MULTI-CRITERIA DECISION ANALYSIS TECHNIQUES INAIRCRAFT CONCEPTUAL DESIGN PROCESS

X. Sun∗ , P. Meng∗∗ , D. Boehnke∗ , S. Lehner∗ , P. D. Ciampa∗ , V. Gollnick∗ , E. Stumpf∗∗∗∗Institute of Air Transportation Systems, German Aerospace Center (DLR), Germany

∗∗Aerospace Engineering, KTH, Sweden∗∗∗Institute of Aeronautics and Astronautics, RWTH Aachen, Germany

xiaoqian.sun@dlr.de; pengfeim@kth.se; daniel.boehnke@dlr.de; stephan.lehner@dlr.de;pier.ciampa@dlr.de; volker.gollnick@dlr.de; stumpf@ilr.rwth-aachen.de

Keywords: MCDA, Weighting Factors, Surrogate Models, Aircraft Design

Abstract

In aerospace systems design, conflicting dis-ciplines and technologies are always involvedin the design process. Multi-Criteria DecisionAnalysis (MCDA) techniques can be helpful toeffectively deal with such situations and makewise design decisions. In this paper, the feasibil-ity and added values of applying the MCDA tech-niques in aircraft design are explored. A new op-timization framework incorporating MCDA tech-niques in aircraft conceptual design process is es-tablished. An improved MCDA method is uti-lized to aggregate the multiple design criteriainto one composite figure of merit, which servesas an objective function in the optimization pro-cess. It is demonstrated that the suitable MCDAmethod with improvement provides a better ob-jective function for the optimization than the tra-ditional weighted sum method.

Considering that the inherent uncertaintiesand subjectivities of the weighting factors havecrucial impacts on the design solution, surrogatemodels for the multiple design criteria in termsof the weighting factors are constructed. Theconstructed surrogate model can provide efficientanalysis tools for uncertainty assessment.

1 Introduction

Multi-Criteria Decision Analysis (MCDA) is aprocess that allows one to make decisions in thepresence of multiple, potentially conflicting cri-teria [15], [7]. Although MCDA as a disciplinehas a relatively short history of about 40 years,over 70 MCDA techniques have been developedfor facilitating the decision making process.

There are typically two strategies when im-plementing MCDA techniques in the engineeringdesign process: a posteriori approach and a prioriapproach [15]. In the a posteriori approach, opti-mization techniques are applied firstly to searchfor a set of best trade-off solutions, usually interms of a Pareto front. Then, MCDA techniquesare used to select the most preferred design solu-tion among several design alternatives from thePareto front, taking multiple evaluation criteriainto consideration simultaneously. In the a pri-ori approach, MCDA techniques are utilized toaggregate the multiple design criteria into onefigure of merit. Then, optimization techniquesare applied to search for the best design solution,with the composite figure of merit as a single ob-jective function.

Multi-objective optimization techniques playan important role in the a posteriori approach.For example, a three-objectives Genetic Algo-rithms (GA) were used to identify the trade-offsbetween environmental performances (noise and

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emission) and operating cost quantitatively [1].A two-objectives GA were applied to the de-sign of an aircraft that uses greener technologies[10]. However, multi-objective GA suffer fromexpensive computation. Furthermore, evolution-ary optimization techniques are often not easilyapplicable for handling a large number of objec-tives [6].

The a priori approach can support designersto quickly assess the compromised design alter-natives and be capable of dealing with large num-ber of objectives. One of the classical a prioriapproaches, the weighted-sum approach (SAW),however, was criticized for over-simplified ag-gregation of the multiple design objectives [8].

In the a priori approach, the weighting fac-tors create a compound figure of merit. Thecompound figure of merit serves as the objec-tive function for optimization. Different weight-ing schemes result in different compound figureof merits. The selection of the figure of merit iscritical to the determination of an optimal design,since if a design is optimized to the wrong figureof merit, it will not be the best design in terms ofthe real important measure. Especially, the inher-ent uncertainties and subjectivities of the weight-ing factors have significant impacts on the designsolution.

