The Heterogeneous Capacitated Vehicle Routing Problem (HCVRP) is an NP-hard combinatorial optimization problem. State-of-the-art neural solvers face difficulties in generalizing to large-scale scenarios after training on small-scale instances. Our experiments reveal that performance degradation is primarily due to the low-rank nature of attention matrix in large-scale instances. This results in insufficient distinction among node features, impacting the accuracy of Markov Decision Processes. Additionally, these models utilize self-attention for vehicle information interaction, but overly incorporate features from others, which suppresses individual features and leads to a deviation from the optimal route. To address these challenges, we propose the Rank-Augmented Neural Solver (RANS), which introduces two key innovations: 1) A simple yet effective mechanism to increase and approximate the upper bound of the attention matrix's rank, enabling the generation of more distinctive node features. 2) A Dual Cross-Attention Module within the vehicle encoder that accurately captures each vehicle's optimal routes while maintaining balanced vehicle collaboration. The experimental results show that RANS performs favorably against the baselines. Notably, when applied to instances with up to 10,000 nodes, RANS achieves an inference time that is merely 13.42% of the best baseline among the neural solvers, while simultaneously reducing the min-max travel time by 23.72%.

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 .

Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning based neural solver, which is primarily featured by an encoder-decoder structured policy. Concretely, on the one hand, a Relativization Filter (RF) is designed to enhance the robustness of the encoder to affine transformations of the instances, so as to potentially improve the quality of the found solutions. On the other hand, a Multi-Attentive Adaptive Active Search (MA3S) is tailored to allow the decoders to strike a balance between the optimality and diversity. Experimental evaluations on benchmark instances demonstrate the superiority of our method over recent neural baselines across different metrics, and its competitive performance against state-of-the-art traditional heuristics with significantly reduced computational time, ranging from 1.3× to 15× faster. Furthermore, we demonstrate that our method can also be applied to the Capacitated Vehicle Routing Problem (CVRP).

Recent advances in neural models have shown considerable promise in solving Traveling Salesman Problems (TSPs) without relying on much hand-crafted engineering. However, while non-autoregressive (NAR) approaches benefit from faster inference through parallelism, they typically deliver solutions of inferior quality compared to autoregressive ones. To enhance the solution quality while maintaining fast inference, we propose DEITSP, a diffusion model with efficient iterations tailored for TSP that operates in a NAR manner. Firstly, we introduce a one-step diffusion model that integrates the controlled discrete noise addition process with self-consistency enhancement, enabling optimal solution prediction through simultaneous denoising of multiple solutions. Secondly, we design a dual-modality graph transformer to bolster the extraction and fusion of features from node and edge modalities, while further accelerating the inference with fewer layers. Thirdly, we develop an efficient iterative strategy that alternates between adding and removing noise to improve exploration compared to previous diffusion methods. Additionally, we devise a scheduling framework to progressively refine the solution space by adjusting noise levels, facilitating a smooth search for optimal solutions. Extensive experiments on real-world and large-scale TSP instances demonstrate that DEITSP performs favorably against existing neural approaches in terms of solution quality, inference latency, and generalization ability.

Learning path recommendation (LPR) aims to provide individualized and effective learning item routes by modeling learners' learning histories and goals, which has been widely considered a essential task in the field of personalized education. Indeed, considerable research efforts have been dedicated to this direction in recent years, focusing on step-based and sequence-based modeling approaches. However, most of existing studies overlook the complementarity between explicit and implicit relationships among knowledge concepts, while failing to harmonize static knowledge structures with dynamic path generation. To this end, in this paper, we propose LIGHT, a knowLedge topology-aware sequence optImization model for enhancing learninG patH recommendaTion. Specifically, we first construct a composite concept graph that incorporates explicit prerequisite relationships and implicit collaborative relationships, achieved by mining interaction statistics and collaborative signals from learners' learning processes. Next, we design a complementary contrastive fusion module to fully capture the interplay between the two relational views of concepts through graph structure learning and contrastive constraints, which enhances the effectiveness of the learned representations. Following this, we introduce a knowledge topology-aware modeling module that integrates structural semantics clustering with candidate path sampling. Finally, we develop a bidirectional sensing path optimization network to deeply model and optimize the sampled paths from a sequential perspective, thereby enhancing modeling efficiency while preserving structural semantics. Extensive experiments on three real-world educational datasets clearly demonstrate the effectiveness of the proposed LIGHT model in the LPR task.

With the widespread adoption of Internet Protocol (IP) communication technology and web-based platforms, cloud manufacturing has become a significant hallmark of Industry 4.0. Integrating graph algorithms into these web-enabled environments is crucial as they facilitate the representation and analysis of complex relationships in manufacturing processes, enabling efficient decision-making and adaptability in dynamic environments. As a key scheduling problem in cloud manufacturing, the flexible job-shop scheduling problem (FJSP) finds extensive applications in real-world scenarios. However, traditional FJSP-solving methods struggle to meet the efficiency and adaptability demands of cloud manufacturing due to generalization issues and excessive computational time, while reinforcement learning-based methods fail to learn relationships between FJSP nodes, such as interactions between operations of different jobs, leading to limited interpretability and performance. To address these issues, we propose a dual operation aggregation graph neural network (GNN) for solving FJSP. Specifically, we decouple the disjunctive graph into two distinct graphs, reducing graph density and clarifying relationships between machines and operations, thus enabling more effective aggregation and understanding by neural networks. We develop two distinct graph aggregation methods to minimize the influence of non-critical machine and operation nodes on decision-making while enhancing the model's ability to account for long-term benefits. Additionally, to achieve more accurate multi-objective estimation and mitigate reward sparsity, we design a reward function that simultaneously considers machine efficiency, schedule balance, and makespan minimization. Extensive experimental results on well-known datasets demonstrate that our model outperforms state-of-the-art models and exhibits excellent generalization capabilities, effectively addressing the challenges of cloud manufacturing.

