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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…

Artificial Intelligence · Computer Science 2025-10-09 Fangting Zhou , Attila Lischka , Balazs Kulcsar , Jiaming Wu , Morteza Haghir Chehreghani , Gilbert Laporte

Deep Reinforcement Learning has enabled the learning of policies for complex tasks in partially observable environments, without explicitly learning the underlying model of the tasks. While such model-free methods achieve considerable…

Machine Learning · Computer Science 2017-01-11 Tanmay Shankar , Santosha K. Dwivedy , Prithwijit Guha

This paper introduces a reinforcement learning approach to optimize the Stochastic Vehicle Routing Problem with Time Windows (SVRP), focusing on reducing travel costs in goods delivery. We develop a novel SVRP formulation that accounts for…

Artificial Intelligence · Computer Science 2024-02-16 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

Optimization problems characterized by both discrete and continuous variables are common across various disciplines, presenting unique challenges due to their complex solution landscapes and the difficulty of navigating mixed-variable…

Optimization and Control · Mathematics 2024-06-03 Haoyan Zhai , Qianli Hu , Jiangning Chen

Reinforcement Learning (RL) has emerged as a transformative approach in the domains of automation and robotics, offering powerful solutions to complex problems that conventional methods struggle to address. In scenarios where the problem…

Robotics · Computer Science 2023-09-04 Meraj Mammadov

The Vehicle Routing Problem with Drones (VRPD) seeks to optimize the routing paths for both trucks and drones, where the trucks are responsible for delivering parcels to customer locations, and the drones are dispatched from these trucks…

Computers and Society · Computer Science 2024-04-23 Navid Mohammad Imran , Myounggyu Won

The use of electric vehicles (EV) in the last mile is appealing from both sustainability and operational cost perspectives. In addition to the inherent cost efficiency of EVs, selling energy back to the grid during peak grid demand, is a…

Artificial Intelligence · Computer Science 2022-04-13 Ajay Narayanan , Prasant Misra , Ankush Ojha , Vivek Bandhu , Supratim Ghosh , Arunchandar Vasan

Recent breakthroughs both in reinforcement learning and trajectory optimization have made significant advances towards real world robotic system deployment. Reinforcement learning (RL) can be applied to many problems without needing any…

Robotics · Computer Science 2019-10-23 Guillaume Bellegarda , Katie Byl

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity…

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable,…

Machine Learning · Computer Science 2021-03-22 Thomas D. Barrett , William R. Clements , Jakob N. Foerster , A. I. Lvovsky

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges:…

Reinforcement learning (RL) problems can be challenging without well-shaped rewards. Prior work on provably efficient RL methods generally proposes to address this issue with dedicated exploration strategies. However, another way to tackle…

Machine Learning · Computer Science 2023-06-21 Qiyang Li , Yuexiang Zhai , Yi Ma , Sergey Levine

Online reinforcement learning (RL) algorithms are often difficult to deploy in complex human-facing applications as they may learn slowly and have poor early performance. To address this, we introduce a practical algorithm for incorporating…

Artificial Intelligence · Computer Science 2022-01-03 Tong Mu , Georgios Theocharous , David Arbour , Emma Brunskill

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous…

Machine Learning · Computer Science 2025-09-23 Ido Greenberg , Piotr Sielski , Hugo Linsenmaier , Rajesh Gandham , Shie Mannor , Alex Fender , Gal Chechik , Eli Meirom

The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive…

The inverse reinforcement learning approach to imitation learning is a double-edged sword. On the one hand, it can enable learning from a smaller number of expert demonstrations with more robustness to error compounding than behavioral…

Machine Learning · Computer Science 2024-06-06 Juntao Ren , Gokul Swamy , Zhiwei Steven Wu , J. Andrew Bagnell , Sanjiban Choudhury

We consider the inverse reinforcement learning (IRL) problem, where an unknown reward function of some Markov decision process is estimated based on observed expert demonstrations. In most existing approaches, IRL is formulated and solved…

Machine Learning · Computer Science 2025-06-27 Hao Zhu , Yuan Zhang , Joschka Boedecker

Reinforcement learning (RL) algorithms have demonstrated promising results on complex tasks, yet often require impractical numbers of samples since they learn from scratch. Meta-RL aims to address this challenge by leveraging experience…

Machine Learning · Computer Science 2020-10-28 Russell Mendonca , Abhishek Gupta , Rosen Kralev , Pieter Abbeel , Sergey Levine , Chelsea Finn

Deep reinforcement learning (DRL) has achieved groundbreaking successes in a wide variety of robotic applications. A natural consequence is the adoption of this paradigm for safety-critical tasks, where human safety and expensive hardware…

Robotics · Computer Science 2022-06-22 Davide Corsi , Raz Yerushalmi , Guy Amir , Alessandro Farinelli , David Harel , Guy Katz

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…

Machine Learning · Computer Science 2023-06-21 Jianan Zhou , Yaoxin Wu , Wen Song , Zhiguang Cao , Jie Zhang