In this paper, the a priori approach of im-plementing MCDA techniques in the design pro-cess is followed. A new multi-criteria optimiza-tion framework incorporating MCDA techniquesin the aircraft conceptual design process is es-tablished, as illustrated in Fig.1. An improvedMCDA method is utilized to aggregate the mul-tiple design criteria into one composite figure ofmerit, which serves as an objective function inthe optimization process. Furthermore, consider-ing the crucial impacts of the weighting factorson the optimized design solution, surrogate mod-els for the multiple design criteria in terms of theweighting factors are constructed.

The paper is organized as follows. Section 2defines the aircraft design decision making prob-lem. Section 3 presents the selection of the mostappropriate MCDA method, through an devel-oped intelligent multi-criteria decision support

system. Section 4 presents the results of apply-ing an improved MCDA method in the proposedmulti-criteria optimization framework. In Sec-tion 5, surrogate model development for designcriteria in terms of weighting factors is discussed.Finally, conclusions are drawn and presented inSection 6.

2 Definition of the Decision Making Problem

The focus of the proposed optimization frame-work is the assessment of the added values ofincorporating MCDA techniques in the aircraftconceptual design process. Thus, in order to keepthe design process transparent, the complexity ofthe design problem is limited. Five design vari-ables for a conceptual aircraft design model areconsidered in this study: wing thickness-to-chordratio, aspect ratio, reference area, cruise Machnumber, and fuselage diameter.

The proposed optimization frameworkis applied to the design of a conventional150-passenger, twin engine airliner with adesign range 3200 km using the concep-tual aircraft design tool VAMPzero(VirtualAircraft Multidisciplinary Analysis and DesignProcesses). VAMPzero is developed at the Ger-man Aerospace Center (DLR e.V.) and licensedunder the Apache 2.0 license [3].

2.1 Identification of Design Criteria

Selection of appropriate design criteria is criticalto the determination of an optimal design. Somerecommendations were provided in [14], whichstated that the design criterion should represent anon-trivial and calculable indication of the worthof the concept, it should be significantly affectedby the design variables and constraints, it shouldhave clear meaning to designers and customers,and it needs clear rationale for methods and fac-tors used for blending if it is blended.

In this study, in order to explore the inter-relationships among the interest of manufactur-ers, the concern of fuel-based emissions, the con-cerns of airliners, and the consideration of pas-senger comfort explicitly, four design criteria are

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MCDA IN AIRCRAFT DESIGN

Initial

design

Analysis

tool

Optimizer

MCDA

method

Objective function:

MCDA Index

Constraints

Update design variables

Wing thickness-to-chord ratio

Wing aspect ratio

Wing reference area

etc.

Operating empty mass

Fuel mass

Comfort level

etc.

Fig. 1 The Framework of Incorporating MCDA Techniques in Aircraft Design

selected to feed into the MCDA method: Op-erating Empty Mass (OEM), fuel mass, utiliza-tion/(block time), and passenger density. Thecommon practice of using Direct Operating Cost(DOC) as an objective function in the optimiza-tion appeared to be not appropriate in this study,considering that DOC has high correlation withall other design criteria. Nevertheless, DOC wastraced as an aircraft performance measure, aswell as aircraft price, fuel cost, and Take-offMass (TOM).

The constraints imposed in the aircraft designprocess are wing span, fuel tank volume, take-offfield length, landing field length, take-off wingloading, and cruise thrust. The design variables,constraints, and design criteria for this simplisticaircraft design model are summarized in Table 1.

3 Selection of an Appropriate MCDAMethod

There are essentially two approaches to solve thedecision making problems: non-compensatoryand compensatory methods [9]. The non-compensatory methods do not permit trade-offsamong criteria, that is to say, a disadvantagein one criterion cannot be offset by an advan-tage in other criterion. Compensatory meth-ods permit trade-offs among criteria, in otherwords, small changes in one criterion can beoffset by opposing changes in any other crite-rion. According to this classification, several

Table 1 The Summary of Design Variables, Con-straints, and Design Criteria in Aircraft Opti-mization Process

