Proactive Depot Discovery: A Generative Framework for Flexible Location-Routing

TL;DR

The paper tackles the Location-Routing Problem (LRP) without predefined depot candidates by proposing a generative DRL framework that jointly learns depot generation and route planning from customer requests. It introduces a Depot Generative Model (DGM) with dual modes (exact depot coordinates or Gaussian sampling) and a Multi-depot Location-Routing Attention Model (MDLRAM) as an attention-based critic/end-to-end solver trained via REINFORCE to minimize $ \mathbb{E}[L_{\text{Sel}}(\mathbf{A})]$. DGM optimizes the depot set through an objective $L_{\text{Gen}}(\mathcal{D}) = L_{\text{MDLR}} + \sum_{i,j}[\lambda \max(d_{ij}-l_{\max},0) + \varepsilon \max(l_{\min}-d_{ij},0)]$, with depots constrained to lie in $[0,1] \times [0,1]$ after sigmoid mapping. Experimental results on synthetic and real-world datasets show that the framework yields lower routing costs than random depot generation, while enabling fast batch inference, with Gaussian sampling offering flexibility and exact placement delivering best-case configurations, suggesting strong potential for rapid depot establishment in disaster relief and other dynamic logistics contexts.

Abstract

The Location-Routing Problem (LRP), which combines the challenges of facility (depot) locating and vehicle route planning, is critically constrained by the reliance on predefined depot candidates, limiting the solution space and potentially leading to suboptimal outcomes. Previous research on LRP without predefined depots is scant and predominantly relies on heuristic algorithms that iteratively attempt depot placements across a planar area. Such approaches lack the ability to proactively generate depot locations that meet specific geographic requirements, revealing a notable gap in current research landscape. To bridge this gap, we propose a data-driven generative DRL framework, designed to proactively generate depots for LRP without predefined depot candidates, solely based on customer requests data which include geographic and demand information. It can operate in two distinct modes: direct generation of exact depot locations, and the creation of a multivariate Gaussian distribution for flexible depots sampling. By extracting depots' geographic pattern from customer requests data, our approach can dynamically respond to logistical needs, identifying high-quality depot locations that further reduce total routing costs compared to traditional methods. Extensive experiments demonstrate that, for a same group of customer requests, compared with those depots identified through random attempts, our framework can proactively generate depots that lead to superior solution routes with lower routing cost. The implications of our framework potentially extend into real-world applications, particularly in emergency medical rescue and disaster relief logistics, where rapid establishment and adjustment of depot locations are paramount, showcasing its potential in addressing LRP for dynamic and unpredictable environments.

Figures (4)

• Figure 1: Overview of the Generative DRL framework for Depot Generation in LRP.
• Figure 2: DGM's dual-mode training.
• Figure 3: The feasible LRP solution in this example consists of 6 single routes, which are simultaneously carried out by multiple vehicles. The routes in same color belongs to a same depot. By linking them together, the feasible solution is formulated in points permutation, as an MDP.
• Figure 4: Visualization of Multivariate Gaussian Distribution outputted by DGM based on customer requests (Gray): Predicted Depot Distribution (Blue), and Optimal Depots Identified (Red).