The Profiled Vehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle–client-specific preferences and constraints, reflecting real‑world requirements such as zone restrictions and service‑level preferences. While recent reinforcement‑learning solvers have shown promising performance, they require retraining for each new profile distribution, suffer from poor representation ability, and struggle to generalize to out‑of‑distribution instances. In this paper, we address these limitations by introducing Unified Solver for Profiled Routing (USPR), a novel framework that natively handles arbitrary profile types. USPR introduces on three key innovations: (i) Profile Embeddings (PE) to encode any combination of profile types; (ii) Multi‑Head Profiled Attention (MHPA), an attention mechanism that models rich interactions between vehicles and clients; (iii) Profile‑aware Score Reshaping (PSR), which dynamically adjusts decoder logits using profile scores to improve generalization. Empirical results on diverse PVRP benchmarks demonstrate that USPR achieves state‑of‑the‑art results among learning‑based methods while offering significant gains in flexibility and computational efficiency. We make our source code publicly available to foster future research.

Effective search methods are crucial for improving the performance of deep generative models at test time. In this paper, we introduce a novel test-time search method, Neural Genetic Search (NGS), which incorporates the evolutionary mechanism of genetic algorithms into the generation procedure of deep models. The core idea behind NGS is its crossover, which is defined as parent-conditioned generation using trained generative models. This approach offers a versatile and easy-to-implement search algorithm for deep generative models. We demonstrate the effectiveness and flexibility of NGS through experiments across three distinct domains: routing problems, adversarial prompt generation for language models, and molecular design.

Combinatorial optimization (CO) is fundamental to several realworld 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 1 .

Combinatorial optimization problems involving multiple agents are notoriously challenging due to their NP-hard nature and the necessity for effective agent coordination. Despite advancements in learning-based methods, existing approaches often face critical limitations, including suboptimal agent coordination, poor generalization, and high computational latency. To address these issues, we propose PARCO (Parallel AutoRegressive Combinatorial Optimization), a general reinforcement learning framework designed to construct high-quality solutions for multi-agent combinatorial tasks efficiently. To this end, PARCO integrates three key novel components: (1) transformer-based communication layers to enable effective agent collaboration during parallel solution construction, (2) a multiple pointer mechanism for low-latency, parallel agent decision-making, and (3) priority-based conflict handlers to resolve decision conflicts via learned priorities. We evaluate PARCO in multi-agent vehicle routing and scheduling problems, where our approach outperforms state-of-the-art learning methods, demonstrating strong generalization ability and remarkable computational efficiency. We make our source code publicly available to foster future research: https://github.com/ai4co/parco.

The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity inequalities (RCIs) are the most fundamental. To generate RCIs, we need to solve the separation problem, whose exact solution takes a long time to obtain; therefore, heuristic methods are widely used. We design a learning-based separation heuristic algorithm with graph coarsening that learns the solutions of the exact separation problem with a graph neural network (GNN), which is trained with small instances of 50 to 100 customers. We embed our separation algorithm within the cutting plane method to find a lower bound for the capacitated VRP (CVRP) with up to 1,000 customers. We compare the performance of our approach with CVRPSEP, a popular separation software package for various cuts used in solving VRPs. Our computational results show that our approach finds better lower bounds than CVRPSEP for large-scale problems with 400 or more customers, whereas CVRPSEP shows strong competency for problems with less than 400 customers. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) [RS-2023-00259550] and the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) [2022-0-01032, Development of Collective Collaboration Intelligence Framework for Internet of Autonomous Things]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0310 .

This paper proposes a reinforcement learning approach for nightly offline rebalancing operations in free-floating electric vehicle sharing systems (FFEVSS). Due to sparse demand in a network, FFEVSS requires relocation of electrical vehicles (EVs) to charging stations and demander nodes, which is typically done by a group of drivers. A shuttle is used to pick up and drop off drivers throughout the network. The objective of this study is to solve the shuttle routing problem to finish the rebalancing work in minimal time. We consider a reinforcement learning framework for the problem, in which a central controller determines the routing policies of a fleet of multiple shuttles. We deploy a policy gradient method for training recurrent neural networks and compare the obtained policy results with heuristic solutions. Our numerical studies show that unlike the existing solutions in the literature, the proposed methods allow solving the general version of the problem with no restrictions on the urban EV network structure and charging requirements of EVs. Moreover, the learned policies offer a wide range of flexibility, resulting in a significant reduction in the time needed to rebalance the network.