{"title":"组合多标准轴向分配问题解决方案时的标准卷积","authors":"L. G. Afraimovich, M. D. Emelin","doi":"10.1134/S0005117924700152","DOIUrl":null,"url":null,"abstract":"<p>This paper is devoted to a classical NP-hard problem, known as the three-index axial assignment problem. Within the corresponding framework, the problem of combining feasible solutions is posed as an assignment problem on the set of solutions containing only the components of selected feasible solutions. The issues of combining solutions for the multicriteria problem with different criteria convolutions are studied. In the general case, the combination problem turns out to be NP-hard. Polynomial solvability conditions are obtained for the combination problem.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":"85 8","pages":"718 - 726"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Criteria Convolutions When Combining the Solutions of the Multicriteria Axial Assignment Problem\",\"authors\":\"L. G. Afraimovich, M. D. Emelin\",\"doi\":\"10.1134/S0005117924700152\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper is devoted to a classical NP-hard problem, known as the three-index axial assignment problem. Within the corresponding framework, the problem of combining feasible solutions is posed as an assignment problem on the set of solutions containing only the components of selected feasible solutions. The issues of combining solutions for the multicriteria problem with different criteria convolutions are studied. In the general case, the combination problem turns out to be NP-hard. Polynomial solvability conditions are obtained for the combination problem.</p>\",\"PeriodicalId\":55411,\"journal\":{\"name\":\"Automation and Remote Control\",\"volume\":\"85 8\",\"pages\":\"718 - 726\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Automation and Remote Control\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0005117924700152\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automation and Remote Control","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1134/S0005117924700152","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Criteria Convolutions When Combining the Solutions of the Multicriteria Axial Assignment Problem
This paper is devoted to a classical NP-hard problem, known as the three-index axial assignment problem. Within the corresponding framework, the problem of combining feasible solutions is posed as an assignment problem on the set of solutions containing only the components of selected feasible solutions. The issues of combining solutions for the multicriteria problem with different criteria convolutions are studied. In the general case, the combination problem turns out to be NP-hard. Polynomial solvability conditions are obtained for the combination problem.
期刊介绍：
Automation and Remote Control is one of the first journals on control theory. The scope of the journal is control theory problems and applications. The journal publishes reviews, original articles, and short communications (deterministic, stochastic, adaptive, and robust formulations) and its applications (computer control, components and instruments, process control, social and economy control, etc.).
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