Units ValuesDesign VariablesThickness-to-chord ratio − [0.1,0.2]Aspect ratio − [8,12]Reference area m2 [80,140]Cruise Mach number − [0.70,0.84]Fuselage diameter m [3.8,4.2]ConstraintsWing span m ≤ 36Fuel mass kg ≤ Fuel tank volumeTake-off field length m ≤ 3000Landing field length m ≤ 2000Take-off wing loading kg/m2 ≤ 600Cruise thrust N ≤ 0.9 Take-off thrustDesign CriteriaOEM kg −Fuel mass kg −Utilization/(block time) − −Passenger density Pax/m2 −

widely used decision making methods are sum-marized in Table 2, where ELECTRE repre-sents for Elimination and Choice Translation Re-ality [2], PROMETHEE stands for PreferenceRanking Organization METHod for EnrichmentEvaluations) method [4], and TOPSIS representsTechnique for Order Preference by Similarity toIdeal Solution [9].

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Table 2 Typical Non-compensatory and Compen-satory Decision Making Methods [9]

Non-compensatory CompensatoryConjunctive method Analytic hierarchy processDisjunctive method Expected utility theoryDominance method Multi-attribute utility theoryELECTRE Multiplicative weightingElimination by aspects PROMETHEELexicographic method Simple additive weightingMaximin method TOPSISMaximax method

3.1 Development of an Intelligent Multi-Criteria Decision Support System

Among various developed MCDA techniques,the selection of the most appropriate method tosolve the aircraft design problem is importantsince the use of inappropriate method often leadsto misleading results. In this study, an intelli-gent knowledge-based decision support systemis developed in MATLAB, which consists of aMCDA library storing the widely used MCDAmethods and a knowledge base providing the in-formation required for the method selection pro-cess. The selection of the most suitable MCDAmethod depends on how the characteristics of themethod match the characteristics of the controlproblem, which is measured by AppropriatenessIndex (AI) [11],[16], as shown in Equation 1.

AI j =n∑

i=1wib ji

b ji =

{1 ifc ji = ai0 ifc ji 6= ai

i = 1,2, ...,n; j = 1,2, ...,m

(1)where n is the number of evaluation criteria usedto examine the decision making methods with re-spect to the given problem, and m is the numberof decision making methods stored in the methodlibrary, {w1,w2, ...,wn} are the weighting factorsfor the evaluation criteria, ai is the value of thei-th characteristic of the decision problem, andc ji is the value of i-th characteristic of the j-thmethod, b ji is a Boolean number depending onthe match of the i-th characteristic of the deci-sion problem and the i-th characteristic of the j-th

method. If the i-th characteristic of the decisionproblem matches the i-th characteristic of the j-thmethod, then b ji = 1; otherwise, b ji = 0.

3.2 Selection of the Most AppropriateMethod using the Intelligent Multi-Criteria Decision Support System

In this example, the selection of the most ap-propriate MCDA method for the aircraft designproblem is presented, through the developed in-telligent multi-criteria decision support system.In order to identify the most appropriate method,16 widely used MCDA methods are studiedand their characteristics are stored in a methoddatabase. To compare the appropriateness of themethods with respect to the given problem, eachmethod is evaluated based on the proposed 12evaluation criteria. The 12 evaluation criteria canbe captured by answering 12 questions relevant tothe characteristics of the methods, as presented inFig.2.

As shown in Fig.2, the infeasible MCDAmethods are eliminated first by the three filterquestions. Considering that in this aircraft de-sign problem, the compound figure of merit forthe four design criteria aggregated by MCDAmethod serves as objective function in the opti-mization, the scoring methods are more appro-priate than the classification methods. Mean-while, all non-compensatory methods are ex-cluded since compensation is allowed in the air-craft optimization process. Moreover, the deci-sion maker’s preference information on the eval-uation criteria can be defined using slide bars inthe integrated user interface, with a subjectivescale of 0 to 10, where 0 stands for extremelyunimportant while 10 represents extremely im-portant.

The AI of the MCDA methods are calcu-lated and presented in Fig.3, where higher scorerepresents more appropriateness of the methodwhen solving the given problem. As indicated inFig.3, TOPSIS gets the highest score among theMCDA methods for the problem under consider-ation, therefore, it is selected as the most appro-priate method in this research.

