Nayeli Gast Zepeda

Federico Berto, Chuanbo Hua, Junyoung Park et al. · pku

Combinatorial optimization (CO) is fundamental to several real-world applications, from logistics and scheduling to hardware design and resource allocation. Deep reinforcement learning (RL) has recently shown significant benefits in solving CO problems, reducing reliance on domain expertise and improving computational efficiency. However, the absence of a unified benchmarking framework leads to inconsistent evaluations, limits reproducibility, and increases engineering overhead, raising barriers to adoption for new researchers. To address these challenges, we introduce RL4CO, a unified and extensive benchmark with in-depth library coverage of 27 CO problem environments and 23 state-of-the-art baselines. Built on efficient software libraries and best practices in implementation, RL4CO features modularized implementation and flexible configurations of diverse environments, policy architectures, RL algorithms, and utilities with extensive documentation. RL4CO helps researchers build on existing successes while exploring and developing their own designs, facilitating the entire research process by decoupling science from heavy engineering. We finally provide extensive benchmark studies to inspire new insights and future work. RL4CO has already attracted numerous researchers in the community and is open-sourced at https://github.com/ai4co/rl4co.

Chuanbo Hua, Federico Berto, Andre Hottung et al.

Transformer-based models have become the dominant paradigm for neural combinatorial optimization (NCO) of vehicle routing problems (VRPs), yet the role of positional encoding (PE) in these architectures remains largely unexplored. Unlike natural language, where tokens are uniformly spaced on a line, routing solutions exhibit several properties that render standard NLP positional encodings inadequate. In this work, we formalize three such structural properties that a routing-aware PE should respect, namely anisometric node distances, cyclic and direction-aware topology, and hierarchical depot-anchored global multi-route structure, combining them with a unifying design principle of geometric grounding. Guided by these criteria, we analyze and compare PE methods spanning NLP, graph-transformer, and routing-specific families, and propose a hierarchical anisometric PE that combines a distance-indexed, circularly consistent in-route encoding with a depot-anchored angular cross-route encoding. Extensive experiments across diverse VRP variants demonstrate that geometry-grounded PE consistently outperforms index-based alternatives, with gains that transfer across problem variants, model architectures, and distribution shifts.

Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda et al.

This paper introduces RouteFinder, a comprehensive foundation model framework to tackle different Vehicle Routing Problem (VRP) variants. Our core idea is that a foundation model for VRPs should be able to represent variants by treating each as a subset of a generalized problem equipped with different attributes. We propose a unified VRP environment capable of efficiently handling any combination of these attributes. The RouteFinder model leverages a modern transformer-based encoder and global attribute embeddings to improve task representation. Additionally, we introduce two reinforcement learning techniques to enhance multi-task performance: mixed batch training, which enables training on different variants at once, and multi-variant reward normalization to balance different reward scales. Finally, we propose efficient adapter layers that enable fine-tuning for new variants with unseen attributes. Extensive experiments on 48 VRP variants show RouteFinder outperforms recent state-of-the-art learning methods. Our code is publicly available at https://github.com/ai4co/routefinder.

André Hottung, Federico Berto, Chuanbo Hua et al. · pku

Designing high-performing heuristics for vehicle routing problems (VRPs) is a complex task that requires both intuition and deep domain knowledge. Large language model (LLM)-based code generation has recently shown promise across many domains, but it still falls short of producing heuristics that rival those crafted by human experts. In this paper, we propose VRPAgent, a framework that integrates LLM-generated components into a metaheuristic and refines them through a novel genetic search. By using the LLM to generate problem-specific operators, embedded within a generic metaheuristic framework, VRPAgent keeps tasks manageable, guarantees correctness, and still enables the discovery of novel and powerful strategies. Across multiple problems, including the capacitated VRP, the VRP with time windows, and the prize-collecting VRP, our method discovers heuristic operators that outperform handcrafted methods and recent learning-based approaches while requiring only a single CPU core. To our knowledge, \VRPAgent is the first LLM-based paradigm to advance the state-of-the-art in VRPs, highlighting a promising future for automated heuristics discovery.