# SSPO: Structure-Aware Similarity-Weighted Preference Optimization for Neural Combinatorial Optimization

arXiv: https://arxiv.org/abs/2608.12443 · HTML: https://mlsanity.com/paper/2608.12443/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 7 of its 14 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 7 of 7)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization](https://mlsanity.com/paper/2503.07580/) (2025)

## Abstract (arXiv)

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 JDmathord.com, confirming practical viability at scale.