Vehicle Routing Problems (VRPs) are a class of NP-hard problems ubiquitous in several real-world logistics scenarios that pose significant challenges for optimization. Neural Combinatorial Optimization (NCO) has emerged as a promising alternative to classical approaches, as it can learn fast heuristics to solve VRPs. However, most research works in NCO for VRPs focus on simplified settings, which do not account for asymmetric distances and travel durations that cannot be derived by simple Euclidean distances and unrealistic data distributions, hindering real-world deployment. This work introduces RRNCO (Real Routing NCO) to bridge the gap of NCO between synthetic and real-world VRPs in the critical aspects of both data and modeling. First, we introduce a new, openly available dataset with real-world data containing a diverse dataset of locations, distances, and duration matrices from 100 cities, considering realistic settings with actual routing distances and durations obtained from Open Source Routing Machine (OSRM). Second, we propose a novel approach that efficiently processes both node and edge features through contextual gating, enabling the construction of more informed node embedding, and we finally incorporate an Adaptation Attention Free Module (AAFM) with neural adaptive bias mechanisms that effectively integrates not only distance matrices but also angular relationships between nodes, allowing our model to capture rich structural information. RRNCO achieves state-of-the-art results in real-world VRPs among NCO methods. We make our dataset and code publicly available at https://github.com/ai4co/real-routing-nco.

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.

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.

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, while CVRPSEP shows strong competency for problems with less than 400 customers.

Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination -- a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose an attention encoder-LSTM decoder hybrid model, in which the decoder's hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for coordinated routing of multiple vehicles than the attention-based model.

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 require 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 the 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 to solve 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.