A graph theoretic approach to problem formulation for multidisciplinary design analysis and optimization

Pate, D.; Gray, Justin S.; German, Brian

doi:10.1007/s00158-013-1006-6

Cited by 22 publications

(23 citation statements)

References 24 publications

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“…Several techniques may be used to ensure this step. The simplest technique is that the partitioning is manually made by studying the coupling degree between the objective functions, the constraints and the design variables or by following approaches that already exist in the literature such as: the graph theory [12], the game theory [13], the Augmented Lagrangian Coordination [14], etc.…”

Section: Description Of the Multi Agent Approach For Mechatronic Desimentioning

confidence: 99%

Multi-agent approach based on a design process for the optimization of mechatronic systems

Guizani

Hammadi

Choley

et al. 2017

Mechanics & Industry

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Mechatronic design optimization is a complex process characterized by an important number of requirements, design variables, constraints and objectives. Therefore, it is very important to decompose efficiently the system design problem into a set of partitions to minimize the computational cost while profiting from the spatial distribution of design tools, working teams and expertise. However, the optimization of the overall design requires incorporating the relevant partitions in order to find the optimum mechatronic design. Efficient strategies of partitioning and coordination should be specified at the conceptual level to have a successful optimization process. In this paper, a new approach based on multi-agent paradigm is proposed for mechatronic design optimization. The proposed approach is applied to the preliminary design case of an electric vehicle to demonstrate its validity and effectiveness.

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Section: Description Of the Multi Agent Approach For Mechatronic Desimentioning

confidence: 99%

Multi-agent approach based on a design process for the optimization of mechatronic systems

Guizani

Hammadi

Choley

et al. 2017

Mechanics & Industry

View full text Add to dashboard Cite

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“…To handle this problem, Moore utilized a secondary source of information outside the dependency graph. Pate et al 18 proposed an alternative dependency graph structure that addressed this problem. Each discipline and each of its variables are represented by separate nodes with directed edges between them describing their dependencies on each other.…”

Section: Dependency Graphmentioning

confidence: 99%

“…Pate et al 18 stated that within a dependency graph, the presence of cycles indicates coupling between the components in the cycle. Cycles can be induced by connections where data is passed directly from an output to an input, or implicitly where an input needs to be varied in order to drive a residual equation to zero.…”

Section: B Cycle Detection and Usagementioning

confidence: 99%

Automatic Evaluation of Multidisciplinary Derivatives Using a Graph-Based Problem Formulation in OpenMDAO

Gray

Hearn

Moore

et al. 2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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The optimization of multidisciplinary systems with respect to large numbers of design variables is best pursued using a gradient-based optimization together with a method that efficiently evaluates coupled derivatives, such as the coupled adjoint method. However, implementing such a method in a problem with more than a few disciplines is time consuming and error prone. To address this issue, we develop an automated procedure for assembling and solving the coupled derivative equations that takes into account the disciplinary couplings using the interdisciplinary dependency graph of the problem. The coupled derivatives can be computed completely analytically, if analytic derivatives are available for all disciplines; otherwise, the coupled derivatives are computed semi-analytically. The procedure determines the disciplinary analyses execution order, detects iterative cycles, and uses this information to converge the coupled analysis, and evaluate the coupled derivatives as efficiently as possible by exploiting sparsity. Sparsity can occur at two levels within a multidisciplinary problem: between disciplines, when certain analyses do not affect all outputs, and within a discipline when, the Jacobian of that discipline is sparse. The numerical procedures are implemented in NASA's OpenMDAO framework, providing a flexible API for declaring discipline-level derivatives that can handle sparsity within a discipline. The tool is demonstrated in two MDO problems: the design of a small satellite and its operation with the objective of maximizing downloaded data to a ground station, and the design of a horizontal-axis wind turbine with the objective of minimizing the cost of energy. In both cases, the method demonstrated improved efficiency by taking advantage of analytic gradients considering sparsity. This new capability in OpenMDAO greatly facilitates the implementation of system-level direct and adjoint coupled derivative evaluations, and is applicable for general problems.

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“…In the words of Pate et al [23], the formulation of these problems has become increasingly complex as the number of analysis tools and design variables included in typical studies has grown. In this context, the problem of determining a feasible data flow between tools to produce a specified set of system-level outputs is combinatorially challenging.…”

Section: Introductionmentioning

confidence: 99%

Graph-based algorithms and data-driven documents for formulation and visualization of large MDO systems

et al. 2018

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A new system is presented that enables the visualization of large multidisciplinary design optimization (MDO) problems and their solution strategy. It was developed within the scope of the European project AGILE. In AGILE, collaborative MDO is performed in large, heterogeneous teams of experts by solving MDO problems using a collection of design and analysis tools. This paper focuses on the visualizations required to support the formulation phase of an MDO project. The Knowledge and graph-based AGILE Design for Multidisciplinary Optimization System (KADMOS), an open-source MDO support system developed by Delft University of Technology, uses graph-based analysis to formulate an MDO problem and its solution strategy, based on the disciplinary analyses available in a repository. The results of KADMOS are stored in the standardized format CMDOWS (Common MDO Workflow Schema), which comprises the entire information on an MDO system. Although, based on Extensible Markup Language, the readability of the CMDOWS file is quite poor also for MDO experts, especially for large MDO systems involving thousands of variables. Providing visualization capabilities to thoroughly inspect the outcome of the different MDO formulation steps becomes a key factor to enable the specification of large MDO systems in a heterogeneous team. Therefore, VISTOMS (VISualization TOol for MDO Systems), a dynamic visualization package, was developed by RWTH Aachen University to enable the visualization and inspection of the different MDO system specification steps, thereby removing one of the main hurdles for using MDO as a development process. The developed visualization capabilities are demonstrated by means of an aerostructural wing design optimization project. Keywords MDO · Visualization · KADMOS · CMDOWS · VISTOMS Abbreviations

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A graph theoretic approach to problem formulation for multidisciplinary design analysis and optimization

Cited by 22 publications

References 24 publications

Multi-agent approach based on a design process for the optimization of mechatronic systems

Multi-agent approach based on a design process for the optimization of mechatronic systems

Automatic Evaluation of Multidisciplinary Derivatives Using a Graph-Based Problem Formulation in OpenMDAO

Graph-based algorithms and data-driven documents for formulation and visualization of large MDO systems

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