The practical deployment of Neural Combinatorial Optimization (NCO) for Vehicle Routing Problems (VRPs) is hindered by a critical sim-to-real gap. This gap stems not only from training on oversimplified Euclidean data but also from node-based architectures incapable of handling the node-and-edge-based features with correlated asymmetric cost matrices, such as those for real-world distance and duration. We introduce RRNCO, a novel architecture specifically designed to address these complexities. RRNCO's novelty lies in two key innovations. First, its Adaptive Node Embedding (ANE) efficiently fuses spatial coordinates with real-world distance features using a learned contextual gating mechanism. Second, its Neural Adaptive Bias (NAB) is the first mechanism to jointly model asymmetric distance, duration, and directional angles, enabling it to capture complex, realistic routing constraints. Moreover, we introduce a new VRP benchmark grounded in real-world data crucial for bridging this sim-to-real gap, featuring asymmetric distance and duration matrices from 100 diverse cities, enabling the training and validation of NCO solvers on tasks that are more representative of practical settings. Experiments demonstrate that RRNCO achieves state-of-the-art performance on this benchmark, significantly advancing the practical applicability of neural solvers for real-world logistics.

Quantum circuits are central to implementing quantum algorithms on quantum devices, where quantum gates must be reversible. Many quantum algorithms rely on Boolean functions, which must therefore be implemented reversibly within quantum circuits. Reversible circuit synthesis provides a way to translate such Boolean functions into reversible circuits. Binary decision diagrams (BDDs) offer a scalable approach to this task, but the resulting BDDs and circuits depend heavily on variable ordering. Existing ordering heuristics commonly minimize BDD size because it is closely tied to the circuit size. However, BDD size is an imperfect proxy for the quantum cost of the synthesized circuit (QCC). We propose , an evolutionary framework that uses an LLM as a heuristic generator for QCC-aware BDD variable ordering. Instead of predicting orderings directly, searches over ordering heuristics initialized from multiple heuristic families. Candidate heuristics directly manipulate variable orderings using standard BDD operations and are selected by downstream QCC. The discovered heuristic, HGA-QE, modifies the sifting step inside a genetic algorithm so that the procedure is better aligned with QCC. Across the benchmark set, HGA-QE achieves a 70.9% tie-or-win rate against the per-function best baseline and is strictly best on 13.5% of the functions. The results demonstrate broadly competitive QCC performance, with HGA-QE showing a clearer relative advantage in strict wins on the two benchmark suites drawn from sources different from the data used for heuristic discovery.

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.

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.

Robot navigation is a crucial task with applications to social robots in dynamic human environments. While Reinforcement Learning (RL) has shown great promise for this problem, the policy quality is highly sensitive to the specification of reward functions. Hand-crafted rewards require substantial domain expertise and embed inductive biases that are difficult to audit or adapt, limiting their effectiveness and leading to suboptimal performance. In this paper, we propose EvoNav, an evolutionary framework that automates the design of robot navigation reward functions via large language models (LLMs). To overcome prohibitively costly policy training, EvoNav evaluates each candidate proposal from the LLM via a progressive three-stage warm-up-boost procedure. EvoNav advances from analytical proxies with low-cost surrogates, such as small datasets and analytic rules, to lightweight rollouts and, finally, to full policy training, enabling computationally efficient exploration under effective feedback. Experiment results show that EvoNav produces more effective navigation policies than manually designed RL rewards and state-of-the-art reward design methods.

