Title: M$^2$GenCO: Multi-task Meta Learning for Generative Combinatorial Optimization
Primary area: learning on graphs and other geometries & topologies
Keywords: Multi-task Neural Combinatorial Optimization, Meta Learning, Generative Models

Abstract: Despite the fast progress, especially recent diffusion-based models for solving Combinatorial Optimization Problems (COPs) on graphs, existing neural solvers mainly learns a narrow task (e.g., uniform TSP) at a time and hardly handle instances with diverse distributions. To fill such gaps, this paper proposes M$^2$GenCO, a multi-task learning paradigm that pioneers the incorporation of generative CO solving into the meta-learning mechanism for graph-based COPs, first formulating "tasks" in meta-learning as distinct problem types instead of instances of the same problem. Additionally, a lightweight graph neural network with a hybrid of task-specific and shared encoding blocks is tailored to instantiate the framework, performing effective joint pre-training on a variety of problem types and efficient fine-tuning to adapt for out-of-distribution scenarios. Further, we establish a comprehensive benchmark comprising 5 classic graph-based COPs with varying scales and multiple distributions, forming 38 distinct test datasets that facilitate standard evaluation of generalizability and adaptability for neural CO solvers, which has not been well developed in literature. Empirically, M$^2$GenCO with only greedy decoders yields an overall 9.16% performance gain with an average 95.6$\times$ acceleration for inference, and achieves concrete state-of-the-arts on all test sets with simple local searchers, maintaining superior solving time against previous neural methods. Meanwhile, the resource and time consumption for training are saved by up to 82\% and 91\%, respectively.