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Recently, the applications of the methodologies of Reinforcement Learning (RL) to NP-Hard Combinatorial optimization problems have become a popular topic. This is essentially due to the nature of the traditional combinatorial algorithms,…

In this paper, we evaluate the use of Reinforcement Learning (RL) to solve a classic combinatorial optimization problem: the Capacitated Vehicle Routing Problem (CVRP). We formalize this problem in the RL framework and compare two of the…

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…

In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems. This approach has a great potential in practical applications because it allows…

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…

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…

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…

Neural Combinatorial Optimization (NCO) has emerged as a powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance…

Deep neural networks based on reinforcement learning (RL) for solving combinatorial optimization (CO) problems are developing rapidly and have shown a tendency to approach or even outperform traditional solvers. However, existing methods…

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…

Vehicle routing problems (VRPs) constitute a core optimization challenge in modern logistics and supply chain management. The recent neural combinatorial optimization (NCO) has demonstrated superior efficiency over some traditional…

Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when…

In recent years new deep learning approaches to solve combinatorial optimization problems, in particular NP-hard Vehicle Routing Problems (VRP), have been proposed. The most impactful of these methods are sequential neural construction…

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…

Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for…

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack…

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.…

In this paper, we propose a new dataset of Capacitated Vehicle Routing Problem instances which are up to two orders of magnitude larger than those in the currently used benchmarks. Despite these sizes might not have an immediate application…

A key challenge in solving a combinatorial optimization problem is how to guide the agent (i.e., solver) to efficiently explore the enormous search space. Conventional approaches often rely on enumeration (e.g., exhaustive, random, or tabu…

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem with broad applications in logistics and transportation. Real-world CVRPs often involve diverse objectives and complex constraints, such as time windows or…