Trajectory prediction is a crucial task in modeling human behavior, especially in safety-critical fields such as social robotics and autonomous vehicle navigation. Traditional heuristics based on handcrafted rules often lack accuracy, while recently proposed deep learning approaches suffer from computational cost, slow inference speed, lack of explainability, and generalization issues that limit their practical adoption in such environments. In this paper, we introduce TrajEvo, a framework that leverages Large Language Models (LLMs) to automatically design trajectory prediction heuristics. TrajEvo employs an evolutionary algorithm to generate and refine prediction heuristics from past trajectory data. We introduce a Cross-Generation Elite Sampling to promote population diversity and a Statistics Feedback Loop allowing the LLM to analyze alternative predictions. Our evaluations show TrajEvo outperforms previous heuristic methods on various real-world datasets, and remarkably outperforms both heuristics and deep learning methods when generalizing to an unseen real-world dataset. TrajEvo represents a first step toward automated design of fast, explainable, and generalizable trajectory prediction heuristics. We make our source code publicly available to foster future research.

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.

Optimizing LLM-based agentic workflows is challenging for scaling AI capabilities. Current methods rely on coarse, end-to-end evaluation signals and lack fine-grained signals on where to refine, often resulting in inefficient or low-impact modifications. To address these limitations, we propose {\our{}}, an Evaluation-Judge-Optimization-Update pipeline. We incorporate reusable, configurable logic blocks into agentic workflows to capture fundamental forms of logic. On top of this abstraction, we design a dedicated Judge module that inspects execution traces -- particularly failed runs -- and assigns rank-based responsibility scores to problematic blocks. These fine-grained diagnostic signals are then leveraged by an LLM-based optimizer, which focuses modifications on the most problematic block in the workflow. Our approach improves sample efficiency, enhances interpretability through block-level diagnostics, and provides a scalable foundation for automating increasingly complex agentic workflows. We evaluate {\our{}} on mathematical reasoning and code generation benchmarks, where {\our{}} achieves superior performance and efficiency compared to existing methods. The source code is publicly available at https://github.com/ma-zihan/JudgeFlow.

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.

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.

This article addresses the critical challenges of chiplet placement and routing optimization in the era of advanced packaging and heterogeneous integration. We present a novel approach that formulates the problem as a signal integrity (SI)-aware hierarchical Markov decision process (MDP), leveraging the place-to-route (P2R) algorithm. Our method uniquely incorporates the universal chiplet interconnect express (UCIe) eye mask specifications to ensure compliance with datarate-dependent signal integrity requirements. Tested on ten benchmark problems, P2R achieved superior results with an average eye-diagram aperture of 0.869 unit interval (UI) in a single iteration, outperforming random search and deep reinforcement learning (RL) by 44.8%. By addressing the combinatorial complexity and hard constraints inherent in chiplet-based designs, this approach enables optimization while ensuring compliance with industry standards. This work represents a significant advancement in optimizing heterogeneous integrated systems, addressing challenges that conventional placement and routing methods cannot adequately solve.

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.

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.

Multi-Agent Reinforcement Learning (MARL) based Multi-Agent Path Finding (MAPF) has recently gained attention due to its efficiency and scalability. Several MARL-MAPF methods choose to use communication to enrich the information one agent can perceive. However, existing works still struggle in structured environments with high obstacle density and a high number of agents. To further improve the performance of the communication-based MARL-MAPF solvers, we propose a new method, Ensembling Prioritized Hybrid Policies (EPH). We first propose a selective communication block to gather richer information for better agent coordination within multi-agent environments and train the model with a Q-learning-based algorithm. We further introduce three advanced inference strategies aimed at bolstering performance during the execution phase. First, we hybridize the neural policy with single-agent expert guidance for navigating conflict-free zones. Secondly, we propose Q value-based methods for prioritized resolution of conflicts as well as deadlock situations. Finally, we introduce a robust ensemble method that can efficiently collect the best out of multiple possible solutions. We empirically evaluate EPH in complex multi-agent environments and demonstrate competitive performance against state-of-the-art neural methods for MAPF. We open-source our code at https://github.com/ai4co/eph- mapf.

