that the DM-DMOEA outperforms other four state-of-the-art DMOEAs in most cases.