{"title":"A Two-Stage Algorithm for the Dynamic Bin Packing Problem\nwith Placement Groups","authors":"A. V. Ratushnyi, Y. A. Kochetov","doi":"10.1134/S1990478925010090","DOIUrl":null,"url":null,"abstract":"<p> A new dynamic bin packing problem relevant to cloud computing is considered. The\ncreation time, deletion time, and required resources are known for each item (virtual machine).\nThe containers (servers) have a NUMA architecture and specific rules for placing the machines.\nThe servers are grouped into racks, and some machines form groups. Each group is divided into\npartitions. Machines from different partitions cannot be placed on the same rack to ensure system\nfault tolerance. The objective is to pack all the machines into the minimum number of racks over\na given planning horizon. A two-stage algorithm is developed to solve the problem: an initial\nsolution is constructed, where some constraints may be violated, followed by iterative\nimprovement using local search aimed at eliminating the violations. Using the proposed approach,\nan average deviation of 3.8% from the lower bound was achieved on open test cases.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"19 1","pages":"92 - 103"},"PeriodicalIF":0.5800,"publicationDate":"2025-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478925010090","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A new dynamic bin packing problem relevant to cloud computing is considered. The
creation time, deletion time, and required resources are known for each item (virtual machine).
The containers (servers) have a NUMA architecture and specific rules for placing the machines.
The servers are grouped into racks, and some machines form groups. Each group is divided into
partitions. Machines from different partitions cannot be placed on the same rack to ensure system
fault tolerance. The objective is to pack all the machines into the minimum number of racks over
a given planning horizon. A two-stage algorithm is developed to solve the problem: an initial
solution is constructed, where some constraints may be violated, followed by iterative
improvement using local search aimed at eliminating the violations. Using the proposed approach,
an average deviation of 3.8% from the lower bound was achieved on open test cases.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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