Recently, neural-guided heuristic algorithms have demonstrated significant advancements in addressing Combinatorial Optimization Problems (COPs). However, these approaches exhibit limitations with respect to their generalizability, and the thoroughness of the exploration within the combinatorial space. In response, this paper introduces the Mixture of Experts Ant Colony Sampler (MoEACS), a nonautoregressive heuristic algorithm guided by deep graph neural network. MoEACS incorporates a Mixture of Experts (MoE) architecture to facilitate the construction of diverse heuristic learners (i.e. experts), thereby diversifying the heuristic generation to enhance the Ant Colony Optimization (ACO) algorithm, an established meta-heuristic algorithm. Furthermore, we propose a novel inference strategy that enhances the search for superior solutions within combinatorial space by preheating the pheromone. Experimental results demonstrate that the MoEACS approach outperforms state-of-the-art (SOTA) ACO across diverse real-world datasets and seven different COPs and achieves performance levels comparable to tailored problem-specific methods in vehicle routing problems. Our source code is available at https://github.com/RenJ-wang/MoEACS .