The rise in instant delivery services necessitates efficient route planning in last-mile delivery scenarios, where new orders arrive dynamically and need to be integrated into existing routes. In such contexts, complete re-optimization of routes are not permitted, and node insertion to existing route sequences is the only viable option. However, many existing heuristics for node insertion, such as the Cheapest Insertion (CI) method, are myopic and often result in suboptimal solutions retrospectively. This paper presents Neuro-Ins, an initial yet novel attempt at harnessing a learning-based framework to handle the insertion of new orders for the Pickup and Delivery Problem (PDP). In contrast to CI, which considers only one node at a time for insertion, Neuro-Ins leverages an Attention-Mechanism (AM) based encoder-decoder structure to collectively consider all nodes to be inserted, thereby enhancing the quality of the eventual solution. To further improve the model's representation of the current route, we introduce a position embedding to enrich the node feature embedding with positional information of the route. Experiments on synthetic and real-world datasets demonstrate that Neuro-Ins, trained by PPO, consistently outperforms CI without compromising computational speed, and it also surpasses the performance of state-of-the-art solution methods implemented in the industry. Our findings emphasize the importance of explicitly considering all nodes to be inserted along with the en-route nodes and their positions in the route, showcasing the efficacy of the proposed AM-based framework in optimizing the instant delivery routes.

Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been demonstrated on entirely random problem instances that inadequately capture real-world scenarios. In this paper, we introduce realistic Traveling Salesman Problem (TSP) scenarios relevant to industrial settings and derive the following insights: (1) The optimal next node (or city) to visit often lies within proximity to the current node, suggesting the potential benefits of biasing choices based on current locations. (2) Effectively solving the TSP requires robust tracking of unvisited nodes and warrants succinct grouping strategies. Building upon these insights, we propose integrating a learnable choice layer inspired by Hypernetworks to prioritize choices based on the current location, and a learnable approximate clustering algorithm inspired by the Expectation-Maximization algorithm to facilitate grouping the unvisited cities. Together, these two contributions form a hierarchical approach towards solving the realistic TSP by considering both immediate local neighbourhoods and learning an intermediate set of node representations. Our hierarchical approach yields superior performance compared to both classical and recent transformer models, showcasing the efficacy of the key designs.

Dispatching vehicle fleets to serve flights is a key task in airport ground handling (AGH). Due to the notable growth of flights, it is challenging to simultaneously schedule multiple types of operations (services) for a large number of flights, where each type of operation is performed by one specific vehicle fleet. To tackle this issue, we first represent the operation scheduling as a complex vehicle routing problem and formulate it as a mixed integer linear programming (MILP) model. Then given the graph representation of the MILP model, we propose a learning assisted large neighborhood search (LNS) method using data generated based on real scenarios, where we integrate imitation learning and graph convolutional network (GCN) to learn a destroy operator to automatically select variables, and employ an off-the-shelf solver as the repair operator to reoptimize the selected variables. Experimental results based on a real airport show that the proposed method allows for handling up to 200 flights with 10 types of operations simultaneously, and outperforms state-of-the-art methods. Moreover, the learned method performs consistently accompanying different solvers, and generalizes well on larger instances, verifying the versatility and scalability of our method.

Estimating the time of arrival is a crucial task in intelligent transportation systems. Although considerable efforts have been made to solve this problem, most of them decompose a trajectory into several segments and then compute the travel time by integrating the attributes from all segments. The segment view, though being able to depict the local traffic conditions straightforwardly, is insufficient to embody the intrinsic structure of trajectories on the road network. To overcome the limitation, this study proposes multi-view trajectory representation that comprehensively interprets a trajectory from the segment-, link-, and intersection-views. To fulfill the purpose, we design a hierarchical self-attention network (HierETA) that accurately models the local traffic conditions and the underlying trajectory structure. Specifically, a segment encoder is developed to capture the spatio-temporal dependencies at a fine granularity, within which an adaptive self-attention module is designed to boost performance. Further, a joint link-intersection encoder is developed to characterize the natural trajectory structure consisting of alternatively arranged links and intersections. Afterward, a hierarchy-aware attention decoder is designed to realize a tradeoff between the multi-view spatio-temporal features. The hierarchical encoders and the attentive decoder are simultaneously learned to achieve an overall optimality. Experiments on two large-scale practical datasets show the superiority of HierETA over the state-of-the-arts.

Arriving on time and total travel time are two important properties for vehicle routing. Existing route guidance approaches always consider them independently, because they may conflict with each other. In this article, we develop a semi-decentralized multiagent-based vehicle routing approach where vehicle agents follow the local route guidance by infrastructure agents at each intersection, and infrastructure agents perform the route guidance by solving a route assignment problem. It integrates the two properties by expressing them as two objective terms of the route assignment problem. Regarding arriving on time, it is formulated based on the probability tail model, which aims to maximize the probability of reaching destination before deadline. Regarding total travel time, it is formulated as a weighted quadratic term, which aims to minimize the expected travel time from the current location to the destination based on the potential route assignment. The weight for total travel time is designed to be comparatively large if the deadline is loose. Additionally, we improve the proposed approach in two aspects, including travel time prediction and computational efficiency. Experimental results on real road networks justify its ability to increase the average probability of arriving on time, reduce total travel time, and enhance the overall routing performance.