{"title":"Six heuristic algorithms for solving the K-minimum volume ellipsoid (K-MVE) problem","authors":"P. Shcherbakov","doi":"10.35470/2226-4116-2020-9-4-198-205","DOIUrl":null,"url":null,"abstract":"We propose six heuristic methods for finding an approximate solution to the following combinatorial problem: GivenN points in the n-dimensional space, find the minimum-size ellipsoid covering exactly N k of them, where k is much less than N. Various assumptions on the nature of the points and their amount are considered; the results of illustrative numerical experiments with the algorithms are discussed.","PeriodicalId":37674,"journal":{"name":"Cybernetics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cybernetics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35470/2226-4116-2020-9-4-198-205","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We propose six heuristic methods for finding an approximate solution to the following combinatorial problem: GivenN points in the n-dimensional space, find the minimum-size ellipsoid covering exactly N k of them, where k is much less than N. Various assumptions on the nature of the points and their amount are considered; the results of illustrative numerical experiments with the algorithms are discussed.
期刊介绍：
The scope of the journal includes: -Nonlinear dynamics and control -Complexity and self-organization -Control of oscillations -Control of chaos and bifurcations -Control in thermodynamics -Control of flows and turbulence -Information Physics -Cyber-physical systems -Modeling and identification of physical systems -Quantum information and control -Analysis and control of complex networks -Synchronization of systems and networks -Control of mechanical and micromechanical systems -Dynamics and control of plasma, beams, lasers, nanostructures -Applications of cybernetic methods in chemistry, biology, other natural sciences The papers in cybernetics with physical flavor as well as the papers in physics with cybernetic flavor are welcome. Cybernetics is assumed to include, in addition to control, such areas as estimation, filtering, optimization, identification, information theory, pattern recognition and other related areas.
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