Solving mixed integer bilinear problems using MILP formulations (Q2848171)
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scientific article; zbMATH DE number 6211559
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving mixed integer bilinear problems using MILP formulations |
scientific article; zbMATH DE number 6211559 |
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25 September 2013
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mixed integer programming
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bilinear problems
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binary expansion
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cutting planes
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0.93742734
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0.9171717
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0.89956105
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0.89809895
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0.8929808
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0.8922618
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Solving mixed integer bilinear problems using MILP formulations (English)
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The paper considers a mixed integer bilinear program, where every bilinear term involves the product of a nonnegative integer variable and and a nonnegative continuous variable. The objectives and constraints of this program are first linearized, and to obtain MILP formulations, the bilinear terms are further studied. This involves a binary expansion of the integer variables and McCormick envelopes. The authors investigate the binary expansion sets in detail, obtaining facets of their convex hull. They derive a branch and cut algorithm for the MILP reformulation. This algorithm is tested on five classes of instances, showing its effectiveness.
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