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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

This research proposes a novel indicator-based hybrid evolutionary approach that combines approximate and exact algorithms. We apply it to a new bi-criteria formulation of the travelling thief problem, which is known to the Evolutionary…

Artificial Intelligence · Computer Science 2018-02-08 Junhua Wu , Sergey Polyakovskiy , Markus Wagner , Frank Neumann

We study a new version of the Traveling Salesperson Problem, called \VectorTSP, where the traveler is subject to discrete acceleration constraints, as defined in the paper-and-pencil game Racetrack (also known as Vector Racer). In this…

Data Structures and Algorithms · Computer Science 2025-02-12 Arnaud Casteigts , Mathieu Raffinot , Mikhail Raskin , Jason Schoeters

The travelling salesman problem (TSP) is a popular NP-hard-combinatorial optimization problem that requires finding the optimal way for a salesman to travel through different cities once and return to the initial city. The existing methods…

Quantum Physics · Physics 2026-01-28 Kapil Goswami , Gagan Anekonda Veereshi , Peter Schmelcher , Rick Mukherjee

In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…

Soft Condensed Matter · Physics 2009-10-30 M. Argollo de Menezes , T. J. P. Penna

There has been a growing interest in the evolutionary computation community to compute a diverse set of high-quality solutions for a given optimisation problem. This can provide the practitioners with invaluable information about the…

Neural and Evolutionary Computing · Computer Science 2022-04-07 Adel Nikfarjam , Aneta Neumann , Frank Neumann

The Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate…

Emerging Technologies · Computer Science 2013-03-27 Jeff Jones , Andrew Adamatzky

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

The Thief Orienteering Problem (ThOP) is a multi-component problem that combines features of two classic combinatorial optimization problems: Orienteering Problem and Knapsack Problem. The ThOP is challenging due to the given time…

Artificial Intelligence · Computer Science 2020-09-01 Jonatas B. C. Chagas , Markus Wagner

The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by…

Artificial Intelligence · Computer Science 2022-04-15 Yongliang Lu , Jin-Kao Hao , Qinghua Wu

We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with…

Statistical Mechanics · Physics 2016-03-15 Bo Sun , Blake Leonard , Peter Ronhovde , Zohar Nussinov

This paper presents a new method for solving an orienteering problem (OP) by breaking it down into two parts: a knapsack problem (KP) and a traveling salesman problem (TSP). A KP solver is responsible for picking nodes, while a TSP solver…

Neural and Evolutionary Computing · Computer Science 2023-02-23 Wei Liu , Tao Zhang , Rui Wang , Kaiwen Li , Wenhua Li , Kang Yang

The Traveling Tournament Problem (TTP) is a well-known benchmark problem in the field of tournament timetabling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue,…

Data Structures and Algorithms · Computer Science 2024-04-18 Jingyang Zhao , Mingyu Xiao , Chao Xu

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Data Structures and Algorithms · Computer Science 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

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 Travelling Salesman Problem - TSP is one of the most explored problems in the scientific literature to solve real problems regarding the economy, transportation, and logistics, to cite a few cases. Adapting TSP to solve different…

Neural and Evolutionary Computing · Computer Science 2024-10-29 Carlos Alberto da Silva Junior , Roberto Yuji Tanaka , Luiz Carlos Farias da Silva , Angelo Passaro

The Traveling Tournament Problem (TTP) is a challenging combinatorial optimization problem that has attracted the interest of researchers around the world. This paper proposes an improved search neighbourhood for the TTP that has been…

Data Structures and Algorithms · Computer Science 2010-07-06 Glenn Langford

TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…

Data Structures and Algorithms · Computer Science 2019-11-12 Yang Li , Junbin Gao , Mingyuan Bai , Chengjun Li , Gang Liu

Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel…

Data Structures and Algorithms · Computer Science 2015-04-16 Sergey Polyakovskiy , Frank Neumann

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…

Neural and Evolutionary Computing · Computer Science 2025-01-28 Kael Silva Araújo , Francisco Márcio Barboza