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.

We present the Generative Flow Ant Colony Sampler (GFACS), a novel meta-heuristic method that hierarchically combines amortized inference and parallel stochastic search. Our method first leverages Generative Flow Networks (GFlowNets) to amortize a multi-modal prior distribution over combinatorial solution space that encompasses both high-reward and diversified solutions. This prior is iteratively updated via parallel stochastic search in the spirit of Ant Colony Optimization (ACO), leading to the posterior distribution that generates near-optimal solutions. Extensive experiments across seven combinatorial optimization problems demonstrate GFACS’s promising performances.

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.

Min-max routing problems aim to minimize the maximum tour length among multiple agents as they collaboratively visit all cities, i.e., the completion time. These problems include impactful real-world applications but are known as NP-hard. Existing methods are facing challenges, particularly in large-scale problems that require the coordination of numerous agents to cover thousands of cities. This paper proposes Equity-Transformer to solve large-scale min-max routing problems. First, we model min-max routing problems into sequential planning, reducing the complexity and enabling the use of a powerful Transformer architecture. Second, we propose key inductive biases that ensure equitable workload distribution among agents. The effectiveness of Equity-Transformer is demonstrated through its superior performance in two representative min-max routing tasks: the min-max multi-agent traveling salesman problem (min-max mTSP) and the min-max multi-agent pick-up and delivery problem (min-max mPDP). Notably, our method achieves significant reductions of runtime, approximately 335 times, and cost values of about 53% compared to a competitive heuristic (LKH3) in the case of 100 vehicles with 1,000 cities of mTSP. We provide reproducible source code: https://github.com/kaist-silab/equity-transformer.

This paper proposes Meta-SAGE, a novel approach for improving the scalability of deep reinforcement learning models for combinatorial optimization (CO) tasks. Our method adapts pre-trained models to larger-scale problems in test time by suggesting two components: a scale meta-learner (SML) and scheduled adaptation with guided exploration (SAGE). First, SML transforms the context embedding for subsequent adaptation of SAGE based on scale information. Then, SAGE adjusts the model parameters dedicated to the context embedding for a specific instance. SAGE introduces locality bias, which encourages selecting nearby locations to determine the next location. The locality bias gradually decays as the model is adapted to the target instance. Results show that Meta-SAGE outperforms previous adaptation methods and significantly improves scalability in representative CO tasks. Our source code is available at https://github.com/kaist-silab/meta-sage.