Neural Embedded Mixed-Integer Optimization for Location-Routing Problems

Waquar Kaleem, Doyoung Lee, Changhyun Kwon, Anirudh Subramanyam

Keywords: neural-embedded optimization, location-routing, vehicle-routing, mixed-integer optimization, neural networks

TL;DR: We present NEO-LRP, a neural-embedded optimization framework that integrates neural surrogates into MIP to solve large-scale location-routing problems efficiently and near-optimally.

Abstract: We propose Neural-Embedded Optimization for the Location-Routing Problem (NEO-LRP), which jointly minimizes facility opening and vehicle routing costs. Deep set and graph neural networks are used to predict vehicle routing costs for arbitrary customer subsets and then used as surrogates within a mixed-integer program. This reformulation significantly reduces model complexity and enables an efficient solution. The modular design supports generalization to various vehicle routing variants and constraints. Computational results on benchmark instances show that the proposed method consistently achieves near-optimal location-allocation solutions with significantly lower runtimes compared to state-of-the-art heuristics, making it a practical approach for large-scale location-routing problems.

Submission Number: 12