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This paper explores the combination of Reinforcement Learning (RL) and search-based path planners to speed up the optimization of flight paths for airliners, where in case of emergency a fast route re-calculation can be crucial. The…

Artificial Intelligence · Computer Science 2026-02-13 Alberto Luise , Michele Lombardi , Florent Teichteil Koenigsbuch

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

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual,…

Neural and Evolutionary Computing · Computer Science 2023-10-31 Sasan Mahmoudinazlou , Changhyun Kwon

Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained…

Neural and Evolutionary Computing · Computer Science 2020-02-05 Jakob Bossek , Katrin Casel , Pascal Kerschke , Frank Neumann

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…

Artificial Intelligence · Computer Science 2023-11-15 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum…

Quantum Physics · Physics 2025-08-12 Monit Sharma , Hoong Chuin Lau

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in…

Machine Learning · Computer Science 2025-02-25 Ke Li , Fei Liu , Zhengkun Wang , Qingfu Zhang

The Multi-Traveling Salesman Problem (MTSP) is a commonly used mathematical model for multi-agent task allocation. However, as the number of agents and task targets increases, existing optimization-based methods often incur prohibitive…

Systems and Control · Electrical Eng. & Systems 2025-12-01 Xiubin Chen

There has been a growing number of machine learning methods for approximately solving the travelling salesman problem. However, these methods often require solved instances for training or use complex reinforcement learning approaches that…

Machine Learning · Computer Science 2022-07-28 Elīza Gaile , Andis Draguns , Emīls Ozoliņš , Kārlis Freivalds

This paper presents a powerful genetic algorithm(GA) to solve the traveling salesman problem (TSP). To construct a powerful GA, I use edge swapping(ES) with a local search procedure to determine good combinations of building blocks of…

Neural and Evolutionary Computing · Computer Science 2014-02-20 Shujia Liu

Model-free deep-reinforcement-based learning algorithms have been applied to a range of COPs~\cite{bello2016neural}~\cite{kool2018attention}~\cite{nazari2018reinforcement}. However, these approaches suffer from two key challenges when…

Machine Learning · Computer Science 2022-06-01 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , A. K. Qin

This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic…

Quantum Physics · Physics 2024-09-24 Yijiang Ma , Tan Chye Cheah

Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL…

Machine Learning · Computer Science 2025-05-14 Mingjun Pan , Guanquan Lin , You-Wei Luo , Bin Zhu , Zhien Dai , Lijun Sun , Chun Yuan

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

The traveling purchaser problem (TPP) is an important combinatorial optimization problem with broad applications. Due to the coupling between routing and purchasing, existing works on TPPs commonly address route construction and purchase…

Optimization and Control · Mathematics 2025-07-03 Haofeng Yuan , Rongping Zhu , Wanlu Yang , Shiji Song , Keyou You , Wei Fan , C. L. Philip Chen

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a…

The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…

Quantum Physics · Physics 2026-05-28 Alessia Ciacco , Luigi Di Puglia Pugliese , Francesca Guerriero

The traveling salesman problem (TSP) is a fundamental NP-hard optimization problem. Over the past decades, traditional heuristic methods have achieved substantial success in solving TSP, yet their performance, particularly for large-scale…

Neural and Evolutionary Computing · Computer Science 2025-08-26 Haoze Lv , Wenjie Chen , Zhiyuan Wang , Shengcai Liu

The multiple Traveling Salesmen Problem (mTSP) is a general extension of the famous NP-hard Traveling Salesmen Problem (TSP), that there are m (m > 1) salesmen to visit the cities. In this paper, we address the mTSP with both the minsum…

Artificial Intelligence · Computer Science 2022-03-01 Jiongzhi Zheng , Yawei Hong , Wenchang Xu , Wentao Li , Yongfu Chen

Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems…

Neural and Evolutionary Computing · Computer Science 2023-05-31 Jakob Bossek , Aneta Neumann , Frank Neumann