Journal ArticleDOI
Spacefilling curves and the planar travelling salesman problem
TLDR
To construct a short tour through points in the plane, the points are sequenced as they appear along a spacefilling curve, so it is easily coded and requires only memory and log operations.Abstract:
To construct a short tour through points in the plane, the points are sequenced as they appear along a spacefilling curve. This heuristic consists essentially of sorting, so it is easily coded and requires only O(N) memory and O(N log N) operations. Its performance is competitive with that of other fast methods.read more
Citations
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The Traveling Salesman Problem: A Case Study in Local Optimization
David S. Johnson,Lyle A. McGeoch +1 more
TL;DR: This chapter discusses how various approaches to combinatorial optimization have been adapted to the TSP and evaluates their relative success in this perhaps atypical domain from both a theoretical and an experimental point of view.
Posted Content
Distributionally Robust Stochastic Optimization with Wasserstein Distance
Rui Gao,Anton J. Kleywegt +1 more
TL;DR: The paper argues that the set of distributions chosen should be chosen to be appropriate for the application at hand, and that some of the choices that have been popular until recently are, for many applications, not good choices.
Journal ArticleDOI
A stochastic and dynamic vehicle routing problem in the Euclidean plane
TL;DR: The model is motivated by applications in which the objective is to minimize the wait for service in a stochastic and dynamically changing environment, a departure from classical vehicle routing problems where one seeks to minimize total travel time in a static, deterministic environment.
Book ChapterDOI
Local Optimization and the Traveling Salesman Problem
TL;DR: This paper surveys the state of the art with respect to the TSP, with emphasis on the performance of traditional local optimization algorithms and their new competitors, and on what insights complexity theory does, or does not, provide.
Journal ArticleDOI
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
TL;DR: It has been over a decade since neural networks were first applied to solve combinatorial optimization problems and the current standing of neural networks for combinatorsial optimization is presented by considering each of the major classes of combinatorially optimization problems.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Journal ArticleDOI
The shortest path through many points
TL;DR: In this paper, it was shown that the length of the shortest closed path through n points in a bounded plane region of area v is almost always asymptotically proportional to √(nv) for large n; and this result was extended to bounded Lebesgue sets in k-dimensional Euclidean space.
Journal ArticleDOI
The Euclidean travelling salesman problem is NP-complete
TL;DR: The Travelling Salesman Problem is shown to be NP-Complete even if its instances are restricted to be realizable by sets of points on the Euclidean plane.
Journal ArticleDOI
Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability
TL;DR: In this article, a limit theorem is established for a class of random processes (called subadditive Euclidean functionals) which arise in problems of geometric probability, such as the length of shortest path through a random sample.
Journal ArticleDOI
Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space
TL;DR: A family of heuristics to solve combinatorial problems such as routing and partitioning that exploit geometry but ignore specific distance measures are described, which seem well-suited to operational problems where time or computing resources are limited.