The increased computational burden may simply reflect the increased size of the MDO problem, with the number of analysis variables and of design variables adding up with each additional discipline.A case of tens of thousands of analysis variables and several thousands of design variables, reported in Berkes (90) for just the structural part of an airframe design, illustrates the dimensionality of the MDO task one has to prepare for. Since solution times for most analysis and optimization algorithms increase at a superlinear. rate, the computational cost of MDO is usually much higher than the sum of the costs of the single-discipline In MDO of complexsystems we alsoface formidable organizational challenges. Theanalysis codes foreachdiscipline havetobemade tointeract withoneanother forthepurpose ofsystem analysis and systemoptimization. The kind andbreadthof interaction is affectedby the MDO formulation. Decisions on thechoice of design variables andon whether tousesingle-level optimization ormultilevel optimization have profound effects onthecoordination anddatatransferbetween analysis codesandthe optimization codeandon the degree of human interactions required. Theinteraction between the modules in thesoftware system ononesideandthe multitude of users organized in disciplinary groups on theothersidemaybecomplicated by departmental divisions intheorganization that performs theMDO.Onemaydiscern three categories ofapproaches to MDO problems,dependingon the way the organizational challenge hasbeen addressed. Twoof these categories represent approaches that concentrated on problem formulationsthat circumventthe organizational challenge, whilethethirddeals with attempts toaddress thischallenge directly.1. Thefirstcategory includes problems withtwo or threeinteracting disciplines where a single analyst canacquire alltherequired expertise. At theanalysis level, thismayleadtothecreation ofa newdiscipline that focuseson the interactionof the involved disciplines, suchasaeroelasticity or thermoelasticity. Thismayleadto MDOwhere designvariables in several disciplines have tobeobtained simultaneously toensure efficient design. Thepast twodecades have created thediscipline ofstructural control, withanalysts whoarewell versed in bothstructures andcontrol system analysis anddesign. There hasalsobeen much workonsimultaneous optimization of structures and control systems (e.g., Haftka, 90). Most ofthepapers inthiscategory represent asingle group of researchers or practitioners workingwith a singlecomputer program, so that organizational challenges were minimized. Because ofthis,it iseasier forresearchers working onproblems inthiscategory todeal withsome oftheissues of complexity of MDOproblems, such as theneed formultiobjective optimization (e.g., Gupta andJoshi, 90,RaoandVenkayya, 92,Grandhi etal., 92,and Dovi andWrenn, 90 In some applications, one may identify a cluster of modules in a system model that exchange very large volumes of data that are not amenable to condensation.In such cases, the computational cost may be subst...
