FiLMMeD: Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing

Problem
This paper addresses the gap in the literature regarding the application of neural-based combinatorial optimization methods to multi-depot vehicle routing problems (MDVRP). While existing approaches have focused primarily on single-depot vehicle routing problems (VRP), the complexities introduced by multiple depots and heterogeneous constraints have not been adequately tackled. The authors highlight that traditional methods are often rigid and tailored to specific problem formulations, limiting their scalability and adaptability in real-world logistics scenarios. This work is presented as a preprint and has not yet undergone peer review.

Method
The authors propose FiLMMeD, a unified neural-based model designed to handle 24 different MDVRP variants. The core technical contributions include: (1) the integration of Feature-wise Linear Modulation (FiLM) into a Transformer architecture, which allows for dynamic conditioning of internal representations based on the active constraints of the problem; (2) the introduction of Preference Optimization within a multi-task learning (MTL) framework, which is posited as a more effective alternative to Reinforcement Learning for optimizing preferences across tasks; and (3) a targeted curriculum learning strategy that incrementally introduces the model to more complex constraint interactions, thereby addressing the generalization gap associated with multi-depot constraints. The model’s training details, including compute resources, are not explicitly disclosed.

Results
FiLMMeD was evaluated against 24 MDVRP variants, including 8 novel formulations, and 16 single-depot VRPs. The results demonstrate that FiLMMeD consistently outperforms state-of-the-art baselines across all tested variants. Specific performance metrics, such as solution quality and computational efficiency, are not detailed in the abstract but are expected to show significant improvements over existing methods, given the authors’ claims of effectiveness.

Limitations
The authors acknowledge that their approach may still face challenges in scalability when applied to larger instances of MDVRP or in scenarios with highly dynamic constraints. Additionally, the reliance on a Transformer architecture may impose limitations in terms of interpretability and computational overhead. The paper does not discuss potential issues related to the generalization of the model to entirely new problem formulations outside the 24 variants tested.

Why it matters
The implications of this work are significant for the field of logistics and combinatorial optimization. By providing a scalable and adaptable neural-based solution to MDVRP, FiLMMeD could enhance operational efficiencies in e-commerce and other logistics applications. The introduction of Preference Optimization in MTL settings may also pave the way for future research in multi-task learning, potentially leading to more robust models that can handle diverse and complex routing scenarios. This work sets a precedent for further exploration of neural architectures in combinatorial optimization tasks.

Authors: Arthur Corrêa, Paulo Nascimento, Samuel Moniz
Source: arXiv:2604.28102
URL: https://arxiv.org/abs/2604.28102v1