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MCDA IN AIRCRAFT DESIGN

Fig. 2 Questions Related to Evaluation Criteria for Method Selection in Aircraft Design Process

Fig. 3 MCDA Methods Ranking List with Scoresin Aircraft Design Process

3.3 An Improved TOPSIS (ITOPSIS)

TOPSIS is one of the most widely used MCDAmethods [9]. TOPSIS is based on the concept thatthe most preferred alternative should have theshortest Euclidean distance to the positive idealsolution and the furthest Euclidean distance fromthe negative ideal solution.

In the original TOPSIS method, when an al-ternative is removed from or added to the candi-date alternatives, the two hypothetical solutionswill probably change and the Euclidean distancesto the two hypothetical ideal solutions will alsochange. Thus, the top-ranked alternative wouldprobably be inconsistent when the candidate al-

ternatives are changed. It has been pointed outthat the cause of rank inconsistency with TOP-SIS lies in the determination of the positive idealsolution and negative ideal solution, and a pairof absolute ideal solutions instead of the relativeideal solutions was introduced to eliminate therank inconsistency of TOPSIS method [5].

In this research, an Improved TOPSIS (ITOP-SIS) will be utilized to aggregate the four designcriteria into one compound figure of merit for op-timization. The positive ideal solution and nega-tive ideal solution are set beforehand in order toavoid the ranking inconsistency. In our case, twokinds of optimizations are conducted for each ofthe four design criteria: minimization and maxi-mization. The positive ideal solutions and nega-tive ideal solutions for the four design criteria aresearched within the results of eight optimizations,as summarized in Table 3. It should be noted thatthe utilization/(block time) ratio is a benefit crite-rion, and the other three are cost criteria.

4 Optimization with Equal Weighting Fac-tors

In this example, based on parametric studies, alldesign variables under investigation are continu-

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Table 3 The Positive Ideal Solution and NegativeIdeal Solution in ITOPSIS

Ideal Fuel Utilization/ Paxsolutions OEM mass (block time) densityPositive 36943 11767 796.86 1.2875Negative 50521 20864 715.08 1.4063

ous, and the objective functions with respect tothe design variables in the conceptual aircraft de-sign tool (VAMPzero) are rather smooth. There-fore, gradient-based methods are used in the op-timization framework.

4.1 Comparison Using Different MCDA In-dices as Objective Functions

The optimization results with equal weightingfactors among the four design criteria when usingITOPSIS index as an objective function are sum-marized in the second column in Table 4. Forthe purpose of comparison, the proposed opti-mization framework is also performed when us-ing weighted sum (SAW) index as an objectivefunction, the optimization results are summarizedin the third column in Table 4.

It is observed from Table 4 that with equallyassigned weighting factors, the optimized designusing ITOPSIS index as an objective function isheavier but more fuel efficient than the designwhich was optimized using SAW index as an ob-jective function.

Furthermore, in the same running environ-ment (Windows 7, 2.66 GHz Intel Core 2 QuadCPU, 4 GB RAM, and Matlab 2010a version),the convergence rates when using ITOPSIS in-dex and using SAW index as objective functionsare summarized in Table 5. It is seen that the op-timization using ITOPSIS index as an objectivefunction need less iterations and less computa-tion time (in seconds) than using SAW index asan objective function.

However, only with the conduction of oneset of weighting factors, it cannot be concludedwhich MCDA method is more appropriate for theoptimization, considering the crucial impact ofthe weighting factors on the optimized design.The roles of the weighting factors in the frame-

Table 5 Comparison of Convergence Rates, Us-ing ITOPSIS Index and SAW Index as ObjectiveFunctions

Objective function Iterations Optimization timeITOPSIS index 5 304SAW index 39 3005

work of incorporating MCDA techniques in air-craft design will be further investigated in the fol-lowing section.

5 Surrogate Model Construction for DesignCriteria in terms of Weighting Factors

The weighting factors have crucial impacts onthe design solution, since the objective functionin the optimization process is aggregated throughthe weighting factors. An uncertainty assess-ment that demonstrates this impact must con-sider different combinations of the weighting fac-tors. However, in the proposed multi-criteria op-timization framework, the computation time forone set of weighting factors is at least 5 minutes.A Monte Carlo based uncertainty analysis with10,000 samples would take at least 35 days. Thelong computation time makes the uncertainty as-sessment an intractable computational task.

