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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

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

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

We present a trajectory optimization algorithm for the traveling salesman problem (TSP) in graphs of convex sets (GCS). Our framework uses an augmented graph of convex sets to encode the TSP specification and solve it exactly as a shortest…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Gael Luna , Tyler Summers

In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the…

Other Computer Science · Computer Science 2012-04-12 Sing Liew

In this paper we present a variational algorithm for the Traveling Salesman Problem (TSP) that combines (i) a compact encoding of permutations, which reduces the qubit requirement too, (ii) an optimize-freeze-reuse strategy: where the…

Artificial Intelligence · Computer Science 2025-10-29 Fabrizio Fagiolo , Nicolò Vescera

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of $m$ salesmen jointly visit all cities from a set of $n$ cities. The mTSP models many important real-life…

Discrete Mathematics · Computer Science 2022-01-07 Kristóf Bérczi , Matthias Mnich , Roland Vincze

Non-autoregressive neural machine translation (NAT) models are proposed to accelerate the inference process while maintaining relatively high performance. However, existing NAT models are difficult to achieve the desired efficiency-quality…

Computation and Language · Computer Science 2023-03-15 Pei Guo , Yisheng Xiao , Juntao Li , Min Zhang

This paper presents the use of non-autoregressive (NAR) approaches for joint automatic speech recognition (ASR) and spoken language understanding (SLU) tasks. The proposed NAR systems employ a Conformer encoder that applies connectionist…

Audio and Speech Processing · Electrical Eng. & Systems 2023-04-24 Mohan Li , Rama Doddipatla

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into…

Data Structures and Algorithms · Computer Science 2012-02-15 Daniel Karapetyan , Gregory Gutin

Transformers have recently dominated the ASR field. Although able to yield good performance, they involve an autoregressive (AR) decoder to generate tokens one by one, which is computationally inefficient. To speed up inference,…

Sound · Computer Science 2023-03-31 Zhifu Gao , Shiliang Zhang , Ian McLoughlin , Zhijie Yan

Most of the recent studies tackling routing problems like the Traveling Salesman Problem (TSP) with machine learning use a transformer or Graph Neural Network (GNN) based encoder architecture. However, many of them apply these encoders…

Machine Learning · Computer Science 2024-03-28 Attila Lischka , Jiaming Wu , Rafael Basso , Morteza Haghir Chehreghani , Balázs Kulcsár

Non-autoregressive (NAR) machine translation has recently achieved significant improvements, and now outperforms autoregressive (AR) models on some benchmarks, providing an efficient alternative to AR inference. However, while AR…

Computation and Language · Computer Science 2021-12-17 Sweta Agrawal , Julia Kreutzer , Colin Cherry

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

The Travelling Salesman Problem (TSP) is one of the most famous optimization problems. The Genetic Algorithm (GA) is one of metaheuristics that have been applied to TSP. The Crossover and mutation operators are two important elements of GA.…

Neural and Evolutionary Computing · Computer Science 2015-04-13 Hassan Ismkhan , Kamran Zamanifar

The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with…

Optimization and Control · Mathematics 2021-09-30 Ulrich Pferschy , Rostislav Stanek

Traveling Salesman Problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number…

Disordered Systems and Neural Networks · Physics 2023-02-13 Mykhaylo Balinskiy , Alexander Khitun

Non-autoregressive translation (NAT) models, which remove the dependence on previous target tokens from the inputs of the decoder, achieve significantly inference speedup but at the cost of inferior accuracy compared to autoregressive…

Computation and Language · Computer Science 2018-12-27 Junliang Guo , Xu Tan , Di He , Tao Qin , Linli Xu , Tie-Yan Liu

The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid…

Quantum Physics · Physics 2025-10-01 Christos Lytrosyngounis , Ioannis Lytrosyngounis

In the landscape of Recommender System (RS) applications, reinforcement learning (RL) has recently emerged as a powerful tool, primarily due to its proficiency in optimizing long-term rewards. Nevertheless, it suffers from instability in…

Information Retrieval · Computer Science 2024-06-11 Ziru Liu , Shuchang Liu , Zijian Zhang , Qingpeng Cai , Xiangyu Zhao , Kesen Zhao , Lantao Hu , Peng Jiang , Kun Gai