Diffusion Learning-guided Evolution for Large-scale Dynamic Multi-Objective Optimization

Large-scale, dynamic multi-objective optimization problems (LSDMOPs) extend traditional DMOPs into high-dimensional decision spaces, reflecting the growing complexity of real-world dynamic systems. However, the effectiveness of existing dynamic multi-objective evolutionary algorithms is severely limited for LSDMOPs, due to inadequate training data, predictions in unknown environments, and large-scale dynamic search spaces. To address these challenges, we propose a diffusion learning-based evolutionary framework, inspired by the intrinsic analogy between iterative evolution of optimization search and stepwise denoising of diffusion model. Firstly, a new training paradigm is designed to treat evolutionary trajectories of population across environments as a learnable supervised source, thereby constructing rich training data to learn the changing patterns of optimal regions in dynamic fitness landscapes. Secondly, we introduce a trajectory alignment loss which encourages the stepwise denoising process to conform to the true population evolutionary behaviors in terms of spatial exploration, convergence trends, and boundary adaptation. Thirdly, a conditional diffusion model-based evolutionary strategy is proposed, which can gradually control denoising direction and intensity using predefined conditions, thereby generating optimization paths from noise toward Pareto-optimal solutions in a new environment. Experimental results demonstrate that the proposed framework outperforms state-of-the-art designs on a typical dynamic multi-objective test suite and real-world large-scale dynamic scenarios.