IC/DC: Surpassing Heuristic Solvers in Combinatorial Optimization with Diffusion Models (2411.00003v2)

Abstract: Recent advancements in learning-based combinatorial optimization (CO) methods have shown promising results in solving NP-hard problems 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 Travelling Salesman Problem (TSP). In this paper, we present IC/DC, a CO framework that operates without any supervision. IC/DC is specialized in addressing 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. 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 not only achieves state-of-the-art performance compared to previous learning methods, but also surpasses well-known solvers and heuristic approaches on Asymmetric Traveling Salesman Problem (ATSP).