mdo: assessment and direction for advancement— an opinion...

Struct Multidisc Optim (2010) 40:17–33DOI 10.1007/s00158-009-0381-5

FORUM ARTICLE

MDO: assessment and direction for advancement—an opinion of one international group

Jeremy Agte · Olivier de Weck · Jaroslaw Sobieszczanski-Sobieski ·Paul Arendsen · Alan Morris · Martin Spieck

Received: 10 October 2008 / Revised: 17 February 2009 / Accepted: 12 March 2009 / Published online: 17 April 2009© Springer-Verlag 2009

Abstract This paper is a summary of topics presentedand discussed at the 2006 European–U.S. Multidiscipli-nary Optimization (MDO) Colloquium in Goettingen,Germany, attended by nearly seventy professionalsfrom academia, industry, and government. An attempt

A previous version of this article was published asAIAA-2007-1905 and presented at the 3rd AIAAMultidisciplinary Design Optimization SpecialistConference, April 2007

J. Agte (B) · O. de WeckDepartment of Aeronautics & Astronautics, MIT,Cambridge, MA, USAe-mail: [email protected]

O. de Wecke-mail: [email protected]

J. Sobieszczanski-SobieskiResearch & Technology Directorate,NASA Langley Research Center,Langley, VA, USAe-mail: [email protected]

P. ArendsenCollaborative Engineering Systems Department,NLR, Amsterdam, The Netherlandse-mail: [email protected]

A. MorrisSchool of Engineering,Cranfield University, Cranfield, Great Britaine-mail: [email protected]

M. SpieckInstitute of Aeroelasticity,German Aerospace Center,Goettingen, Germanye-mail: [email protected]

is made to accurately reflect the issues discussed by thisdiverse group, qualified by interest, experience, and ac-complishment to present an opinion about the state-of-the-art, trends, and developments in MultidisciplinaryDesign Optimization. As such, its main purpose is toprovide suggestions and stimulus for future research inthe field. The predominant content of the colloquiumwas centered on aerospace, with a few contributionsfrom the automotive industry, and this is reflected in thearticle. Due to the timeframe that has passed since theconclusion of the workshop, the authors have updatedtopics where appropriate to reflect observed develop-ments over the past 3 years. Finally, rather thandwelling extensively on past accomplishments and cur-rent capabilities in MDO we focus on the needs andidentified shortcomings from the colloquium whichlead to potential future research directions. A briefMDO background is provided to set the discussion in itsproper context.

Keywords Multidisciplinary design optimization ·MDO · Review · Trends · Current

Abbreviations

F Functional behavior (“performance”) of asystem;

g, h Inequality constraints, equality constraints;i, j Variable, module or subsystem index;m Number of fixed parameters;n Number of design variables;p Vector of (fixed) parameters;x Vector of design variables;N Number of modules or subsystems;

18 J. Agte et al.

Y Module or subsystem inputs;Z Module or subsystem outputs

1 Introduction

This paper is not a formal survey of the field ofMultidisciplinary Design Optimization and the authorsare not a recognized technical committee empoweredto report on MDO. They do, however, represent afairly broad-based group of individuals who are ac-tively involved in MDO, both theory and applications.The group acted as the technical organizing committeefor the 2006 European–U.S. Multi-Disciplinary Opti-mization (MDO) Colloquium that was hosted by theGerman Aerospace Center (DLR) in Goettingen,Germany, from 17–19 May, 2006. The workshop’s em-phasis was on uncovering gaps and shortcomings ratherthan reporting on completed projects and highlightingaccomplishments, and it served as the foundation forthe content of this article. Here, the specific productthat emerged from the exchange of opinions at thecolloquium is a list of specific research issues and devel-opment directions forming an MDO Research Agendathat the Goettingen participants wish to contribute tothe advancement of MDO.

The article complements several other summaryarticles of similar nature, ref. Giesing and Barthelemy(1998), Bartholomew (1998), Alexandrov (2005),Tedford and Martins (2006) and is not a comprehensivereview, as this has been done by Sobieszczanski-Sobieski and Haftka (1997) and others. As such, we so-licit comments to the broader engineering communitywith the purpose of contributing to and inspiringdebate. Due to the broad nature of work that has beenand continues to be done in MDO, the authors admitthat certain important accomplishments may not havebeen equally represented in the three-day workshopand apologize beforehand for any such exclusions. Weemphasize that these exclusions are merely a reflectionof the colloquium audience composition and not aresult of any type of priority rating.

2 Background

The roots of MDO are found in structural optimiza-tion. This is not without good reason as in nearly allengineering systems there is a structure to which othersubsystems attach, and much of the subsystem inter-actions involve the structure as a conduit. In the fieldof optimization the Nonlinear Programming (NLP) for-malism was first transplanted to structural optimization

practice in Schmit’s seminal work on a simple three bartruss (Schmit 1971). The general formulation of an NLPin this context is shown in (1):

min f(x, p

)

x = [x1 . . . xn]T , p = [p1 . . . pm

]T

xi,LB ≤ xi ≤ xi,U B, i = 1, 2, . . . n

s.t. g(x, p

)< 0, h

(x, p

) = 0 (1)

where f is the function to be minimized, x is a n-dimensional vector of design variables with lower andupper bounds, p is a vector of fixed parameters thatinfluence the behavior of the system but cannot befreely chosen (material properties, operating condi-tions, . . . ), and g and h are inequality and equalityconstraints, respectively. This notation can vary butis generally widely accepted. By assigning meaning tothe design variables (e.g. beam cross sections, platethicknesses. . . ) and choosing a relevant objective func-tion (e.g. mass) and constraints (e.g. maximum stresssmaller than safety factor times yield stress) the NLPformalism became widely accepted, originally compet-ing against, and later having been reconciled with,the optimality criteria approach rooted in the time-honored concept of fully-stressed design. In a fewyears, the concept spread throughout structural en-gineering and attracted interest in other disciplines,first in aerospace applications where weight (mass) wascrucial.

Eventually, this led to inclusion of disciplines otherthan structures in the structural optimization loop assources of data, again in aerospace first where in-terdisciplinary coupling to structures was too strongto be neglected. In the next logical step, the designspace (x) was extended to include variables intrinsic tothe other disciplines such as the aerodynamics (airfoiland wing shape), aircraft performance (mission pro-file), and propulsion (engine thermodynamics), initiat-ing MDO on a growth path toward encompassing theentire vehicle as a system.

Consistent with the computer technology limitationsof the time, the first MDO efforts developed at twolevels. At one level, structural, aerodynamics, and air-craft performance analysis codes, all processing math-ematical models whose fidelity could be categorized asmedium by the standard of the day, were nested in asingle optimization loop (Fig. 1) operating on a verylimited (a dozen or less) design variables to optimizea system level objective such as flight range (Fultonet al. 1974). At another level, the number of disciplineswas increased to a more complete set typical for a

MDO: assessment and direction for advancement—an opinion of one international group 19

Analysis

Code

Optimizer

initial

guessoptimal

design

convergence

criterionf k, gk, hk

x0

xk+1

x*

f(xk)

Fig. 1 NLP—simple optimization loop

conceptual design stage at the price of lowered fidelityto gain a fairly realistic representation of the designprocess at that stage (Vanderplaats 1976).

