Neural Combinatorial Optimization via Preference Optimization

Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose Preference Optimization for Combinatorial Optimization (POCO), a training paradigm that leverages solution preferences via objective values. It introduces: (1) an efficient preference pair construction for better explore and exploit solutions, and (2) a novel loss function that adaptively scales gradients via objective differences, removing reliance on reward models or reference policies. Experiments on Job-Shop Scheduling (JSP), Traveling Salesman (TSP), and Flexible Job-Shop Scheduling (FJSP) show POCO outperforms state-of-the-art neural methods, reducing optimality gaps impressively with efficient inference. POCO is architecture-agnostic, enabling seamless integration with existing NCO models, and establishes preference optimization as a principled framework for combinatorial optimization.