Global Optimization by Domain-Image Partitioning-Application to HEN(Faria and Bagajewicz)-11

Global Optimization by Domain-Image Partitioning-Application to HEN(Faria and Bagajewicz)-11

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1 Global Optimization of Nonconvex MINLP Problems by Domain and Image Partitioning: Applications to Heat Exchanger Networks Débora C. Faria and Miguel J. Bagajewicz * University of Oklahoma 100 E. Boyd St, Room T335 Norman, OK 73019 USA Keywords: Global Optimization, Heat Exchanger Networks. (*) Corresponding Author: e-mail: bagajewicz@ou.edu , TE:+1-405-325-5458
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2 Abstract We extend a recently introduced methodology for global optimization of bilinear MINLP models (Faria and Bagajewicz, 2011b). The method for bilinear MINLP problems is based on variable partitioning and bound contraction eventually followed under certain conditions by a combination of branch & bound and bound contraction at each node. We extend the method to full nonconvex MINLP problems by partitioning the image of nonconvex functions in addition to partitioning their domain. To illustrate the method we focus on the Heat Exchanger Network Stagewise model.
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3 Introduction There are several global optimization methods, some even commercially available like BARON (Sahinidis, 1996), COCOS, GlobSol, ICOS, LGO, LINGO, OQNLP, Premium Solver, and others that are well-known like the α BB (Androulakis et al., 1995). Many are described in several books (Sherali and Adams, 1999; Floudas, 2000a; Tawarmalani and Sahinidis, 2002; Horst and Tuy, 2003; Hansen and Walster, 2004) and recent paper reviews (Floudas 2000b; Pardalos et al., 2000; Floudas et al., 2005; Floudas and Gounaris, 2009). Different approaches for global optimization exist: Lagrangean-based approaches (Ben-Tal et al., 1994; Adhya et al., 1999; Kuno and Utsunomiya, 2000; Karuppiah and Grossmann, 2008), disjunctive programming-based methods (Ruiz and Grossmann, 2010), Cutting plane methods (Westerlund et al ., 1998), Intervals analysis arithmetic (Moore, 1966; Hansen, 1979; Ratschek and Rokne; 1988; Moore et al., 1992; Vaidyanathan and El-Halwagi, 1994; Byrne and I. D. L. Bogle, 1999), Branch-and- reduce (Ryoo and Sahinidis, 1995), GMIN- α BB and SMIN- α BB (Adjiman et al. , 1997), spatial branch and bound (Smith and Pantelides, 1997), branch and cut (Kesavan and Barton, 2000a) and branch and contract (Zamora and Grossmann 1998; Zamora and Grossmann, 1999), decomposition through generalized benders decomposition (Geoffrion, 1972) or outer approximation (Duran and Grossmann, 1986; Fletcher and Leyffer, 1994), both restricted to certain class of problems (Bagajewicz and Manousiouthakis, 1991; Sahinidis and Grossmann, 1991) as well as others (Kesavan and Barton, 2000b). The list is not exhaustive and we omit stochastic based methods as they do not guarantee optimality. In previous work (Faria and Bagajewicz, 2011a,b,c) we address problems that contain bilinear terms and univariate concave terms. In particular (Faria and Bagajewicz, 2011b) uses some previously proposed partitioning methods to obtain lower bounds as well as some other techniques: S herali and Alamedinne, 1992; Meyer and Floudas,
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4 2006); Misener and Floudas, 2009; Gounaris and Floudas, 2009; Karuppiah and Grossmann (2006a); Karuppiah and Grossmann (2006b); Bergamini et al., (2005, 2008) Wicaksono and Karimi (2008), Hasan and Karimi (2010), Pham et al. (2009).
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This note was uploaded on 09/05/2011 for the course CHE 5480 taught by Professor Staff during the Spring '11 term at OKCU.

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Global Optimization by Domain-Image Partitioning-Application to HEN(Faria and Bagajewicz)-11

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