Advancing computer technology enabled higher fi-delity codes to be processed faster and gradually eraseddistinction between the above two levels leading tolarge monolithic codes invoking several disciplinarymathematical models in a single optimization loop(see again Fig. 1). Intrinsic practical limitations of themonolithic systems of disciplinary codes soon becameapparent (for large n) and stimulated development ofdecomposition methods intended to break large tasksinto sets of smaller ones while preserving the couplings(Balling and Sobieszczanski-Sobieski 1996). See Fig. 2and a summary in Sobieszczanski-Sobieski and Haftka(1997).

At a high level, one began to distinguish between sys-tem level optimization and subsystem level optimiza-tion, based on the fact that for an internally coupled

Fig. 2 MDO problem decomposed into two levels—NAND @disc. level, SAND @ sys. level

system, the optimal system-level design is not simplya collection of individually optimized subsystems.The subsequent emergence of decomposition methodsbegan to differentiate MDO from pure structural op-timization, although some of the theoretical underpin-nings of the decomposition methodology were adopteddirectly from this field, including various forms of sen-sitivity analysis (Sobieszczanski-Sobieski et al. 1982;Sobieszczanski-Sobieski 1990; Van Keulen et al. 2005)and approximation methods (Barthelemy and Haftka1993), which more recently have become known assurrogate-based methods (Queipo et al. 2005; Simpsonet al. 2004).

It should be noted that decomposition as an ap-proach to break a large optimization problem into anequivalent set of smaller, independent but coordinatedproblems was successfully developed and applied atboth the disciplinary and multidisciplinary levels ofoptimization. At both levels, the motivation for de-composition was the same—compression of the exe-cution time by bringing in more resources, whetherhuman or computational, to operate on the problem athand. However, the decomposition implementations atthe disciplinary and multidisciplinary system levels dif-fered. The former lent itself to a particular partitioningof a set of equations that governed the given discipline.The latter involved many diverse sets of such equationswhose interaction often posed a problem within itself,and in large applications involved a number of differentteams of specialists. That involvement required (andstill requires) dealing with a non-mathematical but cru-cially important set of human factors as a prerequisiteto success.

The above elements combined with the data or-ganization in the format of the design dependencematrix, a.k.a. N-square diagram N2, or design struc-ture matrix DSM (Smith and Eppinger 1997). Thisenabled a set of new decomposition methods sur-veyed in (Sobieszczanski-Sobieski and Haftka 1997).A few examples are Linear Decomposition, Collabo-rative Optimization(Sobieski and Kroo 2000), Concur-rent Subspace Optimization, and Bi-level IntegratedSystem Synthesis (Sobieszczanski-Sobieski et al. 2000).Each of the above decomposition methods contributeda different and specific mathematical solution to theproblem of optimization of a large and complex system.It is their mathematical content that makes them dis-tinct from and complimentary to the Computer AidedDesign-inspired frameworks dedicated to integrationof computer codes in the sense of streamlined datapassing, storage, retrieval, and user interface.

Another relatively recent contribution of MDO isframeworks that allow finding optimal system designs

20 J. Agte et al.

for a set of desired targets or goals. This is importantas designs in industry are often driven by contractualrequirements and not by optimum performance. Suchframeworks typically seek one or more solutions thatmeet a design target within a pre-specified numericalperformance. Frameworks that enable goal-seeking de-sign are, among others, Physical Programming (Messac1996), Analytical-Target-Cascading (Kim et al. 2003)and Isoperformance (de Weck and Jones 2006). Animportant research direction has also been the develop-ment of more powerful model reduction methods thatretain the key information in models, while reducingtheir dimensionality (Willcox and Peraire 2002).

Figure 3 provides a notional timeline of the develop-mental history of MDO.

3 Successes and identified limitations

As one could argue that the ultimate benchmark of aresearch field’s impact is indicated by the realization of

its theories into successful products through industry,the focus in the following examples is on MDO throughan industrial perspective. Numerous MDO applicationmethods in various industrial sectors were presented atthe Germany workshop with the major users of thistype of technology being the aeronautical and auto-motive industries. However, the actual use of genuineMDO methods within industry at large (beyond auto-motive and aerospace) is still rather limited.

3.1 Industrial successes

Within these major industrial sectors the designprocess follows a regular development process involv-ing broadly three levels of models:

1. Preliminary design that uses explicit behaviormodels

2. Configuration design employing implicit low-fidelity models

Topic 1960 65 70 75 80 85 90 95 2000 2005 2008

Schmit's 3 bar truss M

Gen opt codes appear (Aesop, CONMIN)

LaRC 1st MDO SST papers

LaRC SST MDO project

ARC ACSYNT & Applications

LaRC IPAD project

LaRC AOO & MDOB & IRO

EU MOB

AIAA MDO TC

AIAA/USAF bi-annual MAO Symp.

ISSMO World Congress.

NATO AGARD, RTO M M M

ASME annual Auto Design

ICAS bi-annual opt component

AIAA/ASCE SDM

Excel M

Matlab M

Mathematica M

Integration VRD

Integration iSIGHT

Integration ALTAIR

Genesis

Integration Phoenix

Concurrent Computing

Linear decomp. M

Opt Sensit M

System Sensit M

Approximations

Approximation based decomp.

Analytical Target Cascading (Michigan)

Collaborative Optimization (Stanford)

BLISS-LaRC

CSSO-LaRC ND

Visualization UofBuff

Commercialization BLISS M

Genetic Algorithms

Optimality criteria

NASA Glenn NPSS

Fig. 3 Notional MDO timeline (“M” indicates a milestone)


Soph

isti

cati

onof

Opt

imiz

atio

n

Representation of Physics

Disjoint analysis /trade studies

Highly-coupledconceptual designsystems

True Physics Modeling /Multi-Disciplinary Analysis /Optimization

Disjoint / singlediscipline analysis

CFDFEA/FEM

787

777

757/767707D

isjo

intD

isci

plin

ary

Obj

ecti

ves

Inte

grat

edO

bjec

tive

s

Empirical Mathematical Model

707

Fig. 4 Reaching towards full a/c MDO across successive a/cfamilies (adapted from Boeing, 2006 European–U.S. MDO Col-loquium Proceedings)

3. Detailed design that employs implicit high-fidelitymodels

The application of MDO methods and techniquesin industry has, for the most part, started at the detaildesign stage and is now slowly, but steadily, movingupstream into employment at the configuration andpreliminary design stages. This move parallels a similartrend from component level design, with higher fidelitymodels, towards a broader system level optimizationinitially utilizing lower fidelity and/or surrogate mod-eling. Figure 4 is a depiction of Boeing’s systematicprogress towards full aircraft MDO over successive newaircraft families as stepping stones through the years.

As discussed, the initial application of optimizationmethods focused on the creation of satisfactory struc-tures with minimum weight, often employing techniquesat the detailed design stage that sought vertex solutionsin the design space. The field has evolved to the pointwhere major components are optimally designed usingvery large high-fidelity models in four to five iterations,supported by the continued development of more com-plex digital models (Fig. 5).

