Characterization and separation of the $chv\acute{a}tal$ -gomory inequalities = 고모리 부등식의 특성과 절단평면의 생성에 관한 연구

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 462
  • Download : 0
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 ...
Advisors
Park, Sung-Sooresearcher박성수researcher
Description
한국과학기술원 : 산업및시스템공학과,
Publisher
한국과학기술원
Issue Date
2011
Identifier
466353/325007  / 020005147
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 산업및시스템공학과, 2011.2, [ vii, 88 p. ]

Keywords

Cutset Inequalities; Maximal Inequalities; O(n) Separation Heuristic; $Chv\acute{a}tal$-Gomory Inequalities; Multiple Constraints; c-MIR 부등식; cutset inequality; $O(n)$ 절단평면생성 알고리즘; 고모리부등식; 범용절단평면

URI
http://hdl.handle.net/10203/40674
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=466353&flag=dissertation
Appears in Collection
IE-Theses_Ph.D.(박사논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0