logmip: a disjunctive 0–1 non-linear optimizer for process system models
Discrete-continuous non-linear optimization models are frequently used to formulate problems in process system engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and mixed integer non-linear programming (MINLP). Both have advantages and drawb...
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| Veröffentlicht in: | Computers & chemical engineering Jg. 23; H. 4; S. 555 - 565 |
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01.05.1999
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| ISSN: | 0098-1354, 1873-4375 |
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| Abstract | Discrete-continuous non-linear optimization models are frequently used to formulate problems in process system engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and mixed integer non-linear programming (MINLP). Both have advantages and drawbacks depending on the problem they are dealing with. In this work, we describe the theory behind
logmip, a new computer code for disjunctive programming and MINLP. We discuss a hybrid modeling framework that combines both approaches, allowing binary variables and disjunctions for expressing discrete choices. An extension of the logic-based outer approximation (OA) algorithm has been implemented to solve the proposed hybrid model. Computational experience is reported on several examples, which are solved using disjunctive, MINLP and hybrid formulations. |
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| AbstractList | Discrete-continuous non-linear optimization models are frequently used to formulate problems in process system engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and mixed integer non-linear programming (MINLP). Both have advantages and drawbacks depending on the problem they are dealing with. In this work, we describe the theory behind
logmip, a new computer code for disjunctive programming and MINLP. We discuss a hybrid modeling framework that combines both approaches, allowing binary variables and disjunctions for expressing discrete choices. An extension of the logic-based outer approximation (OA) algorithm has been implemented to solve the proposed hybrid model. Computational experience is reported on several examples, which are solved using disjunctive, MINLP and hybrid formulations. |
| Author | E. Grossmann, Ignacio Vecchietti, Aldo |
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| References | Ravemark, E. (1995). Balas (BIB1) 1985; 6 Raman, Grossmann (BIB7) 1994; 18 19(Suppl.), S189–204. Users manual, Department of Chemical Engineering, Carnegie Mellon University. Pittsburgh, PA. Kocis, Grossmann (BIB4) 1989; 13 Tourn, M. (1995). A Viswanathan, Grossmann (BIB10) 1990; 14 program for transforming logic CNF statements into inequalities for Turkay, Grossmann (BIB8) 1996; 20 Nemhauser, Wolsey (BIB5) 1998 Brink, Westerlund (BIB2) 1995; 29 Grossmann, I. E. & Kravanja, Z. (1995). Mixed-integer non-linear programming techniques for process synthesis engineering. Ph.D. thesis. 10.1016/S0098-1354(98)00293-2_BIB3 Viswanathan (10.1016/S0098-1354(98)00293-2_BIB10) 1990; 14 Raman (10.1016/S0098-1354(98)00293-2_BIB7) 1994; 18 10.1016/S0098-1354(98)00293-2_BIB6 10.1016/S0098-1354(98)00293-2_BIB9 Kocis (10.1016/S0098-1354(98)00293-2_BIB4) 1989; 13 Nemhauser (10.1016/S0098-1354(98)00293-2_BIB5) 1998 Turkay (10.1016/S0098-1354(98)00293-2_BIB8) 1996; 20 Balas (10.1016/S0098-1354(98)00293-2_BIB1) 1985; 6 Brink (10.1016/S0098-1354(98)00293-2_BIB2) 1995; 29 |
| References_xml | – reference: Ravemark, E. (1995). – reference: Grossmann, I. E. & Kravanja, Z. (1995). Mixed-integer non-linear programming techniques for process synthesis engineering. – volume: 14 start-page: 769 year: 1990 end-page: 778 ident: BIB10 article-title: A combined penalty function and outer-approximation method for MINLP optimization publication-title: Computers and Chemical Engineering – reference: Tourn, M. (1995). A – year: 1998 ident: BIB5 publication-title: Integer and combinatorial optimization – reference: 19(Suppl.), S189–204. – volume: 20 start-page: 959 year: 1996 end-page: 978 ident: BIB8 article-title: Logic-based algorithms for the optimal synthesis of process networks publication-title: Computers and Chemical Engineering – reference: . Ph.D. thesis. – reference: program for transforming logic CNF statements into inequalities for – volume: 13 start-page: 797 year: 1989 end-page: 819 ident: BIB4 article-title: A modeling and decomposition strategy for the MINLP optimization of process flow-sheets publication-title: Computers and Chemical Engineering – volume: 18 start-page: 563 year: 1994 end-page: 578 ident: BIB7 article-title: Modelling and computational techniques for logic based integer programming publication-title: Computers and Chemical Engineering – reference: . Users manual, Department of Chemical Engineering, Carnegie Mellon University. Pittsburgh, PA. – volume: 6 start-page: 466 year: 1985 end-page: 486 ident: BIB1 article-title: Disjunctive programming and a hierarchy of relaxations for discrete optimization problems publication-title: SIAM Journal on Algorithms for Discrete Mathematics – volume: 29 start-page: 29 year: 1995 end-page: 36 ident: BIB2 article-title: The joint problem of model structure determination and parameter estimation on quantitative IR-spectroscopy publication-title: Chemomet. and Intellig. Lab. Sys. – volume: 13 start-page: 797 issue: 7 year: 1989 ident: 10.1016/S0098-1354(98)00293-2_BIB4 article-title: A modeling and decomposition strategy for the MINLP optimization of process flow-sheets publication-title: Computers and Chemical Engineering doi: 10.1016/0098-1354(89)85053-7 – volume: 20 start-page: 959 issue: 8 year: 1996 ident: 10.1016/S0098-1354(98)00293-2_BIB8 article-title: Logic-based algorithms for the optimal synthesis of process networks publication-title: Computers and Chemical Engineering doi: 10.1016/0098-1354(95)00219-7 – ident: 10.1016/S0098-1354(98)00293-2_BIB6 – volume: 18 start-page: 563 issue: 7 year: 1994 ident: 10.1016/S0098-1354(98)00293-2_BIB7 article-title: Modelling and computational techniques for logic based integer programming publication-title: Computers and Chemical Engineering doi: 10.1016/0098-1354(93)E0010-7 – volume: 29 start-page: 29 issue: 1 year: 1995 ident: 10.1016/S0098-1354(98)00293-2_BIB2 article-title: The joint problem of model structure determination and parameter estimation on quantitative IR-spectroscopy publication-title: Chemomet. and Intellig. Lab. Sys. doi: 10.1016/0169-7439(95)00018-R – ident: 10.1016/S0098-1354(98)00293-2_BIB3 doi: 10.1016/0098-1354(95)87036-9 – year: 1998 ident: 10.1016/S0098-1354(98)00293-2_BIB5 – volume: 14 start-page: 769 issue: 7 year: 1990 ident: 10.1016/S0098-1354(98)00293-2_BIB10 article-title: A combined penalty function and outer-approximation method for MINLP optimization publication-title: Computers and Chemical Engineering doi: 10.1016/0098-1354(90)87085-4 – ident: 10.1016/S0098-1354(98)00293-2_BIB9 – volume: 6 start-page: 466 year: 1985 ident: 10.1016/S0098-1354(98)00293-2_BIB1 article-title: Disjunctive programming and a hierarchy of relaxations for discrete optimization problems publication-title: SIAM Journal on Algorithms for Discrete Mathematics doi: 10.1137/0606047 |
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| Title | logmip: a disjunctive 0–1 non-linear optimizer for process system models |
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