# Study of Robust Features in Formulating Guidance for Heuristic Algorithms for Solving the Vehicle Routing Problem

arXiv: https://arxiv.org/abs/2508.06129 · HTML: https://mlsanity.com/paper/2508.06129/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [Neural Networks for Local Search and Crossover in Vehicle Routing: A Possible Overkill?](https://mlsanity.com/paper/2210.12075/) (2022)
- [Learning to repeatedly solve routing problems](https://mlsanity.com/paper/2212.08101/) (2022)
- [MineReduce: an approach based on data mining for problem size reduction](https://mlsanity.com/paper/2005.07415/) (2020)
- [Shapley Based Residual Decomposition for Instance Analysis](https://mlsanity.com/paper/2305.18818/) (2023)
- [Feature-Guided Metaheuristic with Diversity Management for Solving the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2407.20777/) (2024)

## Abstract (arXiv)

The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its NP-Hard nature. Traditionally, these metaheuristics rely on human-crafted designs developed through empirical studies. However, recent research shows that machine learning methods can be used the structural characteristics of solutions in combinatorial optimization, thereby aiding in designing more efficient algorithms, particularly for solving VRP. Building on this advancement, this study extends the previous research by conducting a sensitivity analysis using multiple classifier models that are capable of predicting the quality of VRP solutions. Hence, by leveraging explainable AI, this research is able to extend the understanding of how these models make decisions. Finally, our findings indicate that while feature importance varies, certain features consistently emerge as strong predictors. Furthermore, we propose a unified framework able of ranking feature impact across different scenarios to illustrate this finding. These insights highlight the potential of feature importance analysis as a foundation for developing a guidance mechanism of metaheuristic algorithms for solving the VRP.