Leveraging Population Dynamics to Steer Efficient Search in Large-Scale Combinatorial Optimization

Abstract

Combinatorial optimization problems pose substantial computational challenges because their feasible solution spaces grow exponentially with problem size. This paper presents a GPU-accelerated augmented Population Annealing Monte Carlo (PAMC) framework for large-scale graph-partitioning problems, with emphasis on Max-Cut and Max-K-Cut. The proposed framework extends conventional PAMC by coupling population-based resampling with two stagnation-driven mechanisms: adaptive temperature control and energy-preserving nonlocal cluster moves. By using population-level optimization history as feedback, these mechanisms regulate the balance between exploration and refinement by reheating stalled populations and enabling collective transitions across locally confined regions of the solution space. Experiments on G-set benchmark instances show that the augmented PAMC framework achieves competitive or lower time-to-solution than reported state-of-the-art baselines on several large Max-Cut instances, while matching or improving solution quality under comparable runtime budgets. The solver also discovers a new best-known solution for the G63 Max-Cut instance and scales to a fully connected 100,000-spin Ising instance. For Max-3-Cut, the same framework establishes new best-known solutions on 36 G-set instances, demonstrating its applicability beyond binary Ising formulations. These results indicate that feedback-controlled population dynamics provide an effective and scalable strategy for steering stochastic search in large-scale combinatorial optimization.