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Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe an…

Data Structures and Algorithms · Computer Science 2023-07-17 William Cook , Keld Helsgaun , Stefan Hougardy , Rasmus T. Schroeder

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…

Data Structures and Algorithms · Computer Science 2019-07-23 Samuel C. Gutekunst , David P. Williamson

We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of…

General Mathematics · Mathematics 2026-03-03 Yılmaz Arslanoğlu

The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to…

Artificial Intelligence · Computer Science 2020-05-28 Jakob Bossek , Pascal Kerschke , Heike Trautmann

The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…

Machine Learning · Computer Science 2020-07-08 Yuwen Yang , Jayant Rajgopal

The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in…

Data Structures and Algorithms · Computer Science 2016-12-20 Wenhong Tian

The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…

Optimization and Control · Mathematics 2026-03-30 Steffen Borgwardt , Zachary Sorenson

The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within…

Artificial Intelligence · Computer Science 2015-08-21 Siamak Ravanbakhsh , Reihaneh Rabbany , Russell Greiner

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

Deep learning has shown significant potential in solving combinatorial optimization problems such as the Euclidean traveling salesman problem (TSP). However, most training and test instances for existing TSP algorithms are generated…

Machine Learning · Computer Science 2025-02-04 Xiayang Li , Shihua Zhang

This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…

Computational Complexity · Computer Science 2010-06-14 Carlos Barron-Romero

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

The Traveling Salesperson problem asks for the shortest cyclic tour visiting a set of cities given their pairwise distances and belongs to the NP-hard complexity class, which means that with all known algorithms in the worst case instances…

Disordered Systems and Neural Networks · Physics 2016-10-18 Hendrik Schawe , Alexander K. Hartmann

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

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

For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…

Statistical Mechanics · Physics 2007-05-23 Henri Orland , Michel Bauer

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based…

Discrete Mathematics · Computer Science 2012-06-18 Jean-Guillaume Fages , Xavier Lorca

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

For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today's computation, we employ one…

Data Structures and Algorithms · Computer Science 2022-07-05 Václav Blažej , Pratibha Choudhary , Dušan Knop , Šimon Schierreich , Ondřej Suchý , Tomáš Valla

The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least…

Data Structures and Algorithms · Computer Science 2015-08-11 Kaarthik Sundar , Sivakumar Rathinam