In this study, in order to facilitate the uncer-tainty assessment of the weighting factors, surro-gate models for the four design criteria in termsof the weighting factors are constructed. Eachpoint of this surrogate model represents an op-timized aircraft design for a given set of theweighting factors. The whole framework of in-corporating MCDA techniques in aircraft designprocess is treated as a black box. An overview ofsurrogate modeling process for design criteria interms of weighting factors is shown in Fig.4.

There are typically four steps in surrogatemodel building process: sample the design spaceusing experimental design, choose a model torepresent the input and output data, select amethod to fit the model, and validate the con-structed model [8]. The construction of surrogatemodels for design criteria in terms of weightingfactors will follow this process.

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MCDA IN AIRCRAFT DESIGN

Table 4 Optimization Results Using ITOPSIS Index and SAW Index as Objective Functions, WhenWeighting Factors are Evenly Distributed

Optimized OptimizedBaseline Design DesignDesign (ITOPSIS) (SAW)

Design VariablesThickness-to-chord ratio 0.13 0.135 0.1304Aspect ratio 9.396 9.414 9.118Reference area (m2) 122.4 117.01 116.9Cruise Mach number 0.78 0.76 0.77Fuselage diameter (m) 4 3.8 3.8Design CriteriaOEM (kg) 40980 38705 38552Fuel mass (kg) 12903 12242 12344Utilization/(block time) 763 752 756.5Passenger density (pax/m2) 1.35 1.4211 1.4211Traced Performance MeasuresDOC (Euro/h) 4818 4588 4612Aircraft price (Euro) 36077718 34397326 34284714Fuel cost (Euro/h) 1686 1571 1596TOM (kg) 73133 70197 70147

5.1 Experimental Design

In order to explore the design space thoroughly,experimental design with spatially uniform dis-tribution is one effective approach. There areseveral space filling strategies [12], among whichLatin Hypercube Sampling (LHS) is one reliablemethod to generate random candidate samples,with guarantee that these samples are relativelyuniformly distributed in the design space [13].

In this study, the weighting factors{w1,w2, ...,wn} generated by experimentaldesign have to satisfy two conditions:

1. 0≤ wi ≤ 1

2. ∑ni=1 wi = 1

The standard LHS meets the condition 1 thatall the factor settings range from 0 to 1. However,for each experimental run, the sum of the factorsettings in each run do not equal to 1. In thiscase, in order to generate experimental designsfulfilling the conditions 1 and 2, standard LHSis conducted first, then the samples generated byLHS are rectified by Dirichlet distribution.

One Modified LHS with Dirichlet Distribution

Dirichlet distribution is a family of continuousmultivariate probability distributions parameter-ized by a vector α = (α1,α2, ...,αk,) of positivereals. Dirichlet distribution is one multivariategeneralization of the beta distribution and is de-fined as Equation 2

Dir(X ,α) =Γ(α1 +α2 + ...+αk)

Γ(α1)Γ(α2)...Γ(αk)

∏(x1α1−1x2

α2−1...xkαk−1)(2)

where X = (x1,x2, ...,xk−1), satisfying xi > 0 and∑

k−1i=1 xi < 1. Besides, xk = 1−x1−x2− ...−xk−1.

In a symmetric Dirichlet distribution, the compo-nents of vector α are equal. If each componentof α is 1, the symmetric Dirichlet distribution isequivalent to a uniform distribution; if each com-ponent of α is bigger than 1, it prefers dense,evenly distributed distribution, and if each com-ponent of α is smaller than 1, it prefers sparsedistribution.

When using the modified LHS with Dirichletdistribution, although the modified sample values

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Weighting factors 1

Weighting factors 2

Weighting factors m

Design criteria values 1

Design criteria values 2

Design criteria values m

.

.

.

.

.

.

Input Output

Initial

design

Analysis

tool

Optimizer

MCDA

method

Objective function:

MCDA Index

Constraints

Update design

variables

Wing thickness-to-chord ratio

Wing aspect ratio

Wing reference area

etc.

