An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms

In this paper a new version of the Outer Approximation for Global Optimization Algorithm by Bergamini et al. [Bergamini, M.L., Aguirre, P., & Grossmann, I.E. (2005a). Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering 29,...

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Veröffentlicht in:Computers & chemical engineering Jg. 32; H. 3; S. 477 - 493
Hauptverfasser: Bergamini, María Lorena, Grossmann, Ignacio, Scenna, Nicolás, Aguirre, Pío
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 24.03.2008
Schlagworte:
Bilinear terms
Concave terms
Global optimization
MINLP
Piecewise relaxation
MINLP
Piecewise relaxation
Global optimization
Bilinear terms
Concave terms
ISSN:0098-1354, 1873-4375
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Zusammenfassung:In this paper a new version of the Outer Approximation for Global Optimization Algorithm by Bergamini et al. [Bergamini, M.L., Aguirre, P., & Grossmann, I.E. (2005a). Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering 29, 1914] is proposed, in order to speed up the convergence in nonconvex MINLP models that involve bilinear and concave terms. Bounding problems are constructed replacing these nonconvex terms by piecewise linear underestimators. These problems, which correspond to mixed-integer linear programs, are solved to generate approximate solutions with improved objective value. When no further feasible solution can be found, this guarantees that the upper bound cannot be improved in the nonconvex problem, thus providing a termination criterion. The new algorithm is applied to five different synthesis problems in the areas of water networks, heat exchanger networks and distillation sequences. The results show a significant reduction in the computational cost compared with the previous version of the algorithm.
ISSN:0098-1354
1873-4375
DOI:10.1016/j.compchemeng.2007.03.011