Blackout DIFUSCO

TL;DR

This paper introduces Blackout Diffusion into the DIFUSCO framework for combinatorial optimization, specifically addressing the Traveling Salesman Problem, by transitioning to a continuous-time model with refined control mechanisms.

Contribution

It is the first application of Blackout Diffusion to combinatorial optimization, proposing a continuous-time diffusion approach with improved scheduling and reverse process techniques.

Findings

Experimental results demonstrate the methods' effectiveness in balancing simplicity and complexity.

The approach offers new insights into diffusion-based combinatorial optimization.

Baseline performance was not exceeded, but the techniques show promise for future improvements.

Abstract

This study explores the integration of Blackout Diffusion into the DIFUSCO framework for combinatorial optimization, specifically targeting the Traveling Salesman Problem (TSP). Inspired by the success of discrete-time diffusion models (D3PM) in maintaining structural integrity, we extend the paradigm to a continuous-time framework, leveraging the unique properties of Blackout Diffusion. Continuous-time modeling introduces smoother transitions and refined control, hypothesizing enhanced solution quality over traditional discrete methods. We propose three key improvements to enhance the diffusion process. First, we transition from a discrete-time-based model to a continuous-time framework, providing a more refined and flexible formulation. Second, we refine the observation time scheduling to ensure a smooth and linear transformation throughout the diffusion process, allowing for a more natural progression of states. Finally, building upon the second improvement, we further enhance the reverse process by introducing finer time slices in regions that are particularly challenging for the model, thereby improving accuracy and stability in the reconstruction phase. Although the experimental results did not exceed the baseline performance, they demonstrate the effectiveness of these methods in balancing simplicity and complexity, offering new insights into diffusion-based combinatorial optimization. This work represents the first application of Blackout Diffusion to combinatorial optimization, providing a foundation for further advancements in this domain. * The code is available for review at https://github.com/Giventicket/BlackoutDIFUSCO.