Operating empty mass

Fuel mass

Comfort level

etc.

Fig. 4 The Overview of Surrogate Modeling Process for Design Criteria in Terms of Weighting Factors

are not strictly uniform any more, Dirichlet dis-tribution can keep the ranges of the sample val-ues larger once they are normalized, while main-taining the appealing Latin properties. In this ex-ample, one hundred sets of weighting factors aregenerated by the LHS with Dirichlet distribution.

5.2 Model Choice and Model Fitting

Response surface models have been widely usedin the surrogate model construction in engineer-ing design [8]. There are several advantages us-ing response surface models, such as ease of im-plementation, minimal efforts required to trainmodels, and ideality for uncertainty analysis. Inthis research, response surface is utilized to con-struct the surrogate models. A widely used statis-tics software package JMP@ is employed to fitresponse surface models.

5.3 Model Validation

The actual values versus the predicted values forthe four design criteria when using ITOPSIS in-dex as an objective function are shown in Fig. 5.For the purpose of comparison, the actual valuesversus the predicted values for the four designcriteria using SAW index as an objective func-tion are also conducted and are shown in Figure6. In the actual by predicted plot, the horizontaldotted blue line represents the mean of the actualvalues, the red line shows the 45 degree diagonalline, and the two red dotted lines show the 95%confidence intervals.

Fig. 5 The Actual by Predicted Plots of OEM,Fuel Mass, Utilization/(Block time), and Passen-ger Density, when using ITOPSIS Index as anObjective Function

The actual by predicted plots illustrate howwell the predicted responses match the actualdata. A quick assessment of the model is to eye-ball a 45 degree pattern in these plots. In ourcase, the scatter plots when using ITOPSIS indexas an objective function and using SAW index asan objective function all follow a 45 degree pat-tern. Specifically, the scatter plots when usingITOPSIS index as an objective function are lessdivergent along the diagonal line than the scat-ter plots when using SAW index as an objectivefunction. This is one indicator of better goodnessof fit when ITOPSIS is used for the multiple cri-teria aggregation than SAW.

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MCDA IN AIRCRAFT DESIGN

Fig. 6 The Actual by Predicted Plots of OEM,Fuel Mass, Utilization/(Block time), and Passen-ger Density, when using SAW Index as an Objec-tive Function

The diagnostics of each response surfacemodel, including R2, R2

Ad j, and Root MeanSquare Error (RMSE) in percentage, are listedin Table 6. R2 measures the proportion of thevariation explained by the regressed polynomialmodel, R2

Ad j adjusts the R2 value to make it morecomparable over models with different numbersof parameters, and RSME estimates the stan-dard deviation of the random error. The per-cent RMSE shown in Table 6 is normalized byits mean of response.

Table 6 The Diagnostics of Response SurfaceModels for Design Criteria, Using ITOPSIS In-dex and SAW Index as Objective Functions

Fuel Utilization/ PaxDiagnostics OEM mass (block time) densityITOPSISR2 0.975 0.964 0.983 0.957R2

Ad j 0.963 0.951 0.976 0.945RMSE 1.56% 1.57% 0.54% 0.74%SAWR2 0.916 0.934 0.973 0.774R2

Ad j 0.9 0.92 0.965 0.743RMSE 2.58% 2.22% 0.66% 1.84%

It is observed from Table 6 that the values ofR2 and R2

Ad j, when ITOPSIS is used for the ag-

gregation of the four design criteria, are all higherthan when SAW is used. The percent RSME,when ITOPSIS is used for the aggregation of thefour design criteria, are all lower than when SAWis used. Especially, R2 of passenger density whenITOPSIS is used is 0.957, while it is only 0.774when SAW is used. The higher values of R2

and R2Ad j and lower values of percent RSME are

strong evidences of goodness of fit. Therefore,it is obtained that the constructed response sur-face models using ITOPSIS for multiple criteriaaggregation are better fitted than using SAW formultiple criteria aggregation.

In conclusion, ITOPSIS index is a better ob-jective function for the optimization frameworkof incorporating MCDA techniques in aircraft de-sign process than the traditional SAW index.

