Logic-based MINLP algorithms for the optimal synthesis of process networks
In this paper, the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations (e.g. if a unit is selected,...
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| Veröffentlicht in: | Computers & chemical engineering Jg. 20; H. 8; S. 959 - 978 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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1996
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| ISSN: | 0098-1354, 1873-4375 |
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| Abstract | In this paper, the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations (e.g. if a unit is selected, apply mass/heat balances; otherwise, set the flow variables to zero). It is first shown that this framework for representing discrete optimization problems greatly simplifies the step of modeling. The outer approximation algorithm is then used as a basis to derive a new logic-based OA solution method which naturally gives rise to NLP sub-problems that avoid zero flows and a disjunctive LP master problem. The initial NLP sub-problems, that provide linearizations for all the terms in the disjunctions, are selected through a set-covering problem for which we consider both the cases of disjunctive and conjunctive normal form logic. The master problem, on the other hand, is converted to mixed-integer form using a convex-hull representation. Furthermore, based on some interesting relations of outer approximation with generalized Benders decomposition, it is also shown that it is possible to derive a logic-based method for the latter algorithm. The proposed algorithm has been tested on several structural optimization problems, including a flowsheet example showing distinct advantages in robustness and computational efficiency when compared to standard MINLP models and algorithms. |
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| AbstractList | In this paper, the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations (e.g. if a unit is selected, apply mass/heat balances; otherwise, set the flow variables to zero). It is first shown that this framework for representing discrete optimization problems greatly simplifies the step of modeling. The outer approximation algorithm is then used as a basis to derive a new logic-based OA solution method which naturally gives rise to NLP sub-problems that avoid zero flows and a disjunctive LP master problem. The initial NLP sub-problems, that provide linearizations for all the terms in the disjunctions, are selected through a set-covering problem for which we consider both the cases of disjunctive and conjunctive normal form logic. The master problem, on the other hand, is converted to mixed-integer form using a convex-hull representation. Furthermore, based on some interesting relations of outer approximation with generalized Benders decomposition, it is also shown that it is possible to derive a logic-based method for the latter algorithm. The proposed algorithm has been tested on several structural optimization problems, including a flowsheet example showing distinct advantages in robustness and computational efficiency when compared to standard MINLP models and algorithms. The mixed integer nonlinear programming problem for the optimal synthesis of process network is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations. An outer approximation (OA) algorithm is used as a basis to derive at a new logic-based OA solution method which gives rise to nonlinear programming sub-problems that avoid zero flows and a disjunctive linear programming master problem. The algorithm is tested on several structural optimization problems. |
| Author | Türkay, Metin Grossmann, Ignacio E. |
| Author_xml | – sequence: 1 givenname: Metin surname: Türkay fullname: Türkay, Metin – sequence: 2 givenname: Ignacio E. surname: Grossmann fullname: Grossmann, Ignacio E. |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3058755$$DView record in Pascal Francis |
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| Keywords | Integer programming Meshed network Mixed programming Logical programming Non linear programming Algorithm Computer aided design Optimization Flowsheet |
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| Title | Logic-based MINLP algorithms for the optimal synthesis of process networks |
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