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Global optimization of nonconvex MINLP by a hybrid branch-and-bound and revised general benders decomposition approach
Alternative TitleInd. Eng. Chem. Res.
Zhu, YS; Kuno, T
2003-02-05
Source PublicationINDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH
ISSN0888-5885
Volume42Issue:3Pages:528-539
AbstractMixed-integer nonlinear programming, MINLP, has played a crucial role in chemical process design via superstructures that always involve discrete and continuous variables. In this paper, a global optimization algorithm for nonconvex MINLP problems is developed by addressing the nonconvexity caused by the nonconvex continuous functions with a convex quadratic underestimator within a branch-and-bound framework, as well as the joint problem caused by the mixed natures of integer and continuous variables through a revised general Benders decomposition (GBD) method, where the latter is designed mainly for three favorable structures, i.e., separable, bilinear, and partly linear, between the two domains of continuous and binary variables. The convergence of the revised GBD method to the global solution of the relaxed MINLP subprobelm over each subregion generated in the above framework is guaranteed by the convex underestimation functions in terms of the twice-differentiable assumptions of the continuous functions and the above three favorable joint structures. Then, the convergence of the proposed hybrid algorithm can be established by the exhaustive partition of the constrained region, the monotonicity of the lower bound, and the reliability of the infeasibility detection. Finally, a very simple example for process design is used to verify the different implementation aspects of the proposed approach, especially the unique underestimator construction and the infeasibility detection in each lower-bounding problem.; Mixed-integer nonlinear programming, MINLP, has played a crucial role in chemical process design via superstructures that always involve discrete and continuous variables. In this paper, a global optimization algorithm for nonconvex MINLP problems is developed by addressing the nonconvexity caused by the nonconvex continuous functions with a convex quadratic underestimator within a branch-and-bound framework, as well as the joint problem caused by the mixed natures of integer and continuous variables through a revised general Benders decomposition (GBD) method, where the latter is designed mainly for three favorable structures, i.e., separable, bilinear, and partly linear, between the two domains of continuous and binary variables. The convergence of the revised GBD method to the global solution of the relaxed MINLP subprobelm over each subregion generated in the above framework is guaranteed by the convex underestimation functions in terms of the twice-differentiable assumptions of the continuous functions and the above three favorable joint structures. Then, the convergence of the proposed hybrid algorithm can be established by the exhaustive partition of the constrained region, the monotonicity of the lower bound, and the reliability of the infeasibility detection. Finally, a very simple example for process design is used to verify the different implementation aspects of the proposed approach, especially the unique underestimator construction and the infeasibility detection in each lower-bounding problem.
KeywordAlgorithm Design
SubtypeArticle
WOS HeadingsScience & Technology ; Technology
DOI10.1021/ie0200813
URL查看原文
Indexed BySCI
Language英语
WOS KeywordALGORITHM ; DESIGN
WOS Research AreaEngineering
WOS SubjectEngineering, Chemical
WOS IDWOS:000180771900014
Citation statistics
Cited Times:14[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Version出版稿
Identifierhttp://ir.ipe.ac.cn/handle/122111/5293
Collection研究所(批量导入)
Affiliation1.Univ Tsukuba, Inst Informat Sci & Elect, Tsukuba, Ibaraki 3058573, Japan
2.Chinese Acad Sci, Inst Proc Engn, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Zhu, YS,Kuno, T. Global optimization of nonconvex MINLP by a hybrid branch-and-bound and revised general benders decomposition approach[J]. INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH,2003,42(3):528-539.
APA Zhu, YS,&Kuno, T.(2003).Global optimization of nonconvex MINLP by a hybrid branch-and-bound and revised general benders decomposition approach.INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH,42(3),528-539.
MLA Zhu, YS,et al."Global optimization of nonconvex MINLP by a hybrid branch-and-bound and revised general benders decomposition approach".INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 42.3(2003):528-539.
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