Within the aircraft industry, an MDO approach isbeing introduced at the detailed design stage by allow-ing disciplines to interact in a loosely coupled manner.Taking this approach, Boeing reports significant gainsin weight reduction on the 787 program, examples ofwhich are indicated in Table 1.

The automotive industry has an apparent lead overthe aerospace community in the use of system leveloptimization with low-fidelity models applied at theconfiguration design stage. Incorporating MDO intothe automotive configuration design phase is presum-ably easier than undertaking this task in the aerospaceindustry as disciplines in automotive engineering aremore loosely coupled. Within the automotive sector,designs are created in a multi-attribute environmentrather than a multi-disciplinary environment. Suchaspects as noise-vibration-harshness (NVH), crashwor-thiness, drivability, etc. provide a coupled design en-vironment where attributes are shared through systemlevel variables. This allows the use of response surfacesand more general design of experiments (DOE) pro-cedures, placing the MDO process firmly within theconfiguration design phase.

Recent developments at Dassualt (Ravachol 2006)are geared towards taking into account that the digitaldesign environment must be integrated with distrib-uted design and manufacturing teams, pushing researchinto creation of methods that can accommodate virtualdesign teams. Additionally, they are focusing on inte-grating manufacturing and downstream requirementsinto the MDO process. This is accomplished by usingLagrange Multipliers, generated at the detailed designstage, to inform engineers involved with the prelimi-nary design stage of important downstream constraints.

3.2 Limitations identified by industry

In addition to the above successes, a number of needsand limitations relating to the use of MDO methodsand tools in industry are evident as listed in Table 2.

Fig. 5 a Lotus optimizedengine bracket (AltairOptiStruc). b Comp.thickness distribution(VR&D)

Optimum Composite Thickness Distribution

22 J. Agte et al.

Table 1 Examples of gainsfrom the application of MDOtechnology

Industrial sector Component/activity Gain from MDO

Aircraft Vertical fin major aircraft Significant increasein effectiveness

Aircraft Nacelle configuration Noise reduction with 15%weight reduction

Aircraft Flight test program Reduced to less than 1 year(normally 2–3 years)

Automotive Optimized structural design Time to achieve acceptablefor crash worthiness level of impact performance

reduced from 1.5 yearsto 1.5 days

The last point, the immaturity of model verifica-tion and validation—especially across a large designspace—is expanded below.

3.3 Model fidelity and validation/verification

An expensive and serious effort is made in most indus-trial sectors to ensure that the computations processused in the design of a product is based on modelsthat have been both verified and, as far as is possible,validated. Validation implies that a finite element orcomputational fluid dynamics model has been com-pared with full scale test and found acceptable. Whereno such tests exist because the product has not yet beenconstructed, structural and aerodynamic specialists willhave devised methods that, in some sense, replicatethe classical validation process using past experience,specific structural or wind tunnel tests and sensitivitystudies. This is very time consuming and expensive butprovides models that can be relied upon to replicate thebehavior of the in-service vehicle.

In the case of an aircraft, when a structural layoutis offered to optimization algorithms within an MDOframework, it is normal to discover that significantchanges in aircraft planform result. An experienced en-gineer would argue that the output from these modelscannot be trusted because the structural and aerody-namic models do not relate to the modified configu-ration. They have not been validated for the modifieddesign. The underlying question being asked is, havingstarted the MDO process with a set of validated andverified models, how far can these models be extendedbefore the results become unreliable? The same ques-tions require answering for all the major industries thatintend on using MDO methods. There is, therefore, areal need for industry to provide a basis whereby MDOmethods can be validated in a manner that provideslimits beyond which MDO results either cannot beaccepted or may only be interpreted as merely trendpointers. It is accepted that this is a non-trivial require-ment and that a significant amount of work is required.However, information is required on the limits of ac-ceptability of MDO results before involved engineers

Table 2 Needs andRequirements for furtherMDO development identifiedby industry

Industry Requirement/limitations identified

Aerospace To take full advantage of composites withunconstrained fiber orientation (not only 0, 90, 45)

Minimize manufacturing and tooling costsComposite electromagnetic effect optimizationFull life cycle business case optimizationIncorporation of MDO methodology in multi-level

efficient strategy, rather than only single levelDesign of truly innovative configurations (e.g. BWB)

Automotive Response surface and design of experiments methodshave difficulty handling the required numberof design variables

Design targets not sufficiently defined to allow the useof MDO, design evolves as more aspects are factoredin over time

Exploit coupling of vehicle physics and manufacturingvia variables shared by both areas

Model verification and validation still immature


make major design decisions based on the output ofsuch systems are made.

3.4 MDO in the workplace

The use and acceptance of MDO in the industry work-place, and to a lesser degree in certain research in-stitutes, hinges upon its functionality at three levels:technical, organizational and cultural. Overcoming thetechnical barrier is probably the easiest of the threeto understand and address. Most MDO ‘advocates’and researchers work to prove MDO’s technical worthon a day to day basis, many times at the expense ofoverlooking the other two levels.

At the organizational level, integration that occurs invery large engineering companies has been limited toexchange of data files between departments (organiza-tional units), while departments retain their disciplinaryfoci. This data exchange facilitates MultidisciplinaryDesign Analysis (MDA) but not true integration. Trueintegration could be demonstrated by the followingexample (based on discussion with K. Bhatia of TheBoeing Company).

Suppose that during the design process, someonewants to move the engines fifteen inches outboard toimprove flow into the engine nacelle. In a integratedprocess, that desire should be communicated to thecomputational infrastructure in a natural language, i.e.“MOVE ENGINES 15 INCHES OUTBOARD,” totrigger adjustments in the math models associated withstructures, aerodynamics, configuration (there might bea flap size to be adjusted), flight mechanics and even“relatively distant” component modification such asvertical tail size, which may need to be adjusted due tothe engine out condition. The MDA with the modelsadjusted would generate data informing the designer ofthe effects of the change. As far as the designer is con-cerned, the computing infrastructure would simply beperforming a background computation to proceed fromthe natural language command to the new data output.

In engineering we are nowhere near the above capa-bility. A note of progress made with video games in thisregard, however, is interesting. For example, in any oneof countless popular combat games the player controlstheir character’s actions by direct console inputs. Theother characters on (and even off) the screen act guidedby analysis combined with a set of rules. This analysis issurprisingly sophisticated. For example, CFD calcula-tions to show the ripple effects when someone is throwninto a pond of water, or enemy character responses thatdiffer every time the game is played. This ‘set of rules’alludes to the use of Artificial Intelligence methods.

Returning to the airplane design, an additional pathmight be to integrate the configuration group with thedisciplinary groups on a similar basis. For instance, fastacting surrogate models would exist as players, wherethe disciplinary teams hold the console and assume theresponsibility for creating and maintaining them, aswell as ensuring the process does not push them be-yond the bounds of validity. If it does, they update thesurrogates. Each team must then have sufficient depthand breadth to monitor, assess, and verify their domainanalyses.

