Training-Free Diffusion-Driven Modeling of Pareto Set Evolution for Dynamic Multiobjective Optimization

TL;DR

This paper introduces DD-DMOEA, a training-free diffusion-based method for dynamic multiobjective optimization that effectively tracks Pareto set evolution without neural training, outperforming existing algorithms in speed and performance.

Contribution

The paper proposes a novel training-free diffusion approach for DMOPs that guides Pareto set evolution using denoising processes and uncertainty-aware adjustments, avoiding neural training.

Findings

DD-DMOEA achieves competitive convergence and diversity.

It provides faster response to environment changes.

Outperforms several state-of-the-art DMOEAs in benchmarks.

Abstract

Dynamic multiobjective optimization problems (DMOPs) feature time-varying objectives, which cause the Pareto optimal solution (POS) set to drift over time and make it difficult to maintain both convergence and diversity under limited response time. Many existing prediction-based dynamic multiobjective evolutionary algorithms (DMOEAs) either depend on learned models with nontrivial training cost or employ one-step population mapping, which may overlook the gradual nature of POS evolution. This paper proposes DD-DMOEA, a training-free diffusion-based dynamic response mechanism for DMOPs. The key idea is to treat the POS obtained in the previous environment as a "noisy" sample set and to guide its evolution toward the current POS through an analytically constructed multi-step denoising process. A knee-point-based auxiliary strategy is used to specify the target region in the new environment, and an explicit probability-density formulation is derived to compute the denoising update without neural training. To reduce the risk of misleading guidance caused by knee-point prediction errors, an uncertainty-aware scheme adaptively adjusts the guidance strength according to the historical prediction deviation. Experiments on the CEC2018 dynamic multiobjective benchmarks show that DD-DMOEA achieves competitive or better convergence-diversity performance and provides faster dynamic response than several state-of-the-art DMOEAs.