COExpander: Adaptive Solution Expansion for Combinatorial Optimization

Despite rapid progress in neural combinatorial optimization (NCO) for solving CO problems (COPs), as the problem scale grows, several bottlenecks persist: 1) solvers of the Global Prediction (GP) paradigm struggle in long-range decisions where the overly smooth intermediate heatmaps impede effective decoding, and 2) solvers of the Local Construction (LC) paradigm are time-consuming and incapable of tackling large instances due to the onerous auto-regressive process. Observing these challenges, we propose a new paradigm named Adaptive Expansion (AE) with its instantiation COExpander, positioned to leverage both advantages of GP and LC. COExpander utilizes informative heatmaps generated by a global predictor, which is learned under the guidance of locally determined partial solutions, to in turn direct the expansion of determined decision variables with adaptive step-sizes. To ensure transparent evaluation, we further take the lead to canonicalize 29 benchmarks spanning 6 popular COPs (MIS, MCl, MVC, MCut, TSP, ATSP) and various scales (50-10K nodes), upon which experiments demonstrate concrete SOTA performance of COExpander over these tasks.