pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

Nicholson, Bethany L.; Siirola, John Daniel; Watson, Jean‐Paul; Zavala, Ví­ctor M.; Biegler, Lorenz T.

doi:10.1007/s12532-017-0127-0

Cited by 106 publications

(60 citation statements)

References 19 publications

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“…The resulting MIDO problem is discretized using eight finite elements (nine mesh points) with three collocation points using the Pyomo environment. [48][49][50] Note that each finite element has a horizon of 0.25 hours, matching the discretization step of the mpMPC. Discretizing the MIDO yields an MINLP problem with 80 binary variables, which is solved with GAMS/BARON 51 with a 15 min limit on the solution time.…”

Section: −ℳ Xmentioning

confidence: 99%

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Burnak

Pistikopoulos

2020

AIChE Journal

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Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed‐integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed‐loop implementation. We use multi‐parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base‐2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.

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Section: −ℳ Xmentioning

confidence: 99%

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Burnak

Pistikopoulos

2020

AIChE Journal

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“…HSL_MA97 is used as the linear solver, 38 and Pyomo.DAE is used to automatically discretize the PDE described in the previous section. 39 As described in the previous section, each pipe is discretized by finite difference in space and implicit Euler in time. The time horizon is 24 hr and divided into 48 segments.…”

Section: Model Structurementioning

confidence: 99%

Dynamic optimization for gas blending in pipeline networks with gas interchangeability control

Kazi

Biegler

et al. 2020

AIChE Journal

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The increasing penetration of unconventional gas and liquefied natural gas poses an operational challenge on existing regional gas networks for gas quality problems. A new dynamic model for natural gas pipeline network with multiple supplies is presented with a special emphasis on gas interchangeability control. Wobbe index serves as gas interchangeability indicator and is calculated by equations derived from rigorous composition‐based partial differential equations. Disjunctive formulation is applied to represent different modes of gas blending due to gas reversal, and the disjunctive model is then reformulated as a nonsmooth model with min/max and absolute value functions, which is solved by a gradient‐based nonlinear program solver after smooth approximation. Moreover, a heuristic algorithm is proposed to tune the penalty parameters in order to focus on different penalty terms while keeping the model well‐conditioned. The developed model and strategy are first tested with a small pipeline network model and then extended to a large model. The results show that the model can effectively manage gas interchangeability issues in pipeline networks within reasonable CPU time.

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“…We used the programming environment of Python coupled with its modeling library, namely Pyomo. Similar approaches in terms of software selection have been presented for Differential and Algebraic Equations (DAE) modeling and optimization in (Nicholson et al, 2018;Nikolić, 2016). By combining Python and Pyomo we have the ability to transform a simplified representation of a mathematical model initially written in LaTeX into a formal AML formulation and eventually optimize it.…”

Section: Functionalitymentioning

confidence: 99%

An integrated platform for intuitive mathematical programming modeling using LaTeX

Triantafyllidis

Papageorgiou

2018

PeerJ Computer Science

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This paper presents a novel prototype platform that uses the same LaTeX mark-up language, commonly used to typeset mathematical content, as an input language for modeling optimization problems of various classes. The platform converts the LaTeX model into a formal Algebraic Modeling Language (AML) representation based on Pyomo through a parsing engine written in Python and solves by either via NEOS server or locally installed solvers, using a friendly Graphical User Interface (GUI). The distinct advantages of our approach can be summarized in (i) simplification and speed-up of the model design and development process (ii) non-commercial character (iii) cross-platform support (iv) easier typo and logic error detection in the description of the models and (v) minimization of working knowledge of programming and AMLs to perform mathematical programming modeling. Overall, this is a presentation of a complete workable scheme on using LaTeX for mathematical programming modeling which assists in furthering our ability to reproduce and replicate scientific work.

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pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

Cited by 106 publications

References 19 publications

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Integrated process design, scheduling, and model predictive control of batch processes with closed‐loop implementation

Dynamic optimization for gas blending in pipeline networks with gas interchangeability control

An integrated platform for intuitive mathematical programming modeling using LaTeX

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