欧几里得容量车辆路径的迭代巡回划分

IF 0.9 3区 数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Claire Mathieu, Hang Zhou
{"title":"欧几里得容量车辆路径的迭代巡回划分","authors":"Claire Mathieu, Hang Zhou","doi":"10.1002/rsa.21130","DOIUrl":null,"url":null,"abstract":"We give a probabilistic analysis of the unit‐demand Euclidean capacitated vehicle routing problem in the random setting. The objective is to visit all customers using a set of routes of minimum total length, such that each route visits at most k$$ k $$ customers. The best known polynomial‐time approximation is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the solution obtained by the ITP algorithm is arbitrarily close to the optimum when k$$ k $$ is either o(n)$$ o\\left(\\sqrt{n}\\right) $$ or ω(n)$$ \\omega \\left(\\sqrt{n}\\right) $$ , and they asked whether the ITP algorithm was “also effective in the intermediate range”. In this work, we show that the ITP algorithm is at best a (1+c0)$$ \\left(1+{c}_0\\right) $$ ‐approximation, for some positive constant c0$$ {c}_0 $$ , and is at worst a 1.915‐approximation.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"93 1","pages":"1056 - 1075"},"PeriodicalIF":0.9000,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Iterated tour partitioning for Euclidean capacitated vehicle routing\",\"authors\":\"Claire Mathieu, Hang Zhou\",\"doi\":\"10.1002/rsa.21130\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a probabilistic analysis of the unit‐demand Euclidean capacitated vehicle routing problem in the random setting. The objective is to visit all customers using a set of routes of minimum total length, such that each route visits at most k$$ k $$ customers. The best known polynomial‐time approximation is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the solution obtained by the ITP algorithm is arbitrarily close to the optimum when k$$ k $$ is either o(n)$$ o\\\\left(\\\\sqrt{n}\\\\right) $$ or ω(n)$$ \\\\omega \\\\left(\\\\sqrt{n}\\\\right) $$ , and they asked whether the ITP algorithm was “also effective in the intermediate range”. In this work, we show that the ITP algorithm is at best a (1+c0)$$ \\\\left(1+{c}_0\\\\right) $$ ‐approximation, for some positive constant c0$$ {c}_0 $$ , and is at worst a 1.915‐approximation.\",\"PeriodicalId\":54523,\"journal\":{\"name\":\"Random Structures & Algorithms\",\"volume\":\"93 1\",\"pages\":\"1056 - 1075\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-12-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Structures & Algorithms\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/rsa.21130\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Structures & Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/rsa.21130","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 1

摘要

本文对随机环境下的单位需求欧几里得有能力车辆路径问题进行了概率分析。目标是使用一组总长度最小的路线访问所有客户,使得每条路线最多访问k个$$ k $$客户。最著名的多项式时间近似是迭代巡回划分(ITP)算法,由Haimovich和rinoy Kan于1985年提出。他们表明,当k $$ k $$为o(n) $$ o\left(\sqrt{n}\right) $$或ω(n) $$ \omega \left(\sqrt{n}\right) $$时,ITP算法得到的解任意接近最优,并询问ITP算法是否“在中间范围内也有效”。在这项工作中,我们证明了ITP算法最多是(1+c0) $$ \left(1+{c}_0\right) $$‐近似值,对于某些正常数c0 $$ {c}_0 $$,最坏是1.915‐近似值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Iterated tour partitioning for Euclidean capacitated vehicle routing
We give a probabilistic analysis of the unit‐demand Euclidean capacitated vehicle routing problem in the random setting. The objective is to visit all customers using a set of routes of minimum total length, such that each route visits at most k$$ k $$ customers. The best known polynomial‐time approximation is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the solution obtained by the ITP algorithm is arbitrarily close to the optimum when k$$ k $$ is either o(n)$$ o\left(\sqrt{n}\right) $$ or ω(n)$$ \omega \left(\sqrt{n}\right) $$ , and they asked whether the ITP algorithm was “also effective in the intermediate range”. In this work, we show that the ITP algorithm is at best a (1+c0)$$ \left(1+{c}_0\right) $$ ‐approximation, for some positive constant c0$$ {c}_0 $$ , and is at worst a 1.915‐approximation.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Random Structures & Algorithms
Random Structures & Algorithms 数学-计算机:软件工程
CiteScore
2.50
自引率
10.00%
发文量
56
审稿时长
>12 weeks
期刊介绍: It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信