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Tightening piecewise McCormick relaxations for bilinear problems
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Abstract(s)
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.
Description
Keywords
Water minimization Nonlinear programming Mathematical modelling Optimization
Pedagogical Context
Citation
Castro, P.M. - Tightening piecewise McCormick relaxations for bilinear problems. In: Computers and Chemical Engineering, 2015, Vol. 72, p. 300-311
Publisher
Elsevier