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

被引:103
作者
Bergamini, Maria Lorena [1 ]
Grossmann, Ignacio [2 ]
Scenna, Nicolas [1 ]
Aguirre, Pio [1 ]
机构
[1] INGAR, Inst Desarrollo & Diseno, Santa Fe, Argentina
[2] Carnegie Mellon Univ, Dept Chem Engn, Pittsburgh, PA 15213 USA
关键词
piecewise relaxation; global optimization; MINLP; bilinear terms; concave terms;
D O I
10.1016/j.compchemeng.2007.03.011
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码:477 / 493
页数:17
相关论文
共 29 条