Dynamic Lagrangian dual and reduced RLT constructs for solving 0–1 mixed-integer programs

In this paper, we consider a dynamic Lagrangian dual optimization procedure for solving mixed-integer 0–1 linear programming problems. Similarly to delayed relax-and-cut approaches, the procedure dynamically appends valid inequalities to the linear programming relaxation as induced by the Reformulat...

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Bibliographic Details
Published in:TOP Vol. 20; no. 1; pp. 173 - 189
Main Authors: Sherali, Hanif D., Smith, J. Cole
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2012
Springer
Subjects:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
90C57
Delayed relax-and-cut approach
90–08
Mixed-integer programming
Dynamic Lagrangian dual
90C11
Reformulation-Linearization Technique (RLT)
Valid inequalities
ISSN:1134-5764, 1863-8279
Online Access:Get full text
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Summary:In this paper, we consider a dynamic Lagrangian dual optimization procedure for solving mixed-integer 0–1 linear programming problems. Similarly to delayed relax-and-cut approaches, the procedure dynamically appends valid inequalities to the linear programming relaxation as induced by the Reformulation-Linearization Technique (RLT). A Lagrangian dual algorithm that is augmented with a primal solution recovery scheme is applied implicitly to a full or partial first-level RLT relaxation, where RLT constraints that are currently being violated by the primal estimate are dynamically generated within the Lagrangian dual problem, thus controlling the size of the dual space while effectively capturing the strength of the RLT-enhanced relaxation. We present a preliminary computational study to demonstrate the efficacy of this approach.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-011-0199-3