Take a Step and Reconsider: Sequence Decoding for Self-Improved Neural Combinatorial Optimization

The constructive approach within Neural Combinatorial Optimization (NCO) treats a combinatorial optimization problem as a finite Markov decision process, where solutions are built incrementally through a sequence of decisions guided by a neural policy network. To train the policy, recent research is shifting toward a 'self-improved' learning methodology that addresses the limitations of reinforcement learning and supervised approaches. Here, the policy is iteratively trained in a supervised manner, with solutions derived from the current policy serving as pseudo-labels. The way these solutions are obtained from the policy determines the quality of the pseudo-labels. In this paper, we present a simple and problem-independent sequence decoding method for self-improved learning based on sampling sequences without replacement. We incrementally follow the best solution found and repeat the sampling process from intermediate partial solutions. By modifying the policy to ignore previously sampled sequences, we force it to consider only unseen alternatives, thereby increasing solution diversity. Experimental results for the Traveling Salesman and Capacitated Vehicle Routing Problem demonstrate its strong performance. Furthermore, our method outperforms previous NCO approaches on the Job Shop Scheduling Problem.