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LAGRANGIAN RELAXATION AND PEGGING TEST FOR LINEAR ORDERING PROBLEMS

By Noriyoshi Sukegawa, Yoshitsugu Yamamoto and Liyuan Zhang

Abstract

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 in 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

Topics: Combinatorial optimization, linear ordering problem, Lagrangian relaxation, Lagrangian dual
Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.4224
Provided by: CiteSeerX
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