Unsupervised Training of Diffusion Models for Feasible Solution Generation in Neural Combinatorial Optimization

TL;DR

This paper introduces IC/DC, an unsupervised diffusion model framework for neural combinatorial optimization that directly learns to generate feasible solutions without problem-specific search, achieving state-of-the-art results on complex problems.

Contribution

The paper presents a novel unsupervised diffusion model architecture for combinatorial optimization that eliminates the need for problem-specific heuristics or search processes.

Findings

Achieves state-of-the-art results on PMSP and ATSP

Does not require problem-specific search or heuristics

Effective in complex two-set item problems

Abstract

Recent advancements in neural combinatorial optimization (NCO) methods have shown promising results in generating near-optimal solutions without the need for expert-crafted heuristics. However, high performance of these approaches often rely on problem-specific human-expertise-based search after generating candidate solutions, limiting their applicability to commonly solved CO problems such as Traveling Salesman Problem (TSP). In this paper, we present IC/DC, an unsupervised CO framework that directly trains a diffusion model from scratch. We train our model in a self-supervised way to minimize the cost of the solution while adhering to the problem-specific constraints. IC/DC is specialized in addressing CO problems involving two distinct sets of items, and it does not need problem-specific search processes to generate valid solutions. IC/DC employs a novel architecture capable of capturing the intricate relationships between items, and thereby enabling effective optimization in challenging CO scenarios. IC/DC achieves state-of-the-art performance relative to existing NCO methods on the Parallel Machine Scheduling Problem (PMSP) and Asymmetric Traveling Salesman Problem (ATSP).