The third level is cultural. People strive to live intheir most comfortable environment and tend to feelhappy there. Only a small minority is positively inclinedtowards far reaching integration. Many fear loss ofcontrol if their domain boundaries open up. Many areconcerned about job security. In management, there ismore openness to advanced ideas at the higher levelsbut the middle level managers tend to operate by con-sensus, busy meeting today’s commitments. They areoften averse to accepting additional risks. These issuesmust be purposefully addressed by those in charge be-fore successful large scale integration can reach the nextlevel. This will likely involve allowing an organization’sengineers a higher failure rate while trying new things.

3.5 Relationship between academia, industry,and government

Another roadblock to further development of MDOthat was discussed at the colloquium exists at the ed-ucational level. There are several areas in need ofimprovement. A primary issue is the lack of educationitself, not only at the university level, but also withinindustry and research organizations.

First addressing the university level, the past 5 to10 years have seen a relatively healthy growth in thenumber of dedicated MDO courses taught to graduatelevel students (although numbers are still small). How-ever, many of these classes are taught as applied mathcourses whose target audiences are limited in scope andoften do not include design engineers. Furthermore,design engineers who do enroll in these courses oftenreceive the instruction too late, at a point in their grad-uate studies after which they have already completedundergraduate conceptual and preliminary design. Co-incidentally, this late consideration of MDO also mir-rors that which occurs in industry and research, whereMDO practices are often not fully realized in the earlystages of design or research development. Althoughthe reasons may be many, this likely also points to alack of education within and between these respectiveinstitutes, where the engineers who can benefit most

24 J. Agte et al.

from MDO applications often are not aware of what isavailable to them until after preliminary design phasesare complete.

Of further concern is the lack of high quality educa-tional material available for use in studying and teach-ing MDO. There are few, if any, undergraduate leveltextbooks that deal either directly (textbooks dedicatedto MDO) or indirectly (textbook incorporating MDOinto its subject matter) with the topic of MDO as itsown field. A number of effective textbooks on designoptimization do exist (Papalambros and Wilde 2000),but they typically only cover a subset of topics.

Additionally, an adequate number of real-world testcases to which MDO methods and practices can beapplied in an academic setting are still missing fromthe educational toolbox. This may partially stem froma relationship between industry and academia that hasnot yet reached its full potential. Often, the modelsrequired for worthwhile MDO analysis, i.e. applying amulti-level MDO method to a complete real-world air-craft configuration, are commercially sensitive data thatindustry does not want to release to external parties.The fact that MDO is ‘multi-disciplinary’ also meansthat the required models cannot be limited to just oneor two components, but rather must provide a rela-tively comprehensive representation of the designedsystem. All of this leads universities to depend on self-developed test cases that are usually very simplified anddo not adequately represent the real-world complex-ities of industrial applications, further strengtheninga barrier that can best be surmounted by continuinggovernment funding.

A central problem inherent to the successful appli-cation of MDO is that it requires a broad range ofengineers, specifically discipline engineers, who under-stand MDO concepts and methods. It is not enough tointegrate an MDO specialist into an organization andexpect this person to exercise the necessary disciplineexpertise to correctly formulate the design problem,make adjustments when necessary, and evaluate theresults at the end. The amount of information andthe complexity of the problems are simply too large.To remedy this, there are several recommendationsthat may improve the education of upcoming designengineers such that the MDO mindset diffuses down toeven the lowest levels of the design organization.

The first of these is to move the initial instructionof MDO concepts from the graduate level down to theundergraduate level. This does not necessarily implythat MDO should be taught as an independent course,but rather that the fundamentals of MDO problem for-mulation, available tools, concept of constraints, etc.,should be taught alongside the more traditional design

course topics. The mechanics of the design space searchfor a constrained minimum as well as development ofsurrogate models tailored to the problem at hand isnow available in many commercial utility codes (seeAppendix). While understanding the way the abovesearch operates is important for successful use, theuser is relieved somewhat from the involvement withmathematical detail and is left free to focus more onthe physics of the problem to be solved. This paradigmchange has a profound potential for changing the wayoptimization is taught to engineering students, allowingMDO instruction from a physical perspective ratherthan a mathematical one, with less focus on the detailsof the algorithms and more on their use.

A second recommendation is directed towards thepartnership between industry and academia. On theside of academia, universities need to increase theirefforts to bring in more experience from seasoned engi-neers. In this manner, they ensure students are exposedto the difficulties of applying MDO in the real-worldand hopefully dissuade them from developing a “push-button” attitude. Industry could help out academiatremendously by working to provide: first, expertise inthe manner described above, and second, a suite oftest cases representative of real-world design problemsto be used in education. As academia is providing thefuture workforce for industry, it would be in industry’sown best interest to do so.

Finally, an effort is urged upon those universitiesalready engaged in the MDO field to work towardsdeveloping useful instructional material on the subjectof MDO in general. Current efforts to familiarize one-self with the topic usually require hours and hours ofsearching though hundreds of technical papers on thesubject and putting it together later in a piecemealfashion. There still remains some disagreement aboutwhether the field is ready for an item such as an ‘MDOHandbook,’ but most agree that a textbook, focusingon MDO from an engineering perspective, is needed.The various companies involved in producing MDOsoftware (see Table 4) could be of invaluable helpin this process as the majority of them have alreadycollected and written volumes worth of optimizationmaterial in support of their own products.

4 Research agenda

The colloquium identified a number of areas that areindeed promising research directions for the furtherdevelopment of MDO. The contents of the papers, pre-sentations, and discussions at the colloquium suggestcategorization of the anticipated MDO research and


Horizontal growth: “More of the Same”Dream Growth: “Q

ualitatively New and Powerful Capabilities”

Ver

tical

Gro

wth

: “T

read

New

Gro

unds

”

Fig. 6 MDO horizontal/vertical growth

development into two orthogonal directions that mightbe labeled “Horizontal Growth” and “Vertical Growth”(Fig. 6). The Horizontal Growth category encompassesdevelopments that improve on the MDO capabilitiesalready established toward greater dimensionalities ofthe applications and extend the application spectrum,e.g., to include the life cycle, economic factors, uncer-tainty, and reliability. This leaves the Vertical Growthlabel to identify developments that are conceptuallyand qualitatively new, for instance optimization of en-tire families of products for cumulative return on in-vestment. The two orthogonal growth directions areexpected to symbiotically reinforce each other into a“dream growth” delivering capabilities that are bothqualitatively new and powerful in terms of the size ofthe problems they will solve.

4.1 Horizontal growth of MDO

4.1.1 Formal classification of MDO problems(breadth vs. depth of coupling)

Classification of MDO (system optimization) problemsin terms of the coupling breadth and coupling strengthyields useful perspective on the utility of optimizationby decomposition. To see it, consider a system modeledby a number of modules, each module generating itsown output Y from input Z, received from some othermodule. The purpose of such system optimization bydecomposition is to make the dimensionally large op-timization more tractable by breaking it into a set ofsmaller tasks, each associated with a single module, plusthe coordination optimization at the system level torestore the temporarily suspended couplings. The cou-pling breadth and strength govern effectiveness of the

decomposition; hence, we need to quantify these quan-tities as system characteristics by well-defined metrics.

