DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Park, Sung-Soo | - |
dc.contributor.advisor | 박성수 | - |
dc.contributor.author | Byun, Jong-Ik | - |
dc.contributor.author | 변종익 | - |
dc.date.accessioned | 2011-12-14T02:41:39Z | - |
dc.date.available | 2011-12-14T02:41:39Z | - |
dc.date.issued | 2011 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=466353&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/40674 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 산업및시스템공학과, 2011.2, [ vii, 88 p. ] | - |
dc.description.abstract | In this thesis, we consider the $Chv\acute{a}tal$ -Gomory inequalities for integer programming problem. Although the $Chv\acute{a}tal$ -Gomory inequalities motivated the cutting plane approaches for combinatorial optimization problems, researches focusing on the practical aspects of the $Chv\acute{a}tal$ -Gomory inequalities seem to be limited. The goal of the research is to provide efficient separation procedures to get strong $Chv\acute{a}tal$ -Gomory inequalities for even multiple constraints. As a result, we provide several standard forms of strong rank 1 $Chv\acute{a}tal$ -Gomory inequalities and efficient separation heuristics even with complexity O(n). To begin with, we investigate the separation problem for the rank 1 $Chv\acute{a}tal$ -Gomory inequalities for the integer knapsack problem. First, we develop a dominant relation in the elementary closure for the knapsack problem. Then, we explicitly describe necessary conditions for an inequality to be a nondominated rank 1 $Chv\acute{a}tal$ -Gomory inequality for the knapsack problem, which we call maximal inequality. Independently, we show that the separation problem can be seen as a series of combinatorial optimization problems. Finally, we show that the optimal solution of the separation problem also falls into the category of the maximal inequalities. The concept of a cover naturally arises in the description of the maximal inequalities. We develop a relationship between the traditional cover inequalities and maximal inequalities. Furthermore, the relationship is expanded to the integer knapsack problem. In short, cover inequalities belong to a subclass of maximal inequalities. Next, we extend the results to the case of $Chv\acute{a}tal$ -Gomory inequalities for multiple constraints with special structure. We explicitly describe a useful condition to find the most-violated rank 1 $Chv\acute{a}tal$ -Gomory inequality for the generalized assignment problem. Then, we observe that the separation problem ... | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Cutset Inequalities | - |
dc.subject | Maximal Inequalities | - |
dc.subject | O(n) Separation Heuristic | - |
dc.subject | Multiple Constraints | - |
dc.subject | c-MIR 부등식 | - |
dc.subject | cutset inequality | - |
dc.subject | 고모리부등식 | - |
dc.subject | 범용절단평면 | - |
dc.title | Characterization and separation of the $chv\acute{a}tal$ -gomory inequalities | - |
dc.title.alternative | 고모리 부등식의 특성과 절단평면의 생성에 관한 연구 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 466353/325007 | - |
dc.description.department | 한국과학기술원 : 산업및시스템공학과, | - |
dc.identifier.uid | 020005147 | - |
dc.contributor.localauthor | Park, Sung-Soo | - |
dc.contributor.localauthor | 박성수 | - |
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