Global optimization of bilinear programs with a multiparametric disaggregation technique

Authors:
Scott Kolodziej;Pedro M. Castro;Ignacio E. Grossmann
Affiliations:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, USA 15213-3890;Laboratório Nacional de Energia e Geologia, Unidade de Modelaçãoe Otimização de Sistemas Energéticos, Lisbon, Portugal 1649-038;Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, USA 15213-3890
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scale much more favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smaller mixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.