The volume of data Z, i.e., the length of the vectorZAB, where A and B designate receiver and sendermodules, respectively, is the metric for the A-to-Bcoupling breadth. The derivatives ∂Yi / ∂Z j serve asmeasures of the A-to-B coupling strength. Engineersoften favor the logarithmic derivative format, (∂Yi /Yi) / (∂Z j / Z j) as one that clearly shows how muchYi changes per unit change of Z j for better supportof judgment involved in design decisions. Calculationof ∂Yi / ∂Z j may be accomplished by any of the well-established sensitivity analysis techniques at the mod-ule (disciplinary) level. Because the derivatives forma matrix sized by the lengths of the vectors Y andZ, the A-to-B coupling strength is not expressible bya single measure, and there is no consensus how toreduce information embedded in the matrix [∂Yi / ∂Z j]to such a single measure. The average augmented withupper and lower bounds or the standard deviation isone of the obvious options. The concept of optimiza-tion by decomposition for a particular system may beexamined in context of that system’s coupling breadthand strength, the two metrics forming the horizontaland vertical coordinate axes, respectively, as illustratedqualitatively in Fig. 7.

The origin of that coordinate system corresponds toa system whose modules are totally uncoupled whosesensitivity analysis degenerates to a set of disjoint mod-ule (disciplinary) sensitivity analyses. That situation,that is seemingly happy because the system decomposi-tion is given and requires no action, has the drawback ofbeing completely devoid of any inter-modular synergythat may be beneficial when exploited intelligently bythe designer. On the other hand, systems at the NE

Coupling Breadth

Co

up

ling

Str

en

gth

Decompose

All-in-One

((Deco

mpose

))

(Deco

mpose

)

Fig. 7 Quantifying utility of decomposition in terms of couplingstrength and breadth in the MDO process

26 J. Agte et al.

corner of the square couple so widely and strongly thatdecomposition may not make the system optimizationtask any easier because dimensionality of the system-level coordination optimization may have dimensional-ity equal to or exceeding the optimization of the samesystem without decomposition. If modules A and Bcouple that way, combining them into a “supermodule”C = A ∪ B may be far better approach than decom-position. The “supermodule” C may correspond to anew discipline and aeroelasticity is a classic example ofthat. At the NW corner we have systems that couplestrongly but narrowly. Optimization by decompositionis most necessary and useful in that area and tech-niques now available are most effective there. Finally,at the SE corner we deal with systems whose couplingis broad but weak. By sound engineering judgmentsuch coupling breadth may be reduced by neglectingthe selected small derivatives to make decompositioneffective. Of course, opportunities to exploit synergyincrease with the distance from the origin of the squarein Fig. 7.

We tend to think of the sensitivity data (gradients)as search-guiding input to an optimization algorithm,but the same data may be directly useful in support ofthe designer’s decision making, especially if properlyvisualized. In fact, these data may be regarded as aquantification of the time-honored notion of the trade-off. Having said that, one must not forget that in anon-linear problem the gradient values computed foran initial design may vary considerably as the opti-mization progresses toward a constrained minimum. Sofar, systematic studies to illustrate the extent of theabove variability in representative applications havenot been widely published and remain a potential issuefor research. Research topics that arise in conjunctionwith the quantification of the system coupling breadthand strength include:

1. Establishing standards for presentation of the cou-pling strength and breadth for their best precisionand utility, considering their use in formal opti-mization as well as in direct support of engineeringjudgment.

2. Quantification of the above metrics in a statisticallymeaningful sample of engineering systems, e.g., air-craft, automobile, ship, etc., to determine averagesand bounds, and their distributions among typicalengineering systems, i.e., mapping typical engineer-ing systems on the diagram in Fig. 7. Further char-acterization of uncertainty propagation through thecoupled systems. All of this information wouldhelp designers in exercising judgment in theirapplications.

3. Extend the above (#2) to illustrate how the sensitiv-ities (gradients) vary in the passage from an initialto the optimal design.

4. Establishing guidelines for the cost and develop-ment of disciplinary math models that are bestsuited for application of MDO. These are not al-ways necessarily the same as those needed for tra-ditional, detailed disciplinary purposes.

5. Further development of the MDO algorithms high-lighted in the Appendix of this paper.

Regarding the propagation of uncertainty men-tioned in the second bullet above, one should acknowl-edge the increasing role that uncertainty in design hastaken and its increasing acceptance by the engineeringcommunity. While not specifically discussed at the 2006workshop, there is a broad list of references on thetopic, a few of which are Oakley et al. (1998), Suesand Cesare (2000), Yang and Gu (2003), Du and Chen(2005), and Allaire and Willcox (2008).

4.1.2 Massively concurrent computing(MCC) in MDO

Technologies for executing many computing and dataprocessing tasks simultaneously are rapidly becomeavailable to engineers. They come in a number offorms, e.g.

– Many processors in one unit. Two or fourprocessors are offered in desktop computers andworkstations.

– Clusters of inexpensive computers, each having ac-cess to a permanent memory of its own as well asto a mass storage shared with other computers. Thenumber of computers in a cluster ranges into thethousands.

– Large number of processors in a single installa-tion supported by local permanent memories and ashared mass storage. The number of processors ex-ceeds now 100,000 and is likely to exceed 1,000,000soon.

– All of the above embedded in networks extendingcontinentally or globally.

– Reconfigurable computers of which the Field-programmable Gate Array (FPGA) is an exam-ple. Software provided with FPGA enables userto transform it into a multi-processor computerdynamically to fit the problem at hand.

The trend toward MCC is motivated by the everincreasing need for computing speed combined withgradual exhaustion of the single, silicon-based proces-sor’s potential for further increase of its processing


rate. This is typically limited by heat generation andmanufacturing cost of ever denser packaging of thetransistors on the chip. It appears that single, silicon-based processor potential for a further speed-up is ofthe order of 1,000. Combining it with a million proces-sors in a supercomputer indicates acceleration of theorder of one billion relative to the computing speedtypically available today. To put this in a perspective,computations that would require one month today(therefore never attempted) could be accomplished inmilliseconds, i.e., practically instantaneously.

Computing at such speeds, if they actually couldbe attained, would support the designer in even themost complex tasks with the same effectiveness a wordprocessor with spelling and grammar check aids a let-ter writer today. This would become “computing atthe speed of thought,” (Sobieszczanski-Sobieski andStoraasli 2004) to mean that design work would bepaced by the engineer’s ability to think, formulate ‘whatif’ questions, and interpret the answers, rather than bywaiting for the answers. There would be an enormousbenefit to human creativity from uninterrupted train ofthought and rapid rate of answers.

However, the preceding paragraph opens with aconditional clause because to utilize MCC technologythe solution algorithm computational speed must bescalable with the number of processors. In engineeringapplications that involve large sets of coupled equationsmost of the present algorithms do not scale up thatway and that impedes severely the user’s acceptanceof MCC technology. The other impediment stems fromthe variety of computer architectures, i.e., the ways inwhich processors communicate, the various levels ofmemories and mass storages, and I/O devices. Thesearchitectures tend to be so diverse that a particularproblem solution running efficiently on one architec-ture may be unacceptably inefficient or not even run atall on another. This requires developers to tailor theirsolutions to the particular architecture at hand, thusdriving up the cost.

