Lagrangian relaxation and pegging test for linear ordering problems

Noriyoshi Sukegawa, Yoshitsugu Yamamoto, Liyuan Zhang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We develop an algorithm for the linear ordering problem, which has a large number of applications such as triangulation of input-output matrices, minimizing total weighted completion time one-machine scheduling, and aggregation of individual preferences. The algorithm is based on the Lagrangian relaxation of a binary integer linear programming formulation of the problem. Since the number of the constraints is proportional to the third power of the number of items and grows rapidly, we propose a modified subgradient method that temporarily ignores a large part of the constraints and gradually adds constraints whose Lagrangian multipliers are likely to be positive at an optimal multiplier vector. We also propose an improvement on the ordinary pegging test by using the problem structure.

Original languageEnglish
Pages (from-to)142-160
Number of pages19
JournalJournal of the Operations Research Society of Japan
Volume54
Issue number4
DOIs
Publication statusPublished - Dec 2011

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Keywords

  • Combinatorial optimization
  • Lagrangian dual
  • Lagrangian relaxation
  • Linear ordering problem
  • Pegging test
  • Subgradient method

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