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Multidisciplinary design optimization: A Survey of architectures
 AIAA Journal
"... 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 ..."
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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 nonspecialists, and a reference detailing all current MDO architectures for specialists. I.
Complete Configuration AeroStructural Optimization Using a Coupled Sensitivity Analysis Method
, 2002
"... This paper focuses on the demonstration of a new integrated aerostructural design method for aerospace vehicles. The approach combines an aerostructural analysis solver, a coupled aerostructural adjoint solver, a geometrybased analysis and design integration strategy, and an effcient gradientba ..."
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Cited by 8 (6 self)
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This paper focuses on the demonstration of a new integrated aerostructural design method for aerospace vehicles. The approach combines an aerostructural analysis solver, a coupled aerostructural adjoint solver, a geometrybased analysis and design integration strategy, and an effcient gradientbased optimization algorithm. The aerostructural solver ensures highly accurate solutions by using highfidelity models for both disciplines as well as a highfidelity coupling procedure. The Euler equations are solved for the aerodynamics and a detailed finite element model is used for the primary structure. The coupled aerostructural adjoint solution is used to calculate the needed sensitivities of aerodynamic and structural cost functions with respect to both aerodynamic shape and structural variables. The geometric outer mold line (OML) serves not only as an interface between the two disciplines for both the state and costate systems, but also as an interface between the numerical optimization algorithm and the highfidelity analyses. Another set of design variables parameterizes a structure of fixed topology. KreisselmeierSteinhauser functions are used to reduce the number of structural constraints in the problem. Sample results comparing a fully coupled aerostructural design with a more traditional sequential optimization are presented.
Augmented Lagrangian Coordination for Distributed Optimal Design in MDO
 Int. J. Numerical Methods Engineering
, 2008
"... Quite a number of coordination methods have been proposed for the distributed optimal design of largescale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for ..."
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Quite a number of coordination methods have been proposed for the distributed optimal design of largescale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for which convergence proofs are available have mostly been developed for socalled quasiseparable problems (i.e. problems with individual subsystems coupled only through a set of linking variables, not through constraints and/or objectives). In this paper, we present a new coordination approach for multidisciplinary design optimization problems with linking variables as well as coupling objectives and constraints. Two formulation variants are presented, offering a large degree of freedom in tailoring the coordination algorithm to the design problem at hand. The first, centralized variant introduces a master problem to coordinate coupling of the subsystems. The second, distributed variant coordinates coupling directly between subsystems. Our coordination approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The proposed coordination algorithms can be shown to converge to Karush–Kuhn–Tucker points of the original problem by using the existing convergence results. We illustrate the flexibility of the proposed approach by showing that the analytical target cascading method of Kim et al. (J. Mech. DesignASME 2003; 125(3):475–480) and the augmented Lagrangian
Distributed Multidisciplinary Design and Collaborative Optimization
 Stanford, California USA, Stanford University
, 2004
"... These notes describe some recent ideas for distributed design and their application to largescale aerospace systems. In this type of multidisciplinary optimization, design tasks are decomposed into domainspecific subproblems, and coordinated to achieve an optimal system. Focusing on collaborative ..."
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These notes describe some recent ideas for distributed design and their application to largescale aerospace systems. In this type of multidisciplinary optimization, design tasks are decomposed into domainspecific subproblems, and coordinated to achieve an optimal system. Focusing on collaborative optimization, one form of design decomposition, the notes detail the methods, summarize recent results, and suggest new variants of these approaches that improve performance. 2.
A Local Convergence Analysis of Bilevel Decomposition Algorithms
, 2004
"... Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decom ..."
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Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems, one per discipline, and a coordinating master problem. A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and analyze their properties. In particular, we show that the proposed problem formulations are mathematically equivalent to the original problem and that the proposed algorithms converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms. Key words. Decomposition algorithms, bilevel programming, nonlinear programming, multidisciplinary design optimization (MDO). 1
ENHANCED COLLABORATIVE OPTIMIZATION: A DECOMPOSITIONBASED METHOD FOR MULTIDISCIPLINARY DESIGN
, 2008
"... Astute choices made early in the design process provide the best opportunity for reducing the life cycle cost of a new product. Optimal decisions require reasonably detailed disciplinary analyses, which pose coordination challenges. These types of complex multidisciplinary problems are best addresse ..."
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Astute choices made early in the design process provide the best opportunity for reducing the life cycle cost of a new product. Optimal decisions require reasonably detailed disciplinary analyses, which pose coordination challenges. These types of complex multidisciplinary problems are best addressed through the use of decompositionbased methods, several of which have recently been developed. Two of these methods are collaborative optimization (CO) and analytical target cascading (ATC). CO was conceived in 1994 in response to multidisciplinary design needs in the aerospace industry. Recent progress has led to an updated version, enhanced collaborative optimization (ECO), that is introduced in this paper. ECO addresses many of the computational challenges inherent in CO, yielding significant computational savings and more robust solutions. ATC was formalized in 2000 to address needs in the automotive industry. While ATC was originally developed for objectbased decomposition, it is also applicable to multidisciplinary design problems. In this paper, both methods are applied to a set of test cases. The goal is to introduce the ECO methodology by comparing and contrasting it with ATC, a method familiar within the mechanical engineering design community. Comparison of ECO and ATC is not intended to establish the computational superiority of either method. Rather, these two methods are compared as a means of highlighting several promising approaches to the coordination of distributed design problems.
