Solving Combinatorial Optimization Problem Over Graph Through QUBO Transformation and Deep Reinforcement Learning

Tianle Pu, Chao Chen, Li Zeng, Shixuan Liu, Rui Sun, Changjun Fan

Abstract: Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs). Many ad-hoc deep learning methods have been proposed to solve these problems, but there still lacks an effective unified framework. In this work, we take a step towards this goal by designing an unified end-to-end deep reinforcement learning framework named CONQUER. CONQUER first translates various COPs into the unified QUBO (Quadratic Unconstrained Binary Optimization) formalization, and afterwards trains a neural QUBO solver to search high-quality strategies, which are then checked and repaired to obtain the solutions for original COPs. The QUBO solver is a purely data-driven neural model, which does not rely on any expert inputs. We adopt the graph transformer network to represent the QUBO graph, so as to effectively capture the features of problem objective and constraints. The Deep Q-network is utilized to train the QUBO solver to find long-sighted solution strategies. Despite being trained solely on small synthetic graphs, CONQUER exhibits promising generality on much larger instances, and can be easily adapted to real-world datasets. Experimentally, we show that CONQUER achieves the state-of-the-art performances on four COPs over graphs, including minimum vertex cover, maximum independent set, maximum clique and maximum cut problem.