Boosting Cross-problem Generalization in Diffusion-Based Neural Combinatorial Solver via Inference Time Adaptation

TL;DR

This paper introduces DIFU-Ada, a training-free inference time adaptation framework that enhances the cross-problem and cross-scale generalization of diffusion-based neural combinatorial solvers, demonstrated on TSP variants.

Contribution

The paper proposes a novel inference-time adaptation method enabling zero-shot transfer of diffusion-based NCO solvers across different problems and scales without additional training.

Findings

Diffusion solver trained on TSP generalizes to PCTSP and OP.

Inference time adaptation achieves competitive zero-shot transfer performance.

Theoretical analysis supports understanding of cross-problem transfer capabilities.

Abstract

Diffusion-based Neural Combinatorial Optimization (NCO) has demonstrated effectiveness in solving NP-complete (NPC) problems by learning discrete diffusion models for solution generation, eliminating hand-crafted domain knowledge. Despite their success, existing NCO methods face significant challenges in both cross-scale and cross-problem generalization, and high training costs compared to traditional solvers. While recent studies on diffusion models have introduced training-free guidance approaches that leverage pre-defined guidance functions for conditional generation, such methodologies have not been extensively explored in combinatorial optimization. To bridge this gap, we propose a training-free inference time adaptation framework (DIFU-Ada) that enables both the zero-shot cross-problem transfer and cross-scale generalization capabilities of diffusion-based NCO solvers without requiring additional training. We provide theoretical analysis that helps understanding the cross-problem transfer capability. Our experimental results demonstrate that a diffusion solver, trained exclusively on the Traveling Salesman Problem (TSP), can achieve competitive zero-shot transfer performance across different problem scales on TSP variants, such as Prize Collecting TSP (PCTSP) and the Orienteering Problem (OP), through inference time adaptation.