We propose a universal Graph Neural Network architecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP). Our architecture can be trained unsupervised with policy gradient descent to generate problem specific heuristics for any CSP in a purely data driven manner. The approach is based on a novel graph representation for CSPs that is both generic and compact and enables us to process every possible CSP instance with one GNN, regardless of constraint arity, relations or domain size. Unlike previous RL-based methods, we operate on a global search action space and allow our GNN to modify any number of variables in every step of the stochastic search. This enables our method to properly leverage the inherent parallelism of GNNs. We perform a thorough empirical evaluation where we learn heuristics for well known and important CSPs from random data, including graph coloring, MaxCut, 3-SAT and MAX-k-SAT. Our approach outperforms prior approaches for neural combinatorial optimization by a substantial margin. It can compete with, and even improve upon, conventional search heuristics on test instances that are several orders of magnitude larger and structurally more complex than those seen during training.
翻译:我们提出一个通用的图形神经网络架构,可以作为任何限制满意度问题(CSP)的端端-2端搜索超常性。我们的架构可以不受政策梯度下降的监管而接受培训,以纯数据驱动的方式,为任何CSP产生问题特定的超常性。我们采取的方法基于一个通用和紧凑的CSP新颖的图形代表,使我们能够用一个GNN处理每一个可能的CSP实例,而不论其限制性、关系或域大小。与以前基于RL的方法不同,我们在全球搜索行动空间运作,允许我们的GNN在随机搜索的每一步骤中修改任何变量。这使我们能够适当地利用GNNS固有的平行性。我们进行了彻底的经验性评估,我们从随机数据(包括图表颜色、MaxCut、3-SAT和MAX-k-SAT)中学习了众所周知和重要的CSP的超常性理论。我们的方法比先前的神经组合组合组合组合组合优化方法大得多。这可以与常规结构搜索相比,甚至改进这些常规结构级搜索比在所看到的结构级测试中要大得多。