6 Conclusions

In this paper, the feasibility and the added val-ues of applying MCDA techniques in aircraft de-sign problems are explored. A new optimizationframework incorporating MCDA techniques foraircraft conceptual design process is established.An intelligent multi-criteria decision support sys-tem is developed to select the most appropriateMCDA method. It is demonstrated that the cho-sen MCDA method with improvement provides abetter objective function for the optimization thanthe traditional weighted sum method.

Furthermore, the weighting factors of the de-sign criteria have significant impacts on the de-sign solution. Surrogate models for the multipledesign criteria in terms of the weighting factorsare constructed. The constructed surrogate mod-els can enable efficient uncertainty assessmentfor the weighting factors.

In future work, hybrid optimizers combininggenetic algorithms and gradient-based methodscould be investigated for aircraft design problemsto provide a more global optimization and in-clude discrete design variables. The applicationof the MCDA techniques could be extended toassess air transportation systems, for balancingsocial, economic, ecological, and technical etc.constraints.

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References

[1] N. Antoine, I. Kroo, K. Willcox, and G. Barter.A framework for aircraft conceptual design andenvironmental performance studies. In 10thAIAA/ISSMO Multidisciplinary Analysis andOptimization Conference, Albany, New York, 30August - 1 September 2004.

[2] R. Benayoun, B. Roy, and N. Sussman. Man-ual de reference du programme electre. Psy-choemtrika, 38:337–369, 1973.

[3] D. Boehnke, B. Nagel, and V. Gollnick. An ap-proach to multi-fidelity in distributed design en-vironments. In IEEE Aerospace Conference,BigSky, USA, 2011.

[4] J. Brans and P. Vincke. A preference rankingorganization method: The promethee methodfor mcdm. Management Science, 31:647–656,1985.

[5] W. Chen. On the problem and eliminationof rank reversal in the application of topsismethod. Operations Research and ManagementScience, 14:50–55, 2005.

[6] K. Deb, A. Sinha, P. Korhonen, and J.Wallenius.An interactive evolutionary multi-objective op-timization method based on progressively ap-proximated value functions. IEEE Transac-tions on Evolutionary Computation, 14:723–739, 2010.

[7] M. Ehrgott, J. Figueira, and S. Greco. Trends inMultiple Criteria Decision Analysis. Springer,2010.

[8] A. Forrester, A. Sobester, and A. Keane. Engi-neering Design via Surrogate Modelling. Wiley,2008.

[9] C. L. Hwang and K. Yoon. Multiple AttributeDecision Making Methods and Applications: AState of the Art Survey. Springer, 1981.

[10] S. Lehner and W. Crossley. Combinational op-timization to include greener technologies ina short-to-medium range commercial aircraft.In The 26th Congress of International Coun-cil of Aeronautical Sciences (ICAS), Anchorage,Alaska, 14-19 September 2008.

[11] Y. Li. An Intelligent Knowledge-based MultipleCriteria Decision Making Advisor for SystemsDesign. PhD thesis, Aerospace Systems DesignLaboratory, School of Aerospace Engineering,

Georgia Institute of Technology, 2007.[12] A. Lovison and E. Rigoni. Adapative sampling

with a lipschitz criterion for a accurate meta-modeling. Communications in Applied and In-dustrial Mathematics, 1:110–126, 2010.

[13] M. D. Mckay, R. J. Beckman, and W. Conover.Comparison of 3 methods for selecting valuesof input variables in the analysis of output froma computer code. Technometrics, 21:239–245,1979.

[14] D. Raymer. Enhancing Aircraft Conceptual De-sign using Multidisciplinary Optimization. PhDthesis, Royal Institute of Technology, 2002.

[15] P. Sen and J. B. Yang. Multiple Criteria Deci-sion Support in Engineering Design. Springer,1998.

[16] X. Sun and Y. Li. An intelligent multi-criteriadecision support system for systems design. In13th Multidisciplinary Analysis and Optimiza-tion (MAO) and 10th Aviation Technology In-tegration and Operations (ATIO) Conference,Texas, USA, 13-15 September 2010.

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