Recent advances toward foundation models for routing problems have shown great potential of a unified deep model for various VRP variants. However, they overlook the complex real-world customer distributions. In this work, we advance the Multi-Task VRP (MTVRP) setting to the more realistic yet challenging Multi-Task Multi-Distribution VRP (MTMDVRP) setting, and introduce SHIELD, a novel model that leverages both sparsity and hierarchy principles. Building on a deeper decoder architecture, we first incorporate the Mixture-of-Depths (MoD) technique to enforce sparsity. This improves both efficiency and generalization by allowing the model to dynamically select nodes to use or skip each decoder layer, providing the needed capacity to adaptively allocate computation for learning the task/distribution specific and shared representations. We also develop a context-based clustering layer that exploits the presence of hierarchical structures in the problems to produce better local representations. These two designs inductively bias the network to identify key features that are common across tasks and distributions, leading to significantly improved generalization on unseen ones. Our empirical results demonstrate the superiority of our approach over existing methods on 9 real-world maps with 16 VRP variants each.

We investigate Graph Neural Networks (GNNs) on heterophilous graphs for node classification. To address the scarcity of useful local information in heterophilous neighborhood, it is often essential to explore global interactions. However, many existing methods in this endeavor are computationally expensive and may suffer from issues like oversquashing. In addition, earlier studies show that GNNs can be outperformed by Multi-Layer Perceptrons on heterophilous graphs, indicating insufficient exploitation of node feature information. To address these limitations, we propose Prototype Mediated GNN (PM-GNN), a novel framework which efficiently captures global feature information using class prototypes. PM-GNN learns multiple class prototypes for each class from raw node features with a soft k-means clustering mechanism. These prototypes are then transferred onto node embeddings via explicit message passing, bypassing local neighborhoods and mitigating oversquashing. PM-GNN can scale to large graphs, outperforming strong baselines on multiple heterophilous datasets.

This paper addresses the challenge of object-centric lay-out generation under spatial constraints, seen in multi-ple domains including floorplan design process. The de-sign process typically involves specifying a set of spa-tial constraints that include object attributes like size and inter-object relations such as relative positioning. Existing works, which typically represent objects as single nodes, lack the granularity to accurately model complex interactions between objects. For instance, often only certain parts of an object, like a room's right wall, interact with adjacent objects. To address this gap, we introduce a factor graph based approach with four latent variable nodes for each room, and a factor node for each constraint. The factor nodes represent dependencies among the variables to which they are connected, effectively capturing constraints that are potentially of a higher order. We then develop message-passing on the bipartite graph, forming a factor graph neu-ral network that is trained to produce a floorplan that aligns with the desired requirements. Our approach is simple and generates layouts faithful to the user requirements, demon-strated by a large improvement in IOU scores over existing methods. Additionally, our approach, being inferential and accurate, is well-suited to the practical human-in-the-loop design process where specifications evolve iteratively, offering a practical and powerful tool for AI-guided design.

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.

Sparsity is an established problem for the next Point-of-Interest (POI) recommendation task, where it hinders effective learning of user preferences from the User-POI matrix. However, learning multiple hierarchically related spatial tasks, and visiting relations between users and POIs, can help to alleviate this sparsity problem. In this article, we propose our Hierarchical Multi-Task Graph Recurrent Network (HMT-GRN) approach, which alleviates the sparsity problem by learning different User-Region matrices of lower sparsities in a multi-task setting. We then perform a Hierarchical Beam Search (HBS) on the different region and POI distributions to hierarchically reduce the search space with increasing spatial granularity and predict the next POI. Our HBS provides efficiency gains by reducing the search space, resulting in speedups of 5 to 7 times over an exhaustive approach. In addition, we propose a selectivity layer to predict if the next POI has been visited before by the user to balance between personalization and exploration. Further, we propose a novel Joint Triplet Loss Learning (JTLL) module to learn visited and unvisited relations between users and POIs for the recommendation task. Experimental results on two real-world Location-Based Social Network (LBSN) datasets show that our proposed approach significantly outperforms baseline and the state-of-the-art methods.

Learning which Point-of-Interest (POI) a user will visit next is a challenging task for personalized recommender systems due to the large search space of possible POIs in the region. A recurring problem among existing works that makes it difficult to learn and perform well is the sparsity of the User-POI matrix. In this paper, we propose our Hierarchical Multi-Task Graph Recurrent Network (HMT-GRN) approach, which alleviates the data sparsity problem by learning different User-Region matrices of lower sparsities in a multi-task setting. We then perform a Hierarchical Beam Search (HBS) on the different region and POI distributions to hierarchically reduce the search space with increasing spatial granularity and predict the next POI. Our HBS provides efficiency gains by reducing the search space, resulting in speedups of 5 to 7 times over an exhaustive approach. In addition, we also propose a novel selectivity layer to predict if the next POI has been visited before by the user to balance between personalization and exploration. Experimental results on two real-world Location-Based Social Network (LBSN) datasets show that our model significantly outperforms baseline and the state-of-the-art methods.

Next destination recommendation is an important task in the transportation domain of taxi and ride-hailing services, where users are recommended with personalized destinations given their current origin location. However, recent recommendation works do not satisfy this origin-awareness property, and only consider learning from historical destination locations, without origin information. Thus, the resulting approaches are unable to learn and predict origin-aware recommendations based on the user's current location, leading to sub-optimal performance and poor real-world practicality. Hence, in this work, we study the origin-aware next destination recommendation task. We propose the Spatial-Temporal Origin-Destination Personalized Preference Attention (STOD-PPA) encoder-decoder model to learn origin-origin (OO), destination-destination (DD), and origin-destination (OD) relationships by first encoding both origin and destination sequences with spatial and temporal factors in local and global views, then decoding them through personalized preference attention to predict the next destination. Experimental results on seven real-world user trajectory taxi datasets show that our model significantly outperforms baseline and state-of-the-art methods.

Next Point-of-Interest (POI) recommendation is a longstanding problem across the domains of Location-Based Social Networks (LBSN) and transportation. Recent Recurrent Neural Network (RNN) based approaches learn POI-POI relationships in a local view based on independent user visit sequences. This limits the model's ability to directly connect and learn across users in a global view to recommend semantically trained POIs. In this work, we propose a Spatial-Temporal-Preference User Dimensional Graph Attention Network (STP-UDGAT), a novel explore-exploit model that concurrently exploits personalized user preferences and explores new POIs in global spatial-temporal-preference (STP) neighbourhoods, while allowing users to selectively learn from other users. In addition, we propose random walks as a masked self-attention option to leverage the STP graphs' structures and find new higher-order POI neighbours during exploration. Experimental results on six real-world datasets show that our model significantly outperforms baseline and state-of-the-art methods.