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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| Published in: | Computers & chemical engineering Vol. 32; no. 3; pp. 477 - 493 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
24.03.2008
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| ISSN: | 0098-1354, 1873-4375 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Bergamini, María Lorena Aguirre, Pío Grossmann, Ignacio Scenna, Nicolás |
| Author_xml | – sequence: 1 givenname: María Lorena surname: Bergamini fullname: Bergamini, María Lorena organization: Instituto de Desarrollo y Diseño, INGAR, Santa Fe, Argentina – sequence: 2 givenname: Ignacio surname: Grossmann fullname: Grossmann, Ignacio organization: Department of Chemical Engineering, Carnegie Mellon University, Pittsburg 15213, USA – sequence: 3 givenname: Nicolás surname: Scenna fullname: Scenna, Nicolás organization: Instituto de Desarrollo y Diseño, INGAR, Santa Fe, Argentina – sequence: 4 givenname: Pío surname: Aguirre fullname: Aguirre, Pío email: paguir@ceride.gov.ar organization: Instituto de Desarrollo y Diseño, INGAR, Santa Fe, Argentina |
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| Keywords | MINLP Piecewise relaxation Global optimization Bilinear terms Concave terms |
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| SubjectTerms | Bilinear terms Concave terms Global optimization MINLP Piecewise relaxation |
| Title | An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms |
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