SPADE: Solving the Multi-Depot Vehicle Routing Problem with Inter-Depot Routes Using Multi-Agent Deep Reinforcement Learning
Bibliographic record
Abstract
The multi-depot vehicle routing problem with inter-depot routes (MDVRP-IDR) represents a pivotal challenge in route optimization, especially in complex supply chain networks with geographically dispersed distribution hubs. With the recent breakthroughs in deep reinforcement learning (DRL) for addressing combinatorial optimization problems (COPs), this paper introduces a novel multi-agent DRL-based framework, termed SParse Attention encoDer and multi-decodEr (SPDE), designed to tackle this critical and complex variant of the vehicle routing problem. SPDE features a Transformer-style policy network, utilizing a sparse graph to model the connectivity between customers and depots. It employs a graph Transformer model for encoding and learning the relationships between the nodes in this graph. Additionally, an attention-based graph pooling technique is introduced to enable the policy model to effectively capture the graph-level structure of each problem instance with minimal computational overhead. To effectively construct vehicle routes, each beginning and ending at one of the depots, for multi-depot routing with inter-depot connections, a decoding module is proposed, where a dedicated decoder is assigned to each vehicle, acting as an agent in a multi-agent system. Through real-world traffic data from two major Canadian cities, Calgary and Edmonton, experimental evaluations demonstrate that SPDE outperforms state-of-the-art DRL-based and heuristic methods. It reduces travel times while demonstrating superior computational efficiency compared to traditional heuristics. Further experiments validate SPDE’s generalizability in effectively solving larger problem instances.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".