Benchmarking multidisciplinary design optimization algorithms

Tedford, Nathan P.; Martins, Joaquim R. R. A.

doi:10.1007/s11081-009-9082-6

Cited by 107 publications

(64 citation statements)

References 20 publications

(26 reference statements)

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“…Without the modifications discussed in this section, the architecture requires a disproportionately large number of function and discipline evaluations [156,157,137,135], assuming it converges at all. When the system-level equality constraints are relaxed, the results from CO are more competitive with those from other distributed architectures [134,145,136] but still compare poorly with those from monolithic architectures.…”

Section: Algorithm 4 Enhanced Collaborative Optimization (Eco)mentioning

confidence: 98%

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Multidisciplinary Design Optimization: A Survey of Architectures

2013

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Multidisciplinary design optimization (MDO) is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of MDO, various methods (architectures) have been developed and applied to solve MDO problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitates the understanding of the various architectures, and how they relate to each other.A classification of the MDO architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both a theoretical and experimental perspective. For each architecture, several applications to the solution of engineering design problems are cited. The result is a comprehensive but straightforward introduction to MDO for non-specialists, and a reference detailing all current MDO architectures for specialists.

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Section: Algorithm 4 Enhanced Collaborative Optimization (Eco)mentioning

confidence: 98%

“…Perez et al [134], Yi et al [135], and Tedford and Martins [136] all compare CSSO to other architectures on low-dimensional test problems with gradient-based optimization. Their results show that CSSO required many more analysis calls and function evaluations to converge to an optimal design.…”

Section: Concurrent Subspace Optimization (Csso)mentioning

confidence: 99%

Multidisciplinary Design Optimization: A Survey of Architectures

2013

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“…This makes MDO architectures subject to the "no free lunch theorem". An analytical scalable problem was introduced by Martins and Tedford 5,6 to highlight the influence of the problem dimensionality on the performance of architectures. This analytical problem has a quadratic objective function and linear inequality constraints, and the governing equations consist of a linear system.…”

Section: Motivationmentioning

confidence: 99%

“…The propane combustion problem was transcribed from the NASA MDO test suite. 7,15 It describes the chemical equilibrium reached during the combustion of propane in air. The variables represent each of the ten combustion products as well as the sum of the products.…”

Section: One-dimensional Restrictionsmentioning

confidence: 99%

On the Consequences of the "No Free Lunch" Theorem for Optimization on the Choice of an Appropriate MDO Architecture

Vanaret¹,

Gallard²,

Martins

2017

18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18241To link to this article: DOI : 10.2514/6.2017-3148 URL : https://doi.org/10. 2514/6.2017-3148 Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Multidisciplinary Design Optimization (MDO) based on high-fidelity models is challenging due to the high computational cost of evaluating the objective and constraints. To choose the best MDO architecture, a trial-and-error approach is not possible due to the high cost of the overall optimization and the complexity of each implementation. We propose to address this issue by developing a generic methodology that applies to any (potentially expensive) design optimization problem. The methodology consists in generating a scalable analytic replacement function that can be quickly computed, yet captures the structure and behavior of the original high-fidelity problem. One crucial characteristic of this replacement model is that the number of inputs and outputs can be set independently, making the problem scalable. This facilitates the evaluation of MDO architectures for the original MDO problem. The methodology is applied to two academic MDO test cases: a supersonic business jet design problem and a propane combustion problem. Well-known architectures (Multidisciplinary Feasible (MDF) and Individual Disciplinary Feasible (IDF)) are benchmarked on various instances to demonstrate the dependency between the performance of the architecture and the dimensions of the problem. The results show that the "no free lunch" theorem of optimization, which states that no particular optimization algorithm holds an advantage over another when considering all possible problems, also applies to the choice of the best suited MDO architecture for an MDO problem with scalable dimensions.

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“…Historically, AAO approaches have performed well in benchmarking tests against other MDO algorithms [45]. Some believe they are the most computationally tractable of all MDO approaches [2], but they are sometimes written off because they create large problems with many equality constraints.…”

Section: Current Limitations and Future Perspectivesmentioning

confidence: 99%

Geometric Programming for Aircraft Design Optimization

Hoburg

Abbeel

2014

AIAA Journal

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We propose formulating conceptual-stage aircraft design problems as geometric programs (GPs), which are a specific type of convex optimization problem. Recent advances in convex optimization offer significant advantages over the general nonlinear optimization methods typically used in aircraft design. Modern GP solvers are extremely fast, even on large problems, require no initial guesses or tuning of solver parameters, and guarantee globally optimal solutions. These benefits come at a price: all objective and constraint functions -the mathematical models that describe aircraft design relations -must be expressed within the restricted functional forms of GP. Perhaps surprisingly, this restricted set of functional forms appears again and again in prevailing physics-based models for aircraft systems. Moreover, we show that for various models that cannot be manipulated algebraically into the forms required by GP, we can often fit compact GP models which accurately approximate the original models. The speed and reliability of GP solution methods makes them a promising approach for conceptual-stage aircraft design problems.

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Benchmarking multidisciplinary design optimization algorithms

Cited by 107 publications

References 20 publications

Multidisciplinary Design Optimization: A Survey of Architectures

Multidisciplinary Design Optimization: A Survey of Architectures

On the Consequences of the "No Free Lunch" Theorem for Optimization on the Choice of an Appropriate MDO Architecture

Geometric Programming for Aircraft Design Optimization

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