Tightening piecewise McCormick relaxations for bilinear problems
We address nonconvex bilinear problems where the main objective is the computation of a tight lowerbound for the objective function to be minimized. This can be obtained through a mixed-integer linearprogramming formulation relying on the concept of piecewise McCormick relaxation. It works by dividi...
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| Format: | article |
| Language: | eng |
| Published: |
2016
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.9/2947 |
| Country: | Portugal |
| Oai: | oai:repositorio.lneg.pt:10400.9/2947 |
| Summary: | We address nonconvex bilinear problems where the main objective is the computation of a tight lowerbound for the objective function to be minimized. This can be obtained through a mixed-integer linearprogramming formulation relying on the concept of piecewise McCormick relaxation. It works by dividingthe domain of one of the variables in each bilinear term into a given number of partitions, while consid-ering global bounds for the other. We now propose using partition-dependent bounds for the latter so asto further improve the quality of the relaxation. While it involves solving hundreds or even thousands oflinear bound contracting problems in a pre-processing step, the benefit from having a tighter formula-tion more than compensates the additional computational time. Results for a set of water network designproblems show that the new algorithm can lead to orders of magnitude reduction in the optimality gapcompared to commercial solvers. |
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