Graph representation and decomposition of ODE/hyperbolic PDE systems

Moharir, Manjiri; Kang, Lixia; Daoutidis, Pródromos; Almansoori, Ali

doi:10.1016/j.compchemeng.2017.07.005

Cited by 21 publications

(10 citation statements)

References 30 publications

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“…Moreover, graphs can be naturally built by combining graphs from different classes (e.g., stochastic PDE optimization). This approach is thus more general than other graph-based abstractions proposed for specific problem classes such as network optimization and control [33,41,55,78,31]. This modeling abstraction also generalizes those used in simulation packages such as Modelica, AspenPlus, gProms, which are tailored to specific physical systems.…”

Section: Graph-based Model Representationsmentioning

confidence: 98%

A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl

Jalving¹,

Shin²,

Zavala³

2020

Preprint

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We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and edges represent connectivity between such subproblems. The abstraction enables the modular construction of highly complex models in an intuitive manner, facilitates the use of graph analysis tools (to perform partitioning, aggregation, and visualization tasks), and facilitates communication of structures to decomposition algorithms. We provide an open-source implementation of the abstraction in the Julia-based package Plasmo.jl. We provide tutorial examples and large application case studies to illustrate the capabilities.

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Section: Graph-based Model Representationsmentioning

confidence: 98%

A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl

Jalving¹,

Shin²,

Zavala³

2020

Preprint

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“…The argument behind this measure is that modular organizations that arise in natural systems are nonrandom. This measure is intuitive and has seen many interesting applications; for instance, this measure has been shown to provide a flexible and powerful tool for the analysis and design of control architectures and for the decomposition of large‐scale optimization problems . A powerful generalization of Newman's measure has been proposed in Reference and here it was shown that systems of high modularity are extremum points of a Hamiltonian function.…”

Section: Introductionmentioning

confidence: 98%

Modularity measures: Concepts, computation, and applications to manufacturing systems

Shao

Zavala

2020

AIChE Journal

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We propose a measure to quantify the modularity of industrial production (manufacturing) systems and optimization formulations to compute it. From a manufacturing perspective, we argue that a system is deemed modular if: (a) the equipment units that comprise it form clusters (modules) of dense connectivity (i.e., difficult module assembly tasks are performed off-site), (b) connectivity between modules is sparse (i.e., easy assembly tasks are performed on-site), (c) the number of modules is small, and (d) the module dimensions facilitate transportation. We show that the measure proposed satisfies these requirements and that it can be computed by solving a convex mixed-integer quadratic program. We provide a discussion on advantages and disadvantages of alternative modularity measures used in different scientific and engineering communities. Our results seek to highlight conceptual and computational challenges that arise from the need to define and quantify modularity in a manufacturing context.

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“…The graph derived from the molecular structure is called the molecular graph. A chemical index can be thought of as a function f : G → R + that maps each molecular structure to a positive real number (See Moharir et al [1], Udagedara et al [3], Shafiei and Saeidifar [4], Crepnjak and Tratnik [5] for more details).…”

Section: Introductionmentioning

confidence: 99%

Wiener polarity index of quasi-tree molecular structures

Tang¹,

Liang²,

Gao³

2018

Open J. Math. Sci

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Abstract.As an important branch of theoretical chemistry, chemical index calculation has received wide attention in recent years. Its theoretical results have been widely used in many fields such as chemistry, pharmacy, physics, biology, materials, etc. and play a key role in reverse engineering. Its basic idea is to obtain compound characteristics indirectly through the calculation of topological index. As a basic structure, quasi-tree structures are widely found in compounds. In this paper, we obtain the maximal value and the second smallest value of quasi-tree graphs of order n.Mathematics Subject Classification: 05C15.

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Graph representation and decomposition of ODE/hyperbolic PDE systems

Cited by 21 publications

References 30 publications

A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl

A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl

Modularity measures: Concepts, computation, and applications to manufacturing systems

Wiener polarity index of quasi-tree molecular structures

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