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs). This paper introduces Language Hyper-Heuristics (LHHs), an emerging variant of Hyper-Heuristics that leverages LLMs for heuristic generation, featuring minimal manual intervention and open-ended heuristic spaces. To empower LHHs, we present Reflective Evolution (ReEvo), a novel integration of evolutionary search for efficiently exploring the heuristic space, and LLM reflections to provide verbal gradients within the space. Across five heterogeneous algorithmic types, six different COPs, and both white-box and black-box views of COPs, ReEvo yields state-of-the-art and competitive meta-heuristics, evolutionary algorithms, heuristics, and neural solvers, while being more sample-efficient than prior LHHs.

Deep reinforcement learning offers notable benefits in addressing combinatorial problems over traditional solvers, reducing the reliance on domain-specific knowledge and expert solutions, and improving computational efficiency. Despite the recent surge in interest in neural combinatorial optimization, practitioners often do not have access to a standardized code base. Moreover, different algorithms are frequently based on fragmentized implementations that hinder reproducibility and fair comparison. To address these challenges, we introduce RL4CO, a unified Reinforcement Learning (RL) for Combinatorial Optimization (CO) library. We employ state-of-the-art software and best practices in implementation, such as modularity and configuration management, to be flexible, easily modifiable, and extensible by researchers. Thanks to our unified codebase, we benchmark baseline RL solvers with different evaluation schemes on zero-shot performance, generalization, and adaptability on diverse tasks. Notably, we find that some recent methods may fall behind their predecessors depending on the evaluation settings. We hope RL4CO will encourage the exploration of novel solutions to complex real-world tasks, allowing the community to compare with existing methods through a unified framework that decouples the science from software engineering. We open-source our library at https://github.com/ai4co/rl4co.

Large-scale multi-agent pathfinding (MAPF) presents significant challenges in several areas. As systems grow in complexity with a multitude of autonomous agents operating simultaneously, efficient and collision-free coordination becomes paramount. Traditional algorithms often fall short in scalability, especially in intricate scenarios. Reinforcement Learning (RL) has shown potential to address the intricacies of MAPF; however, it has also been shown to struggle with scalability, demanding intricate implementation, lengthy training, and often exhibiting unstable convergence, limiting its practical application. In this paper, we introduce Heuristics-Informed Multi-Agent Pathfinding (HiMAP), a novel scalable approach that employs imitation learning with heuristic guidance in a decentralized manner. We train on small-scale instances using a heuristic policy as a teacher that maps each single agent observation information to an action probability distribution. During pathfinding, we adopt several inference techniques to improve performance. With a simple training scheme and implementation, HiMAP demonstrates competitive results in terms of success rate and scalability in the field of imitation-learning-only MAPF, showing the potential of imitation-learning-only MAPF equipped with inference techniques.

We study the problem of optimizing biological sequences, e.g., proteins, DNA, and RNA, to maximize a black-box score function that is only evaluated in an offline dataset. We propose a novel solution, bootstrapped training of score-conditioned generator (BootGen) algorithm. Our algorithm repeats a two-stage process. In the first stage, our algorithm trains the biological sequence generator with rank-based weights to enhance the accuracy of sequence generation based on high scores. The subsequent stage involves bootstrapping, which augments the training dataset with self-generated data labeled by a proxy score function. Our key idea is to align the score-based generation with a proxy score function, which distills the knowledge of the proxy score function to the generator. After training, we aggregate samples from multiple bootstrapped generators and proxies to produce a diverse design. Extensive experiments show that our method outperforms competitive baselines on biological sequential design tasks. We provide reproducible source code: https://github.com/kaist-silab/bootgen.

In this paper, we propose FOCA (First-Order Context-based Adaptation), a learning framework to model sets of systems governed by common but unknown laws that differentiate themselves by their context. Inspired by classical modeling-and-identification approaches, FOCA learns to represent the common law through shared parameters and relies on online optimization to compute system-specific context. Due to the online optimization-based context inference, the training of FOCA involves a bi-level optimization problem. To train FOCA efficiently, we utilize an exponential moving average (EMA)-based method that allows for fast training using only first-order derivatives. We test FOCA on polynomial regression and time-series prediction tasks composed of three ODEs and one PDE, empirically finding it outperforms baselines.

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.