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A comparative theoretical and computational study on robust counterpart optimization / Zukui Li in Industrial & engineering chemistry research, Vol. 50 N° 18 (Septembre 2011) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 50 N° 18 (Septembre 2011) . - pp. 10567-10603 Titre : A comparative theoretical and computational study on robust counterpart optimization : I. robust linear optimization and robust mixed integer linear optimization Type de document : texte imprimé Auteurs : Zukui Li, Auteur ; Ran Ding, Auteur ; Christodoulos A. Floudas, Auteur Année de publication : 2011 Article en page(s) : pp. 10567-10603 Note générale : Chimie industrielle Langues : Anglais (eng) Mots-clés : Optimization Résumé : Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (Le., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed For uncertainty in the left-hand side, right-hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainly sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. DEWEY : 660 ISSN : 0888-5885 En ligne : http://cat.inist.fr/?aModele=afficheN&cpsidt=24523879 [article] A comparative theoretical and computational study on robust counterpart optimization : I. robust linear optimization and robust mixed integer linear optimization [texte imprimé] / Zukui Li, Auteur ; Ran Ding, Auteur ; Christodoulos A. Floudas, Auteur . - 2011 . - pp. 10567-10603. Chimie industrielle Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 50 N° 18 (Septembre 2011) . - pp. 10567-10603 Mots-clés : Optimization Résumé : Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (Le., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed For uncertainty in the left-hand side, right-hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainly sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. DEWEY : 660 ISSN : 0888-5885 En ligne : http://cat.inist.fr/?aModele=afficheN&cpsidt=24523879

A comparative theoretical and computational study on robust counterpart optimization / Zukui Li in Industrial & engineering chemistry research, Vol. 51 N° 19 (Mai 2012) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 51 N° 19 (Mai 2012) . - pp. 6760-6768 Titre : A comparative theoretical and computational study on robust counterpart optimization : II. Probabilistic guarantees on constraint satisfaction Type de document : texte imprimé Auteurs : Zukui Li, Auteur ; Qiuhua Tang, Auteur ; Christodoulos A. Floudas, Auteur Année de publication : 2012 Article en page(s) : pp. 6760-6768 Note générale : Industrial chemistry Langues : Anglais (eng) Mots-clés : Optimization Résumé : Probabilislic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedrai, "interval+ellipsoidal", and "interval+polyhedral" uncertainty sets (Li, Z.; Ding, R.; Floudas, CA A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: L Robust Linear and Robust Mixed Integer Linear Optimization. Ind. Eng. Chem. Res. 2011, 50, 10567). For those robust counterpart optimization formulations, their corresponding probability bounds on constraint satisfaction are derived for different types of uncertainty characteristic (i.e., bounded or unbounded uncertainty, with or without detailed probability distribution information). The findings of this work extend the results in the literature and provide greater flexibility for robust optimization practitioners in choosing tighter probability bounds so as to find less conservative robust solutions. Extensive numerical studies are performed to compare the tightness of the different probability bounds and the conservatism of different robust counterpart optimization formulations. Guiding rules for the selection of robust counterpart optimization models and for the determination of the size of the uncertainty set are discussed. Applications in production planning and process scheduling problems are presented. ISSN : 0888-5885 En ligne : http://cat.inist.fr/?aModele=afficheN&cpsidt=25900232 [article] A comparative theoretical and computational study on robust counterpart optimization : II. Probabilistic guarantees on constraint satisfaction [texte imprimé] / Zukui Li, Auteur ; Qiuhua Tang, Auteur ; Christodoulos A. Floudas, Auteur . - 2012 . - pp. 6760-6768. Industrial chemistry Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 51 N° 19 (Mai 2012) . - pp. 6760-6768 Mots-clés : Optimization Résumé : Probabilislic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedrai, "interval+ellipsoidal", and "interval+polyhedral" uncertainty sets (Li, Z.; Ding, R.; Floudas, CA A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: L Robust Linear and Robust Mixed Integer Linear Optimization. Ind. Eng. Chem. Res. 2011, 50, 10567). For those robust counterpart optimization formulations, their corresponding probability bounds on constraint satisfaction are derived for different types of uncertainty characteristic (i.e., bounded or unbounded uncertainty, with or without detailed probability distribution information). The findings of this work extend the results in the literature and provide greater flexibility for robust optimization practitioners in choosing tighter probability bounds so as to find less conservative robust solutions. Extensive numerical studies are performed to compare the tightness of the different probability bounds and the conservatism of different robust counterpart optimization formulations. Guiding rules for the selection of robust counterpart optimization models and for the determination of the size of the uncertainty set are discussed. Applications in production planning and process scheduling problems are presented. ISSN : 0888-5885 En ligne : http://cat.inist.fr/?aModele=afficheN&cpsidt=25900232

