# Memory-Enhanced Neural Solvers for Routing Problems

arXiv: https://arxiv.org/abs/2406.16424 · HTML: https://mlsanity.com/paper/2406.16424/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 49 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [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)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Self-attention Does Not Need O(n2) Memory](https://mlsanity.com/paper/2112.05682/) (2021)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning](https://mlsanity.com/paper/2010.12367/) (2020)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [Discovered Policy Optimisation](https://mlsanity.com/paper/2210.05639/) (2022)
- [Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2012.10638/) (2020)
- [Efficient Active Search for Combinatorial Optimization Problems](https://mlsanity.com/paper/2106.05126/) (2021)
- [Learning Collaborative Policies to Solve NP-hard Routing Problems](https://mlsanity.com/paper/2110.13987/) (2021)
- [Simulation-guided Beam Search for Neural Combinatorial Optimization](https://mlsanity.com/paper/2207.06190/) (2022)
- [Exploratory Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1909.04063/) (2019)
- [BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2301.03313/) (2023)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization](https://mlsanity.com/paper/2210.03475/) (2022)
- [Learning to schedule job-shop problems: Representation and policy learning using graph neural network and reinforcement learning](https://mlsanity.com/paper/2106.01086/) (2021)
- [Combinatorial Optimization with Policy Adaptation using Latent Space Search](https://mlsanity.com/paper/2311.13569/) (2023)
- [PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimization](https://mlsanity.com/paper/2402.14048/) (2024)
- [Large-Scale Retrieval for Reinforcement Learning](https://mlsanity.com/paper/2206.05314/) (2022)
- [Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimization](https://mlsanity.com/paper/2306.02688/) (2023)
- [Discovering Temporally-Aware Reinforcement Learning Algorithms](https://mlsanity.com/paper/2402.05828/) (2024)
- [Learning to Solve Combinatorial Graph Partitioning Problems via Efficient Exploration](https://mlsanity.com/paper/2205.14105/) (2022)

## Built on by (most cited first, 4 of 4)

- [Breaking the Performance Ceiling in Reinforcement Learning requires Inference Strategies](https://mlsanity.com/paper/2505.21236/) (2025)
- [CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization](https://mlsanity.com/paper/2602.08210/) (2026)
- [Latent Guided Sampling for Combinatorial Optimization](https://mlsanity.com/paper/2506.03672/) (2025)
- [Retrieval-Warmed Energy-Based Reasoning: A Five-Arm Ablation Methodology for Diffusion-as-Inference on Structured Reasoning Tasks](https://mlsanity.com/paper/2606.26476/) (2026)

## Abstract (arXiv)

Routing Problems are central to many real-world applications, yet remain challenging due to their (NP-)hard nature. Amongst existing approaches, heuristics often offer the best trade-off between quality and scalability, making them suitable for industrial use. While Reinforcement Learning (RL) offers a flexible framework for designing heuristics, its adoption over handcrafted heuristics remains incomplete. Existing learned methods still lack the ability to adapt to specific instances and fully leverage the available computational budget. Current best methods either rely on a collection of pre-trained policies, or on RL fine-tuning; hence failing to fully utilize newly available information within the constraints of the budget. In response, we present MEMENTO, an approach that leverages memory to improve the search of neural solvers at inference. MEMENTO leverages online data collected across repeated attempts to dynamically adjust the action distribution based on the outcome of previous decisions. We validate its effectiveness on the Traveling Salesman and Capacitated Vehicle Routing problems, demonstrating its superiority over tree-search and policy-gradient fine-tuning; and showing that it can be zero-shot combined with diversity-based solvers. We successfully train all RL auto-regressive solvers on large instances, and verify MEMENTO's scalability and data-efficiency: pushing the state-of-the-art on 11 out of 12 evaluated tasks.