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The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing…

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution…

Exploring machine learning techniques for addressing vehicle routing problems has attracted considerable research attention. To achieve decent and efficient solutions, existing deep models for vehicle routing problems are typically trained…

This study addresses a gap in the utilization of Reinforcement Learning (RL) and Machine Learning (ML) techniques in solving the Stochastic Vehicle Routing Problem (SVRP) that involves the challenging task of optimizing vehicle routes under…

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a…

This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to…

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

Complex real-life routing challenges can be modeled as variations of well-known combinatorial optimization problems. These routing problems have long been studied and are difficult to solve at scale. The particular setting may also make…

Many real-world vehicle routing problems involve rich sets of constraints with respect to the capacities of the vehicles, time windows for customers etc. While in recent years first machine learning models have been developed to solve basic…

Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high…

Due to the practical importance of vehicle routing problems (VRP), there exists an ever-growing body of research in algorithms and (meta)heuristics for solving such problems. However, the diversity of VRP domains creates the separate…

Deep reinforcement learning (DRL) has been used to learn effective heuristics for solving complex combinatorial optimisation problem via policy networks and have demonstrated promising performance. Existing works have focused on solving…

In this paper we present a new approach to tackle complex routing problems with an improved state representation that utilizes the model complexity better than previous methods. We enable this by training from temporal differences.…

Despite the extensive research efforts and the remarkable results obtained on Vehicle Routing Problems (VRP) by using algorithms proposed by the Machine Learning community that are partially or entirely based on data-driven analysis, most…

Neural models produce promising results when solving Vehicle Routing Problems (VRPs), but often fall short in generalization. Recent attempts to enhance model generalization often incur unnecessarily large training cost or cannot be…

Motivated by the promising advances of deep-reinforcement learning (DRL) applied to cooperative multi-agent systems we propose a model and learning procedure to solve the Capacitated Multi-Vehicle Routing Problem (CMVRP) with fixed fleet…

In recent years, reinforcement learning (RL) methods have emerged as a promising approach for solving combinatorial problems. Among RL-based models, POMO has demonstrated strong performance on a variety of tasks, including variants of the…

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given…

Vehicle routing problem (VRP) is a typical discrete combinatorial optimization problem, and many models and algorithms have been proposed to solve the VRP and its variants. Although existing approaches have contributed a lot to the…