Robust optimization for process scheduling under uncertainty / Zukui Li in Industrial & engineering chemistry research, Vol. 47 n°12 (Juin 2008) 

Public ISBD [article]  in Industrial & engineering chemistry research > Vol. 47 n°12 (Juin 2008) . - p. 4148–4157 Titre : Robust optimization for process scheduling under uncertainty Type de document : texte imprimé Auteurs : Zukui Li, Auteur ; Ierapetritou, Marianthi G., Auteur Année de publication : 2008 Article en page(s) : p. 4148–4157 Note générale : Bibliogr. p. 4157 Langues : Anglais (eng) Mots-clés : Process  scheduling;  Robust  optimization;  Stochastic  programming  method Résumé : This paper addresses the uncertainty problem in process scheduling using robust optimization. Compared to the traditional-scenario-based stochastic programming method, robust counterpart optimization method has a unique advantage, in that the scale of the corresponding optimization problem does not increase exponentially with the number of the uncertain parameters. Three robust counterpart optimization formulations―including Soyster’s worst-case scenario formulation, Ben-Tal and Nemirovski’s formulation, and a formulation proposed by Bertsimas and Sim―are studied and applied to uncertain scheduling problems in this paper. The results show that the formulation proposed by Bertsimas and Sim is the most appropriate model for uncertain scheduling problems, because it has the following advantages: (i) the model has the same size as the other formulations, (ii) it preserves its linearity, and (iii) it has the ability to control the degree of conservatism for every constraint and guarantees feasibility for the robust optimization problem. En ligne : http://pubs.acs.org/doi/abs/10.1021/ie071431u [article] Robust optimization for process scheduling under uncertainty [texte imprimé] / Zukui Li, Auteur ; Ierapetritou, Marianthi G., Auteur . - 2008 . - p. 4148–4157. Bibliogr. p. 4157 Langues : Anglais (eng) in Industrial & engineering chemistry research > Vol. 47 n°12 (Juin 2008) . - p. 4148–4157 Mots-clés : Process  scheduling;  Robust  optimization;  Stochastic  programming  method Résumé : This paper addresses the uncertainty problem in process scheduling using robust optimization. Compared to the traditional-scenario-based stochastic programming method, robust counterpart optimization method has a unique advantage, in that the scale of the corresponding optimization problem does not increase exponentially with the number of the uncertain parameters. Three robust counterpart optimization formulations―including Soyster’s worst-case scenario formulation, Ben-Tal and Nemirovski’s formulation, and a formulation proposed by Bertsimas and Sim―are studied and applied to uncertain scheduling problems in this paper. The results show that the formulation proposed by Bertsimas and Sim is the most appropriate model for uncertain scheduling problems, because it has the following advantages: (i) the model has the same size as the other formulations, (ii) it preserves its linearity, and (iii) it has the ability to control the degree of conservatism for every constraint and guarantees feasibility for the robust optimization problem. En ligne : http://pubs.acs.org/doi/abs/10.1021/ie071431u