Rethinking Efficiency in Neural Combinatorial Optimization: Batched Preference Optimization with Mamba

We study efficiency as a first-class objective in Neural Combinatorial Optimization (NCO) and present ECO, an efficient learning framework that combines batched preference optimization with a Mamba backbone. Instead of tightly interleaving every policy update with on-policy rollouts, ECO decouples trajectory generation from gradient updates through two stages: supervised warm-up on pre-computed solutions and iterative Direct Preference Optimization (DPO) on batched candidate sets generated by the current policy. We pair this learning pipeline with a mixed Mamba encoder-decoder that reduces encoder memory growth and recurrent decoding-state cost on long sequences while retaining the standard autoregressive candidate-scoring step. A local-search-guided bootstrapping strategy is further used during training to widen preference margins and stabilize iterative improvement. Importantly, local search is only used to construct stronger preference pairs during training and is never invoked at inference time. On TSP and CVRP, ECO is best or competitive across most compared neural baselines, with clear advantages in memory usage and throughput. We provide additional analysis on complexity decomposition, permutation sensitivity, evaluation fairness, and the contribution of each design component.