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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 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

We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal,…

Optimization and Control · Mathematics 2026-05-04 Max Bannach , Giacomo Acciarini , Dario Izzo

This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the…

Optimization and Control · Mathematics 2016-04-15 Mayank Baranwal , Brian Roehl , Srinivasa M. Salapaka

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

Computational Complexity · Computer Science 2025-09-01 Mrinalkanti Ghosh

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

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…

Data Structures and Algorithms · Computer Science 2012-08-14 Olaf Mersmann , Bernd Bischl , Heike Trautmann , Markus Wagner , Frank Neumann

The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs.…

Data Structures and Algorithms · Computer Science 2015-08-14 Ola Svensson

We analyze two classic variants of the Traveling Salesman Problem using the toolkit of fine-grained complexity. Our first set of results is motivated by the Bitonic TSP problem: given a set of $n$ points in the plane, compute a shortest…

Data Structures and Algorithms · Computer Science 2016-07-12 Mark de Berg , Kevin Buchin , Bart M. P. Jansen , Gerhard Woeginger

We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…

Data Structures and Algorithms · Computer Science 2011-07-07 Sylvia Boyd , René Sitters , Suzanne van der Ster , Leen Stougie

We study the metric $s$-$t$ path Traveling Salesman Problem (TSP). [An, Kleinberg, and Shmoys, STOC 2012] improved on the long standing $\frac{5}{3}$-approximation factor and presented an algorithm that achieves an approximation factor of…

Data Structures and Algorithms · Computer Science 2015-03-17 Zhihan Gao

Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on…

Robotics · Computer Science 2017-08-01 Miroslav Kulich , Roman Sushkov , Libor Přeučil

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

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We…

The Lin-Kernighan-Helsguan (LKH) heuristic is a classic local search algorithm for the Traveling Salesman Problem (TSP). LKH introduces an $\alpha$-value to replace the traditional distance metric for evaluating the edge quality, which…

Data Structures and Algorithms · Computer Science 2025-01-09 Long Wang , Jiongzhi Zheng , Zhengda Xiong , Kun He

The Quadratic Travelling Salesman Problem (QTSP) is to find a least-cost Hamiltonian cycle in an edge-weighted graph, where costs are defined on all pairs of edges such that each edge in the pair is contained in the Hamiltonian cycle. This…

Discrete Mathematics · Computer Science 2019-06-19 Brad Woods , Abraham Punnen

The Traveling Salesperson Problem (TSP) is one of the best-known combinatorial optimisation problems. However, many real-world problems are composed of several interacting components. The Traveling Thief Problem (TTP) addresses such…

Neural and Evolutionary Computing · Computer Science 2020-06-08 Jakob Bossek , Aneta Neumann , Frank Neumann

Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…

Statistical Mechanics · Physics 2023-07-06 Guilherme França , Alessandro Barp , Mark Girolami , Michael I. Jordan

For several combinatorial optimization problems over random structures, the theory of local weak convergence from probability and the cavity method from statistical physics can be used to deduce a recursive equation for the distribution of…

Probability · Mathematics 2014-05-07 Mustafa Khandwawala

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest…

Artificial Intelligence · Computer Science 2026-02-03 Wei Huang , Hanchen Wang , Dong Wen , Wenjie Zhang