Existing neural solvers for Multi-Objective Combinatorial Optimization Problems (MOCOPs) commonly adopt decomposition-based strategies that scalarize an MOCOP into multiple subproblems associated with distinct weight vectors. However, they either inject weights only once during decoding, limiting weight-conditioned context modeling, or primarily during encoding, causing weight-signal dilution during decoding. Moreover, preference optimization methods rely on purely random sampling to construct solution pairs for training solvers, which often produces less informative pairs and thus leads to low training effectiveness. To better address these limitations, we propose an efficient Weight-Conditioned neural solver (WeCon). Specifically, we design an encoder layer with three attention blocks and our proposed Gated Residual Fusion (GRF) block to facilitate harmonious interaction between instance features and weights, thereby generating informative weight-conditioned context. We further introduce a plug-and-play Residual Fusion (RF) block in the decoder to alleviate weight-signal dilution. Finally, we propose Efficient Preference Optimization (EPO), which constructs high-quality solutions, thereby generating more informative pairs to improve training effectiveness. Experiments on four MOCOP variants across different problem scales and distribution patterns demonstrate that WeCon achieves HyperVolume (HV) values comparable to SOTA solver POCCO-W, while reducing inference time by 40%. Ablation studies validate the contributions of all designs.
Neural combinatorial optimization (NCO) relies on parallel solution sampling for training, yet existing methods fail to fully exploit the rich information latent in a co-sampled solution group. Preference-optimization methods anchor on the single best solution and discard fine-grained quality and structural signal from all other peers-a failure we term gradient signal polarization. Mean-based baselines instead weight peers uniformly, so structurally near-identical peers flood the baseline with redundant information and keep gradient variance high-a failure we term baseline redundancy. We propose SSPO (Structure-Aware Similarity-Weighted Preference Optimization), which scores all B sampled solutions jointly through a dissimilarity-weighted leave-one-out baseline: structurally distinct peers receive higher weight, resolving both failures in a single mechanism. The baseline uses zero-parameter, problem-adaptive solution embeddings built from the encoder's existing node representations. Experiments on TSP, EFL, and JSP benchmarks show consistent gains over prior best-anchor and uniform-weight baselines. A direct comparison against uniform RLOO on TSP and EFL confirms that structure-aware weighting is the primary driver of improvement. The SSPO-trained EFL policy has been deployed in a production facility-location system at JD.com, confirming practical viability at scale.
Combinatorial optimization problems (COPs) underpin many real-world decisions, but their exponentially large search spaces make high-quality solutions costly to obtain. Neural combinatorial optimization (NCO) learns fast construction policies, typically with reinforcement learning (RL), while preference-based NCO improves sample efficiency by learning from relative solution quality. However, existing preference objectives combine two distinct design choices in manually specified, one-size-fits-all formulations: what learning signal to extract from each solution pair and how to weight each pair relative to the sampled set. We present AutoPref, the first LLM-guided framework for automated preference-objective discovery in NCO. AutoPref factorizes the objective into a pairwise loss program, which defines the learning signal, and a set-aware weighting program, which determines each pair's relative contribution. Their composition forms a unified programmatic objective space containing existing preference objectives as special cases. To make its search tractable, we introduce a staged conditional search strategy with behavioral gates that filter inadmissible programs before short-horizon training and evaluation. Across TSP, CVRP, FFSP, and JSSP, AutoPref consistently outperforms strong hand-designed baselines across problem scales, demonstrating the benefits and scalability of automated objective discovery for NCO.
Deep neural networks based on reinforcement learning (RL) for solving combinatorial optimization (CO) problems are developing rapidly and have shown a tendency to approach or even outperform traditional solvers. However, existing methods overlook an important distinction: CO problems differ from other traditional problems in that they focus solely on the optimal solution provided by the model within a specific length of time, rather than considering the overall quality of all solutions generated by the model. In this paper, we propose Leader Reward and apply it during two different training phases of the Policy Optimization with Multiple Optima (POMO) model to enhance the model's ability to generate optimal solutions. This approach is applicable to a variety of CO problems, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP), and the Flexible Flow Shop Problem (FFSP), but also works well with other POMO-based models or inference phase's strategies. We demonstrate that Leader Reward greatly improves the quality of the optimal solutions generated by the model. Specifically, we reduce the POMO's gap to the optimum by more than 100 times on TSP100 with almost no additional computational overhead.