Title On the Coordination of Multidisciplinary Design Optimization Using Expert Systems Andrew R. Price1, Andy J. Keane1, and Carren M.E. Holden2 1 School of Engineering Sciences, University of Southampton, Southampton, SO17 1BJ, UK 2 Airbus Operations Ltd., Bristol, BS99 7AR, UK a.r.price@soton.ac.uk 1 Introduction In the design of complex engineering systems involving multiple disciplines it is critical that the interactions between the subsystems of the problem are ac- counted for. Only by considering the fully coupled system can an optimal design emerge. Formal multidisciplinary design optimization (MDO) methods [1] fall into two broad categories; 1) monolithic formulations where a single optimizer addresses the whole problem and 2) multilevel methods where the problem is decomposed along disciplinary lines and optimization takes place at both a sys- tem and domain level. The single optimizer approach is simple to implement but can scale poorly for larger problems and increasing number of disciplines. It may also prove problematic in an industrial setting to bring all of the domain analysis tools under the control of a single optimizer. Multilevel architectures promote discipline autonomy. The system level is responsible for managing interactions between disciplines. Such an approach allows design teams to work in relative isolation based upon targets set at the system level. If MDO methods are to be accepted in an industrial context they must support this form of distributed design optimization for both organizational and computational reasons. In this work a related approach is proposed; that of replacing the formal system level optimizer with an expert system to reason over information from the domains and make decisions about changes to the common design variables vector or bounds. Such an approach sacrifices, possibly elusive, guarantees of convergence for potentially attractive returns in the enterprise. 2 Coordination of MDO Using an Expert System An investigative framework has been developed exploiting an expert system as the coordinating process for multidisciplinary design optimization. This system level “master” process has access to a central repository of information which details both the present state of the design and the history of the MDO search. Data mining is employed to analyze the content of this database to present the expert system with facts about features in the domain and system level opti- mization data. The expert system employs a rule base to make decisions about C. Blum and R. Battiti (Eds.): LION 4, LNCS 6073, pp. 212–215, 2010. c© Springer-Verlag Berlin Heidelberg 2010 On the Coordination of MDO Using Expert Systems 213 how the domain level design optimizations should proceed. The results of the reasoning of the expert system are written into the central database and the domains, acting asynchronously, perform the next local optimization as resource becomes available. The expert system controls the design process by specifying the bounds and parameters provided as input to the domain optimizers work- ing on their part of the decomposed problem. A rule base has been developed that solves the design problem by narrowing in on single values for the shared design variables through systematic reduction of their bounds, by managing the exchange and relaxation of the state coupling variables between the domains and by specifying the start points for the domain optimizers. In this work, the performance of the rule base is explored using two types of optimizer in the domains; a sequential quadratic program and a genetic algorithm. To assess the performance of the rule based coordination a number of stan- dard MDO algorithms from the literature have been implemented in Matlab using the SQP method fmincon. These include the methods: Multiple Disci- pline Feasible (MDF) [2], Individual Discipline Feasible (IDF) [2], All-At-Once (AAO), Collaborative Optimization [3], Bi-Level Integrated System Synthesis (BLISS) [4] and Multidisciplinary Design Optimization based on Independent Subspaces (MDOIS) [5]. A number of MDO problems have also been assembled from the literature ranging from simple numerical constructs, through relatively simple preliminary aircraft design problems to a cut-down and decomposed ver- sion of a commercial aircraft wing design tool. The problems have been imple- mented in both the rule base framework and the Matlab MDO framework to enable comparison of performance in both qualitative and quantitative terms. We present the results of the application of the MDO methods to two example MDO problems. The first numerical problem is taken from the third exam- ple study presented in Yi et al. [6] involving two disciplines. The second is a subsonic passenger aircraft design problem described by Lewis [7]. The prob- lem is also composed of two domains; an aerodynamics model and a weights model. 3 Results The results for the Yi3 problem are presented in Table 1. This minimization problem is solved by all methods and the rule base (RB) performs well in this instance. The global optimum value of the system objective function f = 0.5 is found exactly when using the SQP optimizer in the domains and is found less accurately when using the GA in the domains. However, it is noted that the problem does not have a unique global optimum and admits a number of solutions with the optimal system objective function value f = 0.5. The sin- gle optimizer methods all solve the problem using only two or three system level iterations. The bi-level methods need significantly more iterations for this problem. The MDO methods solve the problem to the tolerances set for the optimizers with the exception of CO which does not converge well. The rule base approach requires 8 and 18 system level iterations for the SQP and GA 214 A.R. Price, A.J. Keane, and C.M.E. Holden Table 1. Performance of MDO methods for the Yi et al. example 3 Method Objective Function Maximum Constraint (g ≤ 0) Number system iterations Domain-1 analysis calls Domain-2 analysis calls MDF 0.5000 0.0000 2(5) 281 281 IDF 0.5000 1.1102 × 10−16 2 19 19 AAO 0.5000 −2.2204 × 10−16 3 33 33 CO 0.4998 2.0609 × 10−4 148 19530 18376 BLISS 0.5000 2.6671 × 10−7 66(66) 4941 4950 MDOIS 0.5000 −4.2723 × 10−8 21(21) 1168 1184 RB (SQP) 0.5000 0.0000 8 280 225 RB (GA) 0.5008 −7.4939 × 10−4 18 25550 25550 domain level optimizers respectively and is competitive with the other bi-level methods. The performance of the algorithms is broadly comparable with the per- formance