We demonstrate that this assumption imposes performance limitations in particular on difficult problem instances.

To this end, we introduce Poppy, a simple training procedure for populations.

Unsupervised learning (UL)-based solvers for combinatorial optimization (CO) train a neural network that generates a soft solution by directly optimizing the CO objective using a continuous relaxation strategy. These solvers offer several advantages over traditional methods and other learning-based methods, particularly for large-scale CO problems.

We introduce Policy Optimization with Multiple Optima (POMO), anend-to-end approach forbuildingsuchaheuristic solver.POMO isapplicable to a wide range of CO problems.

These problems are still dealt9 with hand-crafted heuristics asacommon practice. Traditional heuristic techniques used inOR, however,haveremarkable performance.

GFlowNet policies can efficiently find high-quality solutions.

Fortunately, researchers in operations research (OR) have developed ways to tackle these NP-hard problems in practice, mixed integer programming (MIP) and meta-heuristics being two of the most general and popular approaches.