Solving Packing Problems by Conditional Query Learning

Neural Combinatorial Optimization (NCO) has shown the potential to solve traditional NP-hard problems recently. Previous studies have shown that NCO outperforms heuristic algorithms in many combinatorial optimization problems such as the routing problems. However, it is less efficient for more complicated problems such as packing, one type of optimization problem that faces mutual conditioned action space. In this paper, we propose a Conditional Query Learning (CQL) method to handle the packing problem for both 2D and 3D settings. By embedding previous actions as a conditional query to the attention model, we design a fully end-to-end model and train it for 2D and 3D packing via reinforcement learning respectively. Through extensive experiments, the results show that our method could achieve lower bin gap ratio and variance for both 2D and 3D packing. Our model improves 7.2% space utilization ratio compared with genetic algorithm for 3D packing (30 boxes case), and reduces more than 10% bin gap ratio in almost every case compared with extant learning approaches. In addition, our model shows great scalability to packing box number. Furthermore, we provide a general test environment of 2D and 3D packing for learning algorithms. All source code of the model and the test environment is released.