In the long run, that means the existing solution al-gorithms in engineering physics will have to be revisedand probably mostly replaced by new ones that areintrinsically parallel, therefore, naturally scalable. Thecellular automata approach to fluid dynamics is oneexample of such replacement. In the short and interimoutlook, coarse grained parallelism offers a way toutilize MCC technology in many applications immedi-ately. In the coarse-grained mode, existing code is repli-cated over N processors unchanged, and executed withdifferent inputs to carry out N tasks in the time of one.

Furthermore, the introduction of MCC as a new in-frastructure serving engineers ought to change the ‘util-

ity metric’ by which various analysis and optimizationmethods are evaluated and compared. Traditionally,numerical efficiency, roughly defined as the numberof arithmetical operations to solve the problem, wassuch a metric. It was ‘natural’ when a single processorperformed the operations but it needs to be replaced ina multiprocessor environment. A metric better suited togauge a numerical method utility in that environment isthe method’s capability to distribute numerical opera-tions for concurrent execution over as many processorsas possible to compress the elapsed time needed toobtain a solution, even at the price of increasing thetotal number of operations in that compressed time.

Fortunately, MDO provides an abundance of op-portunities for parallelism, e.g., finite difference tech-niques for sensitivity analysis, genetic algorithms foroptimization, Design of Experiments applications, andvarious decomposition schemes. This enables MDO ap-plication to very large problems without waiting for theengineering solution codes to be rewritten. Researchtopics that arise in conjunction with MCC utilizationin MDO:

1. Identify engineering analysis applications that re-quire such excessive elapsed computing times that,despite the need, they are not attempted, e.g.,full car crash simulation, unsteady aerodynamicswith high temperature and high altitude chemistryeffects.

2. Develop scalable solution algorithms for problemsselected from the above set, e.g., Finite ElementAnalysis, or CFD.

3. Demonstrate a coarse-grained MDO applicationusing more than 10,000 processors, e.g., a fulloptimization of an automobile including crashconstraints.

4. Negotiate with the computer science community asingle standard for presenting MCC machines todevelopers of the solution algorithms in engineer-ing physics. Considering that the above developersare physicists and engineers, the purpose of thestandard would be to hide the details and diver-sity of MCC architectures to enable creation ofMCC codes of permanent value. It would then bea separate task for computer science specialists toimplement such codes written against the standardon a particular architecture.

5. Numerical benchmarking and human-in-the-loopexperiments to measure the effectiveness of MDOapproaches and methods relative to current bestpractices that use optimization at the componentlevel.

28 J. Agte et al.

6. Development of surrogate models adaptable to thecomplexity of the design space to strike a properbalance between the cost, driven by the numberof the DOE points, and the sparsity of the DOEcoverage of the design space. This is in recognitionof the danger that sparse coverage combined withnonlinearity of the model may leave important fea-tures of the model undetected, hiding between thesparsely located DOE points.

4.2 Vertical growth of MDO

4.2.1 Creativity, cognition and flexibility

Optimization, whether disciplinary or MDO, beginswith laying down a concept that potentially may solvethe design problem at hand. This initialization is a start,from which the design process begins moving towardsa final design. Thus, the optimization state-of-the-artis limited to quantification of the initial design alreadyestablished qualitatively by a human creativity processthat, so far, is poorly understood and subject to researchin the field of the cognition science. In optimization, thehuman creativity translates formally into a definition ofthe design space and its requirements, whose parame-terization determines at the outset what the proposeddesign may potentially become and what it can nevertransform to. Thus the design space acts as an enablerand ultimate constraint at the same time (initializationof an aircraft configuration to a monoplane, including avariable for the wing position, produces a monoplane,the wing high or low or in a mid-location, but never abi-plane). Likewise, mutations in Genetic Algorithmsmerely explore at random the established design spacewithout transcending its definition, i.e., without addingany new coordinate axes.

Finally, traditional MDO assumes that a system suchas an aircraft or automobile is design for fixed require-ments. Some requirements, however, change over timeand can involve significant redesigns at a later time.These redesigns can be expensive and move the systemaway from its optimum configuration. MDO shouldbe applied to finding areas where flexibility can beembedded to optimize systems for a range of futurescenarios (de Weck et al. 2004).

The obvious possibility of just adding new dimen-sions to the design space after the search has begundoes not address the ultimate constraint issue becausethe meaning of any new design variable is defined bythe way it enters the underlying mathematical modeland must originate in the mind of the designer. Gen-eralization of the very concept of the design spaceto enable qualitative transformation of that space by

adding, redefining, and removing design variables si-multaneously with the numerical search would simulatewhat to a competent designer comes naturally andapparently is one of the intrinsic capabilities of the hu-man mind. Lifting the optimization to that level wouldadvance it from its present role of a designer’s aid to therole of a designer himself with profound consequencesthat are difficult even to imagine today. The fact thatone sees only limited, if any, presentations at currentMDO conferences alluding to the above as an issue isevidence that the optimization community has grownaccustomed to considering optimization as merely adesigner’s aid, and, on the other hand, it attests to thedifficulty of the problem.

The science of cognition that includes probing hu-man inventiveness is still far from understanding theunderlying mental processes. Opinions vary betweenextremes. One extreme view is that creativity is noth-ing more than a random juxtaposition of the conceptspresent in the immense base of common knowledge offacts and relationships accumulated in every person’smind. Its pole opposite asserts that the human mindis endowed with capabilities beyond what science canexplain. One does not need to choose between theabove opposites to recommend a pragmatic positionthat the movement of optimization in general, andMDO in particular, from being merely a designer’s aidtoward the ultimate new paradigm of simulating whata designer really does will require a collaboration withcognition science and its emerging companion scienceof complexity (Gero 2006). Research topics suggestedby the above discussion:

1. Cognition and complexity sciences literature sur-vey focused on determining whether any conceptshave already emerged that may be ready to beexploited as connection points between the state-of-the-art of optimization and these sciences.

2. Investigate whether it is possible to generalize theconcept of design mutation as practiced in GA toinclude the design space redefinition reflected inthe underlying mathematical model.

3. Include the notion of time and future redesignsin design optimization in order to allow systemsto be changed and reconfigured over time withoutmoving too far away from their static optima.

4.2.2 Designing and co-optimizing families of productsand Systems-of-Systems

Many systems are no longer designed as individual,isolated products, but as part of a larger product orsystem family. This requires including considerations


of modularity and especially commonality in the MDOprocess. While much MDO work has been done in thisarea in academia, little of it gets used in industrial prac-tice. This is mainly so because commonality decisionscan only be made while taking into account their costimpact and the influence on customer demand, in addi-tion to the traditional technical performance evaluationthat MDO can provide (Willcox and Wakayama 2003).

