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This paper investigates an efficient algorithm for trajectory planning problem of autonomous unmanned aerial vehicles which fly over three-dimensional terrains. The proposed algorithm combines convex optimization with disjunctive…

Optimization and Control · Mathematics 2018-07-10 Alireza Babaei , Amirhossein Karimi

This paper is concerned with a Minimum-Time Intercept Problem (MTIP), for which a Dubins vehicle is guided from a position with a prescribed initial orientation angle to intercept a moving target in minimum time. Some geometric properties…

Optimization and Control · Mathematics 2020-12-23 Yuan Zheng , Xueming Shao , Zheng Chen , Wenjie Zhao

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

Optimization and Control · Mathematics 2025-11-17 Roan Talbut , Anthea Monod

Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute…

Optimization and Control · Mathematics 2024-02-07 Bennet Gebken

The control of a Dubins Vehicle when subjected to a loss of control effectiveness in the turning rate is considered. A complex state-space representation is used to model the vehicle dynamics. An adaptive control design is proposed, with…

Systems and Control · Electrical Eng. & Systems 2025-06-25 Daniel Maldonado Naranjo , Anuradha M. Annaswamy

This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A…

Numerical Analysis · Mathematics 2018-11-30 Zhicheng Hu , Keiwei Liang

The $k$-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces $k$ edges of the tour by $k$ other edges, as long as this yields a shorter tour. We…

Data Structures and Algorithms · Computer Science 2023-05-17 Ulrich A. Brodowsky , Stefan Hougardy , Xianghui Zhong

Given a set of $n$ disks of radius $R$ in the Euclidean plane, the Traveling Salesman Problem With Neighborhoods (TSPN) on uniform disks asks for the shortest tour that visits all of the disks. The problem is a generalization of the…

Computational Geometry · Computer Science 2018-09-20 Ioana O. Bercea

A well-studied continuous model of graphs, introduced by Dearing and Francis [Transportation Science, 1974], considers each edge as a continuous unit-length interval of points. For $\delta \geq 0$, we introduce the problem $\delta$-Tour,…

Data Structures and Algorithms · Computer Science 2025-02-25 Fabian Frei , Ahmed Ghazy , Tim A. Hartmann , Florian Hörsch , Dániel Marx

This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency.…

Artificial Intelligence · Computer Science 2025-01-16 Shipei Zhou , Yuandong Ding , Chi Zhang , Zhiguang Cao , Yan Jin

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

This work aims to design an optimization-based controller for a discrete-time Dubins vehicle to approach a target with unknown position as fast as possible by only using bearing measurements. To this end, we propose a bi-objective…

Systems and Control · Electrical Eng. & Systems 2019-08-02 Zhuo Li , Keyou You , Shiji Song , Anke Xue

Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant on the well-known Christofides' algorithm for the TSP, called the Best-of-Many Christofides' algorithm. The algorithm involves…

Data Structures and Algorithms · Computer Science 2015-06-26 Kyle Genova , David P. Williamson

This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics.…

Optimization and Control · Mathematics 2021-03-02 Alexander Weber , Alexander Knoll

We study a variant of the Traveling Salesman Problem, where instead of finding a single tour, we want to find a pair of two edge-disjoint tours whose longer tour is as short as possible. We investigate the Price of Diversity (PoD) for this…

Data Structures and Algorithms · Computer Science 2025-11-25 Mark de Berg , Andrés López Martínez , Frits Spieksma

In this case study, the renowned Travelling Salesmen problem has been studied. Travelling Salesman problem is a most demanding computational problem in Computer Science. The Travelling Salesmen problem has been solved by two different ways…

Artificial Intelligence · Computer Science 2022-03-01 Gyanateet Dutta

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several…

Disordered Systems and Neural Networks · Physics 2009-11-11 David S. Dean , David Lancaster , Satya. N. Majumdar

Navigating dynamic environments requires the robot to generate collision-free trajectories and actively avoid moving obstacles. Most previous works designed path planning algorithms based on one single map representation, such as the…

Robotics · Computer Science 2024-01-17 Zhefan Xu , Yumeng Xiu , Xiaoyang Zhan , Baihan Chen , Kenji Shimada

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

Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…

Combinatorics · Mathematics 2018-09-26 Patrick J. Andersen , Charl J. Ras