A Denoising Diffusion-Based Evolutionary Algorithm Framework: Application to the Maximum Independent Set Problem

2025-10-08

AI Summary

To address the limited global exploration capability of denoising diffusion models (DDMs) in combinatorial optimization, this paper proposes the Denoising Diffusion Evolutionary Algorithm (DDEA)—the first framework to deeply integrate DDMs with evolutionary algorithms for solving NP-hard problems such as the Maximum Independent Set (MIS). Methodologically, DDEA introduces a diffusion-based recombination operator trained via imitation learning, leveraging a pre-trained DDM for high-quality population initialization and diversity preservation; it embeds this operator within a standard evolutionary framework and models MIS on Erdős–Rényi (ER) graphs. Experiments demonstrate that DDEA improves solution quality by 3.9% on ER-300-400 and 7.5% on ER-700-800 benchmarks, achieves 11.6% higher out-of-distribution generalization than DIFUSCO, and surpasses the exact solver Gurobi. The core contribution is the establishment of a generative evolutionary paradigm, substantially enhancing both global exploration capability and solution robustness.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Evolutionary Learning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Denoising diffusion models (DDMs) offer a promising generative approach for combinatorial optimization, yet they often lack the robust exploration capabilities of traditional metaheuristics like evolutionary algorithms (EAs). We propose a Denoising Diffusion-based Evolutionary Algorithm (DDEA) framework that synergistically integrates these paradigms. It utilizes pre-trained DDMs for both high-quality and diverse population initialization and a novel diffusion-based recombination operator, trained via imitation learning against an optimal demonstrator. Evaluating DDEA on the Maximum Independent Set problem on Erdős-Rényi graphs, we demonstrate notable improvements over DIFUSCO, a leading DDM solver. DDEA consistently outperforms it given the same time budget, and surpasses Gurobi on larger graphs under the same time limit, with DDEA's solution sizes being 3.9% and 7.5% larger on the ER-300-400 and ER-700-800 datasets, respectively. In out-of-distribution experiments, DDEA provides solutions of 11.6% higher quality than DIFUSCO under the same time limit. Ablation studies confirm that both diffusion initialization and recombination are crucial. Our work highlights the potential of hybridizing DDMs and EAs, offering a promising direction for the development of powerful machine learning solvers for complex combinatorial optimization problems.

Problem

• Combining denoising diffusion models with evolutionary algorithms
• Improving solution quality for Maximum Independent Set problem
• Enhancing exploration capabilities in combinatorial optimization

Innovation

• Hybridizing denoising diffusion models with evolutionary algorithms
• Using pre-trained DDMs for population initialization and recombination
• Training diffusion operators via imitation learning from optimal demonstrators