Tightening concise linear reformulations of 0-1 cubic programs

A common strategy for solving 0-1 cubic programs is to reformulate the non-linear problem into an equivalent linear representation, which can then be submitted directly to a standard mixed-integer programming solver. Both the size and the strength of the continuous relaxation of the reformulation de...

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Bibliographic Details
Published in:Optimization 2016-04, Vol.65 (4), p.877-903
Main Author: Forrester, Richard J.
Format: Article
Language:English
Subjects:
0-1 cubic program
Integer programming
Linear programming
Linearization
Mathematical analysis
Nonlinearity
Optimization
Programming
reformulation-linearization technique (RLT)
Representations
Tightening
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Summary:A common strategy for solving 0-1 cubic programs is to reformulate the non-linear problem into an equivalent linear representation, which can then be submitted directly to a standard mixed-integer programming solver. Both the size and the strength of the continuous relaxation of the reformulation determine the success of this method. One of the most compact linear representations of 0-1 cubic programs is based on a repeated application of the linearization technique for 0-1 quadratic programs introduced by Glover. In this paper, we develop a pre-processing step that serves to strengthen the linear programming bound provided by this concise linear form of a 0-1 cubic program. The proposed scheme involves using optimal dual multipliers of a partial level-2 RLT formulation to rewrite the objective function of the cubic program before applying the linearization. We perform extensive computational tests on the 0-1 cubic multidimensional knapsack problem to show the advantage of our approach.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2015.1091821