Increasingly, vehicles operate as parts of larger net-works and operational requirements include interoper-ability with other vehicles. Examples include the designof a sea base (naval logistics) among others (Wolf2005). When applying MDO to System-of-Systemsproblems the performance of an individual vehicle be-comes subjugated to the performance of the overallSystem-of-Systems (SoS) (Crossley and DeLaurentis2006). In some cases, sub-optimality in one vehiclewould be deliberately accepted for the benefit of theoverall system. However, since the key feature of SoSis that individual vehicles can still perform useful func-tions independently (principle of functional indepen-dence Maier 1999) this is a challenging problem. Insome cases existing bi-level methods might be extendedto multiple levels, in other cases entirely new ways ofthinking about the problem might have to be generated.Research questions in this area encompass:

Optimizing which design variables, components andmodules to make common between variants of vehiclesor products in a family of systems that is tailored to spe-cific applications. While much work has already beendone in this area, a stronger relationship between de-sign variables and physical elements of form must be es-tablished and economic factors must be accounted for.

Systems-of-Systems are an emerging applicationfor MDO where vehicles are treated as subsys-tems of a larger ensemble of systems and vehicles(Sobieszczanski-Sobieski and Storaasli 2004). One ofthe challenges of System-of-Systems optimization thatmust be addressed is that the boundaries and member-ship in the SoS can vary dynamically over time.

4.2.3 The need to integrate manufacturing into MDO

There are very few references alluding to the title sub-ject. However, one example, presented by R. J. Yangof Ford Motor Co. at the 2006 European–U.S. MDOColloquium, did so by showing the effect structuralmodification in the car body may have on both the carperformance and its manufacturing cost, hence, indi-rectly on the return on investment. This case suggestsapplication of MDO to the product life cycle with Re-turn on Investment (ROI) or Net Present Value (NPV)

as the objective, and encompassing both the vehiclephysics and its manufacturing process.

The uniqueness of Ford’s presentation at the col-loquium is symptomatic of the prevailing practicewhereby the design of the vehicle manufacturingprocess is to a large extent divided from the physics-based design of the vehicle to be manufactured, withonly a limited amount of information crossing the di-vide. That divide impedes maximization of ROI (NPV)taken as a quantity representative of the highest-levelobjectives of a commercial enterprise. A passengeraircraft configuration design provides an example. Sim-plifying the example to make the point, consider thewing aspect ratio, AR, as a design variable typicallyconsidered in the physics-based vehicle design phase.That variable strongly affects the aircraft aerodynamicefficiency hence it impacts, indirectly, the aircraft pro-ductivity reflected in the cost per seat mile. In general,larger AR (subject to constraints, of course) reducesthe seat mile cost potentially increasing the airlineprofit, consequently enabling the aircraft builder to sellthe aircraft at a higher price. On the other hand, higheraspect ratio wing of the same total area is generallymore expensive to make. The ROI depends, amongother factors, on the trade-off between the selling price,operating cost and the manufacturing cost so it couldbe maximized by an MDO process spanning the physic-based vehicle design and the manufacturing and opera-tions process design.

For such an MDO process to operate in context ofthe above-simplified example, the mathematical modelmust exist that relates the cost per seat mile to AR.Similarly, a mathematical model is needed to assess themanufacturing cost as a function of AR. Both modelsexist in the current practice and MDO tools are applica-ble on both sides of the physics/manufacturing divide.What has not become a part of the practice as yet isan MDO loop to manipulate AR as a variable activeon both sides of the trade-off involving both modelsdefined in the foregoing to reveal dependency of thattradeoff on AR. Knowing that dependency would en-able design of the vehicle and its manufacturing processtogether toward maximum ROI or NPV. Researchtopics that arise in conjunction with unification of thephysics-based vehicle design with design of its manu-facturing process are as follows:

1. Select a design case of a vehicle in which manufac-turing cost is sensitive to physical variables tradi-tionally decided in the vehicle configuration design.

2. Identify mathematical models for the vehiclephysics and for the vehicle manufacturing, both

30 J. Agte et al.

models sharing as many design variables aspossible.

3. Apply an MDO system optimization including thevehicle physics and manufacturing to demonstratebenefit from such unified optimization for maximiz-ing a quantity such as ROI and NPV, contrastingthe result with that obtained from disjoint treat-ment of the vehicle physics and manufacturing.

5 Summary and concluding remarks

The paper is based on observations from the 2006European–U.S. Multidisciplinary Design OptimizationColloquium and outlines the authors’ opinion of thestate-of-the-art of Multidisciplinary Design Optimiza-tion and its industrial applications rooted in majorprevious developments, briefly reviewed for a historicalcontext. The MDO theory and means of implemen-tation are examined as constituents of the state-of-the-art, linked to principal commercial sources andproviders. The paper points to the technology of Mas-sively Concurrent Computing, and its distributed vari-ant, now becoming ubiquitous as a key enabler thatalready begins to make possible what was impossiblebefore and is certain to open new areas of applicationsin the future.

With the foregoing as a definition of a current MDOinfrastructure, a number of industrial applications arebrought up as lessons learned and indicators of limi-tations. Since MDO developments require a relativelyhigh front-end cost and deferred benefit, these devel-opments rely to a large extent on government spon-sorships whose specific, recent, principal instances arediscussed, with references to crucially important partic-ipation of the academic community in contributing re-search and education of future MDO practitioners andindustry as a primary user and provider of challengesand case studies.

Future developments of MDO are projected in twoorthogonal but mutually reinforcing directions: a hor-izontal growth for more capability, spanning an evergreater repertoire of applications using existing theoryand tools, and a vertical growth attacking qualitativelynew problems with innovative solutions to explorenew, uncharted territory for potentially even greaterbenefits.

A key issue included in the vertical growth categoryis the present limitation of MDO in particular andoptimization in general. Specifically, the confinement ofthe search for optimal design to the space qualitativelydefined by the initial choice of the variable coordinateaxes and problem parameterization. The paper spec-

ulates that breaking out of that restricting mold willrequire collaboration with cognitive science and studiesof the inner workings of human mind and its intrinsiccreativity, likely to extend far beyond MDO and itsengineering origin.

The third direction of future MDO developments,regarded as a resultant of the above two, is a “dreamtrend” that combines the increasing power of the well-established approaches with the capability to solveproblems that heretofore remain beyond the MDOtheory and practice boundary.

Looking forward along the above axis, the paperrecommends specific research topics to the attentionof the research community, practitioners, and researchand development sponsors. Definitions of these specifictopics constitute the concrete, tangible product of thepaper.

Acknowledgements We acknowledge the support of DLR, theGerman Aerospace Center, Goettingen, Germany, in organizingthe colloquium, as well as the invaluable contributions of all thosewho attended. Additionally, special acknowledgement goes toKumar Bhatia of the Boeing Company for his comments anddiscussion, especially in the development of Section 3.4.

Appendix

A MDO theory and frameworks

The issue of system decomposition began to ariseover two decades ago, followed by the developmentof several formal MDO methods each characterizedin large part by the ways and means for partitioningthe system optimization into sub-tasks and representingthe couplings (interactions) among the subtasks. It islargely these decomposition frameworks’ approachesthat set MDO apart from straight applications of NLPtechniques in engineering design.

