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A common strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. However, while specific restart strategies have been developed for specific…

Artificial Intelligence · Computer Science 2016-09-14 Tobias Friedrich , Timo Kötzing , Markus Wagner

The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimization problem with the goal to design shifts to cover prearranged bus tours. The objective takes into account the operational cost as well as the satisfaction of drivers.…

Optimization and Control · Mathematics 2026-04-23 Lucas Kletzander , Tommaso Mannelli Mazzoli , Nysret Musliu , Pascal Van Hentenryck

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

The Travelling Salesman Problem (TSP) is a classical NP-hard problem and has broad applications in many disciplines and industries. In a large scale location-based services system, users issue TSP queries concurrently, where a TSP query is…

Artificial Intelligence · Computer Science 2021-04-15 Kangfei Zhao , Shengcai Liu , Yu Rong , Jeffrey Xu Yu

The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…

Quantum Physics · Physics 2018-05-29 Karthik Srinivasan , Saipriya Satyajit , Bikash K. Behera , Prasanta K. Panigrahi

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

Deep learning approaches have shown promising results in solving routing problems. However, there is still a substantial gap in solution quality between machine learning and operations research algorithms. Recently, another line of research…

Artificial Intelligence · Computer Science 2021-09-20 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , Babak Abbasi , A. K. Qin

Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and…

Quantum Physics · Physics 2025-09-30 Hikaru Wakaura

The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the…

Computational Complexity · Computer Science 2021-02-26 Omar Cheikhrouhou , Ines Khoufi

Evolutionary algorithms excel in solving complex optimization problems, especially those with multiple objectives. However, their stochastic nature can sometimes hinder rapid convergence to the global optima, particularly in scenarios…

Neural and Evolutionary Computing · Computer Science 2024-05-10 Zeyi Wang , Songbai Liu , Jianyong Chen , Kay Chen Tan

In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the…

Discrete Mathematics · Computer Science 2019-08-14 Tuhin Sahai , Adrian Ziessler , Stefan Klus , Michael Dellnitz

In this paper, we present a new mutation operator, Hybrid Mutation (HPRM), for a genetic algorithm that generates high quality solutions to the Traveling Salesman Problem (TSP). The Hybrid Mutation operator constructs an offspring from a…

Neural and Evolutionary Computing · Computer Science 2012-03-23 Otman Abdoun , Chakir Tajani , Jaafar Abouchabka

The traveling salesman problem (TSP) and the graph partitioning problem (GPP) are two important combinatorial optimization problems with many applications. Due to the NP-hardness of these problems, heuristic algorithms are commonly used to…

Data Structures and Algorithms · Computer Science 2025-02-04 Ali Dasdan

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

The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…

Machine Learning · Computer Science 2021-03-05 Xavier Bresson , Thomas Laurent

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

This paper proposes a two-phase framework to solve an optimal multi-target Lambert rendezvous problem. The first phase solves a series of single-target rendezvous problems for all departure-arrival object pairs to generate the elementary…

Optimization and Control · Mathematics 2018-02-21 Jun Bang , Jaemyung Ahn

We introduce a new bounding approach called Continuity* C*, which provides optimality guarantees for the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relaxes the continuity constraints on the agent's tour by partitioning…

Robotics · Computer Science 2024-12-04 Allen George Philip , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

The Multiple Traveling Salesman Problem (MTSP) extends the traveling salesman problem by assigning multiple salesmen to visit a set of targets from a common depot, with each target visited exactly once while minimizing total tour length. A…

Optimization and Control · Mathematics 2026-04-28 Abhay Singh Bhadoriya , Deepjyoti Deka , Kaarthik Sundar

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits…

Robotics · Computer Science 2024-10-28 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset
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