Learning Dominant States in Elementary Resource Constrained Shortest Path Problems

In this work, we investigate whether machine learning can be leveraged to identify promising states in dynamic programming algorithms, focusing on Elementary Resource Constrained Shortest Path Problems (ERCSPP). More in detail, we solved 41 single resource instances from SPPRCLIB using iterative relaxation techniques through the PathWyse library, systematically collecting all generated states (i.e. labels). We designed ad-hoc features computable in constant time and constructed two datasets: one containing all generated labels (G) and another with only those inserted into data pools (I), totaling several hundred million labels. Machine learning tools are then employed to explore these datasets, revealing significant patterns between successive relaxations. Leveraging these insights, we propose a normalization approach and apply supervised learning techniques to distinguish dominating states, both within subsequent relaxations of the same problem and in previously unseen instances. Our results demonstrate the effectiveness of this approach on Dataset G, while for Dataset I, performance varies, showing strong results within the same instance but declining for unseen ones. We therefore propose a data-driven policy that leverages trained models to prioritize the extension of promising labels during dynamic programming. Preliminary evaluation shows consistent reductions in the number of extended states across almost all instances, with speedups emerging on larger ones, supporting the viability of data-driven dynamic programming algorithms.