While numerous such methods have been intro-duced, evolved, tested, and applied (some successfullyand some unsuccessfully) over the past two decades,here we discuss only three of the more mainstreamdevelopments and realize that there are others thatmerit consideration as well. This short discussion in-cludes: Bi-Level Integrated System Synthesis (BLISS),referenced in Sobieszczanski-Sobieski et al. (2000) andSobieszczanski-Sobieski et al. (2003); CollaborativeOptimization (CO), referenced in Sobieski and Kroo(2000) and Braun (1996); and a more recent decom-position technique called Analytical Target Cascading(ATC), referenced in Kim et al. (2003) and Kim (2001).For the sake of completeness, Concurrent SubspaceOptimization (CSSO) is also briefly reviewed below. A


summary of various similarities and differences be-tween methods is shown in Table 3.

Bi-Level Integrated System Synthesis has been un-der development at NASA Langley Research Centersince 1996 and has undergone various changes overtime. This algorithm uses an approximation techniqueto represent a range of optimized subsystem or sub-task designs, upon which the system-level optimizeroperates with the goal of minimizing an overall sys-tem objective function. Although the choice of theapproximation technique is left up to the user, responsesurfaces and Kriging are the two most commonly usedand tested. The connection between the system andsubsystem levels is preserved through the formation ofthe subsystem objective function, f = w1Y1 + w2Y2 +. . . + wiYi. Here, a range of weighting coefficients (wi)

are appended to each output (Yi) of each subsystem,included as independent variables in the formationof the approximation model, and then treated as de-sign variables in the system level optimization. In thismanner, the system level optimizer essentially variesthe weighting coefficients to explore different designattributes imparted by the subsystem optimizations.

Whereas BLISS uses weighting coefficients to directsubsystem outputs such that they populate the entiredesign space before reaching the system level optimiza-tion, Collaborative Optimization uses target values ofthe design and state variables, created at the systemlevel, to steer the outcome of subsystem optimizationsin a more step-wise manner. CO was originally devel-oped at Stanford University in 1996 and, like BLISS,has undergone various changes and improvements overthe past decade. The most recent variant is found inRoth and Kroo (2008). The subsystems receive targetsfor interdisciplinary parameters from the system level,which they then try to match while converging to afeasible design. The typical subsystem objective func-tion, f = (XT,1− XSS,1)

2 + (XT,2− XSS,2)2 + . . . + (XT,i−

XSS,i)2, is formulated such the subsystem controlled

parameters (XSS,i) are allowed to deviate from the

target value (XT,i) in order to ensure a feasible designis met. Optimum values of the subsystem objectivefunction are then returned to the system level wherenew targets are set and the process continues untilconvergence. Although the traditional CO algorithmdoes not use approximation models, response surfacesand other surrogate models have been used in severalcases to enhance certain aspects of the method.

Analytical Target Cascading, which was initially de-veloped at the University of Michigan in 2001, is uniquein that it is not specifically intended as a competitorto BLISS or CO but offers a very flexible, multi-level,hierarchical approach to the decomposition probleminto which other formal MDO methods may possiblybe integrated. Although the mathematical formulationsof ATC and CO are similar, ATC was designed forproblems which are object or component aligned ratherthan discipline aligned. Design targets cascade downfrom the uppermost level, which may be the vehi-cle level or even the management/enterprise level, toeach respective sublevel, typically defined by variousphysical components of the design. Adjacent sublevelsthen iterate successively to convergence in a pair-wisefashion until the entire system converges. Achievingconvergence of the overall system is one of the keychallenges in successfully implementing ATC. Severalversions have been successfully implemented, the mostrecent of which is found in Tosserams et al. (2008).

Concurrent Subspace Optimization (CSSO) was ini-tially developed at NASA Langley Research Center in1988 and subsequently expanded in a series of papersfrom the University of Notre Dame Sobieszczanski-Sobieski and Haftka (1997) into several variants sodiverse that they no longer constitute a single method.In the initial version, the subspace objective functionsare formulated as the subspace contributions to theoverall system objective. The subspaces are responsi-ble for meeting local constraints as well as constraintsfrom other subspaces, approximated through sensitiv-ity derivatives obtained from the Global Sensitivity

Table 3 Overview of MDO decomposition frameworks

Method BLISS CO ATC CSSO

TraitSystem-level analysis required? No No No YesSubspace sensitivity analysis required? No No No Yes# of levels Two Two Multiple TwoPartitioned by: Disc. analys. Disc. analys. Object/component Disc. analys.Subspace optimization influenced by targets? Yes, indirectlya Yes Yes No

Autonomous subspace optimizations? Yes Yes Yes Yes

aOf interesting note is that the BLISS subspace objective function could also be formulated as that of CO and ATC with the targetvalue taking the role of the weighting coefficient. However, in the BLISS method, slow convergence and possible non-feasibility of thereturned solution have led to the use of the weighting coefficients as the preferred alternative

32 J. Agte et al.

Table 4 Overview ofcommercially availablesoftware tools in support ofMDO

General purpose tools Embedded optimization Process integration tools

Excel (Microsoft) SolidWorks-Cosmos ModelCenter, CenterLink (Phoenix Int.)Matlab (Mathworks) GENESIS (VRD) iSIGHT, FIPER (Engineous)Mathematica (Wolfram) modeFRONTIER(Esteco)

Equations (GSE). Variants include the use of neuralnets, response surfaces, variable sharing between sub-spaces, and numerous other refinements.

Software tools and MDO providers

Software tools now available commercially to sup-port multidisciplinary design optimization have evolvedover the last two decades and can be classified intothree broad categories:

(a) general purpose optimization tools,(b) embedded optimization tools, and(c) dedicated process integration and design opti-

mization (PIDO) tools.

General purpose tools (Excel, Matlab, and Mathe-matica) are general software environments and pro-grams that can capture both the model of the systemthat is to be optimized, as well as the optimizer inthe same environment. Typically, these tools are easyto learn and use, but their computational performancetends to break down for large problems. Also, thesetools do not easily integrate high-performance engi-neering codes (such as CFD, FEM etc. . . ). For educa-tional purposes, however, the general purpose tools arethe preferred choice due to their simplicity. The em-bedded optimization tools are a recent trend, where ex-isting engineering design and analysis tools (e.g. CADSolidworks) are starting to incorporate within theman embedded optimization capability. While useful forlocal optimization, this capability typically only benefitsone engineering discipline at a time. Finally, a smallindustry has recently started to emerge in order toprovide a process integration and design optimizationcapability (PIDO). The focus is on integrating a firm’snatural design processes with multidisciplinary designoptimization. Popular tools operate at the individualdesktop level (ModelCenter, iSIGHT) or more recentlyat the team or even at the enterprise level (CenterLink,FIPER). Here the focus is on data management, con-figuration control, workflow management and ease ofintegration of disparate analysis codes.

Increasingly, firms are migrating from in-housecustom-made solutions to commercially available toolssuch as the ones listed in Table 4.

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mdo: assessment and direction for advancement— an opinion...

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