World Congresses of Structural and Multidisciplinary Optimization
, 2005
"... In this research, a reliability based topology optimization (RBTO) for structural design methodology using the Hybrid Cellular Automata (HCA) method is proposed. More specifically, a decoupled reliability based design optimization (RBDO) approach is utilized, so that the topology optimization is sep ..."
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In this research, a reliability based topology optimization (RBTO) for structural design methodology using the Hybrid Cellular Automata (HCA) method is proposed. More specifically, a decoupled reliability based design optimization (RBDO) approach is utilized, so that the topology optimization is separate from the reliability analysis. In this paper, a maximum allowable displacement failure mode is considered. In this methodology, starting from a continuum design space of uniform material distribution and initial uncertain variable values, a deterministic topology optimization is followed by a reliability assessment of the resulting structure to determine the most probable point of failure (MPP) for the current structure. The MPP is determined with respect to the maximum allowable deflection of the structure when loaded. This is generally a computationally expensive process using traditional techniques due to the large number of design variables associated with topology optimization problem. However, combining the e#cient methods of the nongradient HCA algorithm with the decoupled approach for RBDO aims to reduce this burden. The topology optimization was without constraint in previous applications of the HCA method. To accommodate RTBO, a mechanism for a global constraint for maximum allowable displacement is developed. This paper details the methodology for the sixsigma design of structures using topology optimization.
7 MDO Architectures
"... els  a hierarchy  as well as complex coupling between the divisions. Figure 1: Organization of an aircraft company. Figure 2: Flow chart for an aircraft design procedure. MDO is concerned with the development of strategies that utilize current numerical analyses and optimization techniques to ..."
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els  a hierarchy  as well as complex coupling between the divisions. Figure 1: Organization of an aircraft company. Figure 2: Flow chart for an aircraft design procedure. MDO is concerned with the development of strategies that utilize current numerical analyses and optimization techniques to enable the automation of the design process of a multidisciplinary system. One of the big challenges is to make sure that such a strategy is scalable and that it will work in realistic problems. Traditionally, designers have resorted to a series of parametric studies to make design decisions. This involves plotting a figure of merit or constraint versus one or three design parameters. This studies are limited because of the inherent di#culty of visualizing data that has more than three dimensions. In addition, the computational cost of such studies is proportional to p n where p is the number of points evaluated in each direction and n is the number of design variables. Why MDO? . Paramet
7 MDO Architectures
"... evels  a hierarchy  as well as complex coupling between the divisions. Figure 1: Organization of an aircraft company. Figure 2: Flow chart for an aircraft design procedure. MDO is concerned with the development of strategies that utilize current numerical analyses and optimization techniques t ..."
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evels  a hierarchy  as well as complex coupling between the divisions. Figure 1: Organization of an aircraft company. Figure 2: Flow chart for an aircraft design procedure. MDO is concerned with the development of strategies that utilize current numerical analyses and optimization techniques to enable the automation of the design process of a multidisciplinary system. One of the big challenges is to make sure that such a strategy is scalable and that it will work in realistic problems. Traditionally, designers have resorted to a series of parametric studies to make design decisions. This involves plotting a figure of merit or constraint versus one or three design parameters. This studies are limited because of the inherent di#culty of visualizing data that has more than three dimensions. In addition, the computational cost of such studies is proportional to p n where p is the number of points evaluated in each direction and n is the number of design variables. 3 Why MDO? . Par
ON THE RELATIONSHIP BETWEEN BILEVEL DECOMPOSITION ALGORITHMS AND DIRECT INTERIORPOINT METHODS.
, 2004
"... Engineers have been using bilevel decomposition algorithms to solve certain nonconvex largescale optimization problems arising in engineering design projects. These algorithms transform the largescale problem into a bilevel program with one upperlevel problem (the master problem) and several lowe ..."
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Engineers have been using bilevel decomposition algorithms to solve certain nonconvex largescale optimization problems arising in engineering design projects. These algorithms transform the largescale problem into a bilevel program with one upperlevel problem (the master problem) and several lowerlevel problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used bilevel decomposition algorithms may fail to converge even when the starting point is very close to the minimizer. In this paper, we establish a relationship between a particular bilevel decomposition algorithm, which only performs one iteration of an interiorpoint method when solving the subproblems, and a direct interiorpoint method, which solves the problem in its original (integrated) form. Using this relationship, we formally prove that the bilevel decomposition algorithm converges locally at a superlinear rate. The relevance of our analysis is that it bridges the gap between the incipient local convergence theory of bilevel decomposition algorithms and the mature theory of direct interiorpoint methods.