  This paper introduces the Generative Flow Ant Colony Sampler (GFACS), a
neural-guided probabilistic search algorithm for solving combinatorial
optimization (CO). GFACS integrates generative flow networks (GFlowNets), an
emerging amortized inference method, with ant colony optimization (ACO), a
promising probabilistic search algorithm. Specifically, we use GFlowNets to
learn a constructive policy in combinatorial spaces for enhancing ACO by
providing an informed prior distribution over decision variables conditioned on
input graph instances. Furthermore, we introduce a novel off-policy training
algorithm for scaling conditional GFlowNets into large-scale combinatorial
spaces by leveraging local search and shared energy normalization. Our
experimental results demonstrate that GFACS outperforms baseline ACO algorithms
in seven CO tasks and is competitive with problem-specific heuristics for
vehicle routing problems.
