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Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to…

Artificial Intelligence · Computer Science 2022-02-15 Zizhen Zhang , Zhiyuan Wu , Hang Zhang , Jiahai Wang

Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces…

Artificial Intelligence · Computer Science 2020-06-03 Quentin Cappart , Thierry Moisan , Louis-Martin Rousseau , Isabeau Prémont-Schwarz , Andre Cire

Deep reinforcement learning (DRL)-based combinatorial optimization (CO) methods (i.e., DRL-NCO) have shown significant merit over the conventional CO solvers as DRL-NCO is capable of learning CO solvers less relying on problem-specific…

Machine Learning · Computer Science 2023-01-06 Minsu Kim , Junyoung Park , Jinkyoo Park

We explore the impact of learning paradigms on training deep neural networks for the Travelling Salesman Problem. We design controlled experiments to train supervised learning (SL) and reinforcement learning (RL) models on fixed graph sizes…

Machine Learning · Computer Science 2019-11-01 Chaitanya K. Joshi , Thomas Laurent , Xavier Bresson

This study proposes an end-to-end framework for solving multi-objective optimization problems (MOPs) using Deep Reinforcement Learning (DRL), that we call DRL-MOA. The idea of decomposition is adopted to decompose the MOP into a set of…

Neural and Evolutionary Computing · Computer Science 2020-04-28 Kaiwen Li , Tao Zhang , Rui Wang

Recent advancements in the flexible job-shop scheduling problem (FJSSP) are primarily based on deep reinforcement learning (DRL) due to its ability to generate high-quality, real-time solutions. However, DRL approaches often fail to fully…

Artificial Intelligence · Computer Science 2024-03-15 Imanol Echeverria , Maialen Murua , Roberto Santana

Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning…

Machine Learning · Computer Science 2025-01-03 Qi Li , Zhiguang Cao , Yining Ma , Yaoxin Wu , Yue-Jiao Gong

We introduce Limited Rollout Beam Search (LRBS), a beam search strategy for deep reinforcement learning (DRL) based combinatorial optimization improvement heuristics. Utilizing pre-trained models on the Euclidean Traveling Salesperson…

Machine Learning · Computer Science 2024-12-16 Federico Julian Camerota Verdù , Lorenzo Castelli , Luca Bortolussi

The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…

Machine Learning · Computer Science 2025-01-09 Yong Liang Goh , Wee Sun Lee , Xavier Bresson , Thomas Laurent , Nicholas Lim

Tradable credit schemes (TCS) are an increasingly studied alternative to congestion pricing, given their revenue neutrality and ability to address issues of equity through the initial credit allocation. Modeling TCS to aid future design and…

Machine Learning · Computer Science 2025-04-14 Xiaoyi Wu , Ravi Seshadri , Filipe Rodrigues , Carlos Lima Azevedo

This paper gives a detailed review of reinforcement learning (RL) in combinatorial optimization, introduces the history of combinatorial optimization starting in the 1950s, and compares it with the RL algorithms of recent years. This paper…

Machine Learning · Computer Science 2023-10-04 Yunhao Yang , Andrew Whinston

The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…

Machine Learning · Computer Science 2025-08-13 Michael Li , Eric Bae , Christopher Haberland , Natasha Jaques

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…

Machine Learning · Computer Science 2024-05-24 Chaoyang Wang , Pengzhi Cheng , Jingze Li , Weiwei Sun

Reinforcement Learning (RL) is increasingly applied to large-scale decision-making problems like logistics, scheduling, and recommender systems, but existing algorithms struggle with the curse of dimensionality in such large discrete action…

Machine Learning · Computer Science 2026-05-12 Heiko Hoppe , Fabian Akkerman , Wouter van Heeswijk , Maximilian Schiffer

The collaboration and interaction of multiple robots have become integral aspects of smart manufacturing. Effective planning and management play a crucial role in achieving energy savings and minimising overall costs. This paper addresses…

Robotics · Computer Science 2025-06-16 Ziren Xiao , Ruxin Xiao , Chang Liu , Xinheng Wang

The following interdisciplinary article presents a memetic algorithm with applying deep reinforcement learning (DRL) for solving practically oriented dual resource constrained flexible job shop scheduling problems (DRC-FJSSP). From research…

Machine Learning · Computer Science 2023-07-10 Felix Grumbach , Nour Eldin Alaa Badr , Pascal Reusch , Sebastian Trojahn

Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural…

Machine Learning · Computer Science 2023-12-05 Zhiqing Sun , Yiming Yang

Recent work applying deep reinforcement learning (DRL) to solve traveling salesman problems (TSP) has shown that DRL-based solvers can be fast and competitive with TSP heuristics for small instances, but do not generalize well to larger…

Machine Learning · Computer Science 2021-10-07 Wenbin Ouyang , Yisen Wang , Shaochen Han , Zhejian Jin , Paul Weng

Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…

Artificial Intelligence · Computer Science 2019-10-01 Antoine François , Quentin Cappart , Louis-Martin Rousseau

Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…

Machine Learning · Computer Science 2020-07-21 Wenpeng Wei , Toshiko Aizono
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