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This paper reports on the first international competition on AI for the traveling salesman problem (TSP) at the International Joint Conference on Artificial Intelligence 2021 (IJCAI-21). The TSP is one of the classical combinatorial…

In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once,…

Data Structures and Algorithms · Computer Science 2020-10-01 Eranda Cela , Vladimir G. Deineko , Gerhard J. Woeginger

This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformulations that approximate the Euclidean distances and…

Artificial Intelligence · Computer Science 2025-07-08 Hiba Bederina

In the preliminary trajectory design of the multi-target rendezvous problem, a model that can quickly estimate the cost of the orbital transfer is essential. The estimation of the transfer time using solar sail between two arbitrary orbits…

Computational Engineering, Finance, and Science · Computer Science 2019-10-08 Yu Song , Shengping Gong

The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one…

Discrete Mathematics · Computer Science 2025-07-02 Timothée Corsini , Jessica Enright , Laura Larios-Jones , Kitty Meeks

We initiate the study of online routing problems with predictions, inspired by recent exciting results in the area of learning-augmented algorithms. A learning-augmented online algorithm which incorporates predictions in a black-box manner…

Data Structures and Algorithms · Computer Science 2022-07-01 Hsiao-Yu Hu , Hao-Ting Wei , Meng-Hsi Li , Kai-Min Chung , Chung-Shou Liao

We describe a hybrid procedure for solving the traveling salesman problem (TSP) to provable optimality. We first sparsify the instance, and then use a hybrid algorithm that combines a branch-and-cut TSP solver with a Hamiltonian cycle…

Data Structures and Algorithms · Computer Science 2017-05-22 Vladimir Ejov , Michael Haythorpe , Serguei Rossomakhine

We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…

Computational Geometry · Computer Science 2016-03-22 Glencora Borradaile , David Eppstein

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

The orienteering problem (OP) is a combinatorial optimization problem that seeks a path visiting a subset of locations to maximize collected rewards under a limited resource budget. This article presents a systematic PRISMA-based review of…

Optimization and Control · Mathematics 2025-12-19 Songhao Shen , Yufeng Zhou , Qin Lei , Zhibin Wu

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

The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…

Data Structures and Algorithms · Computer Science 2021-04-05 Lucas Porto Maziero , Fábio Luiz Usberti , Celso Cavellucci

Spatial puzzles composed of rigid objects, flexible strings and holes offer interesting domains for reasoning about spatial entities that are common in the human daily-life's activities. The goal of this work is to investigate the automated…

Artificial Intelligence · Computer Science 2019-03-11 Thiago Freitas dos Santos , Paulo E. Santos , Leonardo A. Ferreira , Reinaldo A. C. Bianchi , Pedro Cabalar

This work presents solutions to the Traveling Salesperson Problem with precedence constraints (TSPPC) using Deep Reinforcement Learning (DRL) by adapting recent approaches that work well for regular TSPs. Common to these approaches is the…

Machine Learning · Computer Science 2022-09-20 Christian Löwens , Inaam Ashraf , Alexander Gembus , Genesis Cuizon , Jonas K. Falkner , Lars Schmidt-Thieme

This study proposes an end-to-end framework for solving multi-objective optimization problems (MOPs) using Deep Reinforcement Learning (DRL), that we call DRL-MOA. The idea of decomposition is adopted to decompose the MOP into a set of…

Neural and Evolutionary Computing · Computer Science 2020-04-28 Kaiwen Li , Tao Zhang , Rui Wang

Proper parameter configuration is a prerequisite for the success of Evolutionary Algorithms (EAs). While various adaptive strategies have been proposed, it remains an open question whether all control dimensions contribute equally to…

Neural and Evolutionary Computing · Computer Science 2026-03-24 Hongyu Wang , Yuhan Jing , Yibing Shi , Enjin Zhou , Haotian Zhang , Jialong Shi

The traveling purchaser problem (TPP) is an important combinatorial optimization problem with broad applications. Due to the coupling between routing and purchasing, existing works on TPPs commonly address route construction and purchase…

Optimization and Control · Mathematics 2025-07-03 Haofeng Yuan , Rongping Zhu , Wanlu Yang , Shiji Song , Keyou You , Wei Fan , C. L. Philip Chen

This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in…

Machine Learning · Computer Science 2019-10-15 Chaitanya K. Joshi , Thomas Laurent , Xavier Bresson

Integrated task and motion planning has emerged as a challenging problem in sequential decision making, where a robot needs to compute high-level strategy and low-level motion plans for solving complex tasks. While high-level strategies…

Artificial Intelligence · Computer Science 2018-02-19 Siddharth Srivastava , Nishant Desai , Richard Freedman , Shlomo Zilberstein

Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…

Data Structures and Algorithms · Computer Science 2015-10-16 Yunpeng Li