DIFUSCO-LNS: Diffusion-Guided Large Neighbourhood Search for Integer Linear Programming

Shengyu Feng, Zhiqing Sun, Yiming Yang

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Keywords: Large Neighborhood Search, Diffusion Models, Combinatorial Optimization Solvers

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TL;DR: We developed a novel ILP solver that combines the strengths of carefully engineered traditional solvers in symbolic reasoning and the generative power of a neural diffusion model within the Large Neighborhood Search (LNS) framework.

Abstract: Integer Linear Programming (ILP) is a powerful and flexible framework for modeling and solving a variety of combinatorial optimization problems. This paper introduces a novel ILP solver, namely DIFUSCO-LNS, which combines the strengths of carefully engineered traditional solvers in symbolic reasoning and the generative power of a neural diffusion model in graph-based learning for the Large Neighborhood Search (LNS) approach. Our diffusion model treats the destroy policy in LNS as a generative problem in the discrete $\{0, 1\}$-vector space and is trained to imitate the high-quality Local Branching (LB) destroy heuristic through iterative denoising. Specifically, this addresses the unimodal limitation of other neural LNS solvers with its capability to capture the multimodal nature of optimal policies during variable selection. Our evaluations span four representative MIP problems: MIS, CA, SC, and MVC. Experimental results reveal that DIFUSCO-LNS substantially surpasses prior neural LNS solvers.

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Submission Number: 4304