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Convex hull discretization approach to the global optimization of pooling problems / Viet Pham in Industrial & engineering chemistry research, Vol. 48 N°4 (Février 2009) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 48 N°4 (Février 2009) . - pp. 1973–1979 Titre : Convex hull discretization approach to the global optimization of pooling problems Type de document : texte imprimé Auteurs : Viet Pham, Auteur ; Carl Laird, Auteur ; Mahmoud El-Halwagi, Auteur Année de publication : 2009 Article en page(s) : pp. 1973–1979 Note générale : Chemical engineering Langues : Anglais (eng) Mots-clés : Pooling  problem  Convex-hull  Mixed  integer  linear  program Résumé : The pooling problem is an important optimization problem that is encountered in process operation and scheduling. Because of the presence of bilinear terms, the traditional formulation is nonconvex. Consequently, there is a need to develop computationally efficient and easy-to-implement global-optimization techniques. In this paper, a new approach is proposed based on three concepts: linearization by discretizing nonlinear variables, preprocessing using implicit enumeration of the discretization to form a convex-hull which limits the size of the search space, and application of integer cuts to ensure compatibility between the original problem and the discretized formulation. The continuous quality variables contributing to the bilinear terms are first discretized. The discretized problem is a mixed integer linear program (MILP) which is globally solvable in a computationally effective manner using the branch and bound method. The merits of the proposed approach are illustrated with case studies from literature and comparison with published results. En ligne : http://pubs.acs.org/doi/abs/10.1021/ie8003573 [article] Convex hull discretization approach to the global optimization of pooling problems [texte imprimé] / Viet Pham, Auteur ; Carl Laird, Auteur ; Mahmoud El-Halwagi, Auteur . - 2009 . - pp. 1973–1979. Chemical engineering Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 48 N°4 (Février 2009) . - pp. 1973–1979 Mots-clés : Pooling  problem  Convex-hull  Mixed  integer  linear  program Résumé : The pooling problem is an important optimization problem that is encountered in process operation and scheduling. Because of the presence of bilinear terms, the traditional formulation is nonconvex. Consequently, there is a need to develop computationally efficient and easy-to-implement global-optimization techniques. In this paper, a new approach is proposed based on three concepts: linearization by discretizing nonlinear variables, preprocessing using implicit enumeration of the discretization to form a convex-hull which limits the size of the search space, and application of integer cuts to ensure compatibility between the original problem and the discretized formulation. The continuous quality variables contributing to the bilinear terms are first discretized. The discretized problem is a mixed integer linear program (MILP) which is globally solvable in a computationally effective manner using the branch and bound method. The merits of the proposed approach are illustrated with case studies from literature and comparison with published results. En ligne : http://pubs.acs.org/doi/abs/10.1021/ie8003573