figures reported in Yi et al. [6] with the slightly greater number of func- tion calls required in our framework likely attributable to the higher tolerances used. Table 2 summarizes the results for the subsonic aircraft design problem. A con- sistent optimum is not found across the methods investigated but the rule base performs well compared to the other bi-level methods (CO, BLISS, MDOIS). The rule based approach (GA) and the MDF method find the best results. CO and BLISS exhibit poor performance for this problem and do not converge to an acceptable feasible solution. For BLISS it is possible that the trust region algorithm could be improved here but the performance of the algorithm on this problem, and others in our test suite, shows that it will often take the search to the bounds of the design variables. Conversely, the rule base in this case, finds a solution close to that of MDF. The broader search achieved using a GA in the domains provides an advantage over SQP for these problems. This also indicates that performance gains may be possible by improving the rules for managing the domain optimization start points. Table 2. Performance of MDO methods for the subsonic aircraft design problem Method Objective Function Maximum Constraint (g ≤ 0) Number system iterations Domain-1 analysis calls Domain-2 analysis calls MDF −2.0676 −5.7335 × 10−11 13(27) 668 668 IDF −2.0152 0.0 5 67 67 AAO −1.9629 −1.4627 × 10−4 5 127 127 CO −2.0139 3.1050 × 10−2 250∗ 156177 469726 BLISS −1.6035 6.8202 × 10−2 7(7) 148 148 MDOIS −1.9706 −6.9561 × 10−7 8(8) 297 308 RB (SQP) −1.9735 0.0 46 2406 923 RB (GA) −2.0549 −4.7834 × 10−5 70 86870 94024 On the Coordination of MDO Using Expert Systems 215 4 Discussion and Conclusions The rule base approach is found to work well and has the advantage that it is relatively straight forward to integrate into existing organizational infrastruc- ture. However, further work is required to assess whether the pragmatic rule base approach, that sacrifices formal guarantees of convergence, will be truly competitive across a large range of MDO problem. The relative ease with which a rule based system level control process can be implemented and managed is a significant advantage over methods like BLISS which can prove difficult to implement. Both BLISS and CO require domain experts to optimize constructs of the process rather than investigate the physics of the problem. Initial studies have involved a number of MDO problems ranging from simple numerical schemes, through basic aircraft sizing studies to a cut-down commer- cial in-house design tool. The initial rule base works by managing the bounds of the shared design variable vector until the enclosed hyper-volume converges to a specified tolerance and all domains are feasible. The performance of the rule base is found to be competitive for a range of MDO problems (of which only two are presented herein). Future work will extend the use of data mining of domain optimizers for improved feature recognition and development of a more sophisticated rule base to improve performance across the range of problems assembled. Acknowledgments The work is funded by the TSB funded NGCW/MDOW project and Airbus UK whose support is gratefully acknowledged. References 1. Sobieszczanski-Sobieski, J., Haftka, R.T.: Multidisciplinary aerospace design opti- mization: survey of recent developments. Structural and Multidisciplinary Optimiza- tion 14, 1–23 (1997) 2. Cramer, E.J., Dennis, J.J.E., Frank, P.D., Lewis, R.M., Shubin, G.R.: Problem Formulation for Multidisciplinary Optimization. SIAM Journal on Optimization 4, 754–776 (1994) 3. Braun, R.: Collaborative Optimization: An Architecture for Large-Scale Distributed Design. PhD Thesis, Stanford University (1996) 4. Sobieszczanski-Sobieski, J., Agte, J.S., Sandusky, R.R.: Bilevel Integrated System Synthesis. AIAA Journal 38, 164–172 (2000) 5. Shin, M.-K., Park, G.-J.: Multidisciplinary design optimization based on indepen- dent subspaces. International Journal for Numerical Methods in Engineering 64, 599–617 (2005) 6. Yi, S., Shin, J., Park, G.: Comparison of MDO methods with mathematical exam- ples. Structural and Multidisciplinary Optimization 35, 391–402 (2008) 7. Lewis, K.: An Algorithm for Integrated Subsystem Embodiment and System Syn- thesis. PhD Thesis, Georgia Institute of Technology, Atlanta (1997) On the Coordination of Multidisciplinary Design Optimization Using Expert Systems Introduction Coordination of MDO Using an Expert System Results Discussion and Conclusions References << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Gray Gamma 2.2) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (ISO Coated v2 300% \050ECI\051) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.3 /CompressObjects /Off /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Perceptual /DetectBlends true /DetectCurves 0.1000 /ColorConversionStrategy /sRGB /DoThumbnails true /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts false /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 149 /ColorImageMinResolutionPolicy /Warning /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 150 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.40 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 149 /GrayImageMinResolutionPolicy /Warning /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.40 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 599 /MonoImageMinResolutionPolicy /Warning /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.) /HUN /ITA /JPN /KOR /LTH /LVI /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR /POL /PTB /RUM /RUS /SKY /SLV /SUO /SVE /TUR /UKR /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.) /DEU >> /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ << /AsReaderSpreads false /CropImagesToFrames true /ErrorControl /WarnAndContinue /FlattenerIgnoreSpreadOverrides false /IncludeGuidesGrids false /IncludeNonPrinting false /IncludeSlug false /Namespace [ (Adobe) (InDesign) (4.0) ] /OmitPlacedBitmaps false /OmitPlacedEPS false /OmitPlacedPDF false /SimulateOverprint /Legacy >> << /AddBleedMarks false /AddColorBars false /AddCropMarks false /AddPageInfo false /AddRegMarks false /ConvertColors /ConvertToCMYK /DestinationProfileName () /DestinationProfileSelector /DocumentCMYK /Downsample16BitImages true /FlattenerPreset << /PresetSelector /MediumResolution >> /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ] >> setdistillerparams << /HWResolution [2400 2400] /PageSize [595.276 841.890] >> setpagedevice