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ApplicationsofEvolutionaryStrategiestoOptimalDesignofMechanicalSystems
37
inequalityconstraintsaffectingsomecharacteristicsoftheresponseofthe
system
(2.2)
Inthisexpression,τisthetimedurationduringwichtheresponseofthe
systemisexamined;qisthevectorofconfigurationparametersofthesystem.
Inordertosimplifyitsmathematicaltreatmentandthedeterminationofderiva-
tives[1,11]inparticular,theinequality(2.2)isgenerallytransformedintoan
equivalenttimeindependentformΨ,accordingto:
wheretheequivalentoperator<>isdefinedby
(2.3)
(2.4)
Thespaceofdesignvariables,eventuallyboundedby(2.1)canbecon-
tinuousordiscrete.
Themethodsabletosolvesuchaproblemcanbeclassifiedinthreeprin-
cipalcategories:
enumerativemethodswhichsystematicallyexamineallpossiblecombina-
tionsofdesignvariablesandselectthebestone.Thesemethodshavethe
advantagetobeveryrobustandtoonlyneedaComputerAidedDesign
simulationcodewithnooptimizationprocedure.Unfortunately,theyare
unpracticableforlargeproblemsastheywouldneedaprohibitivecomputa-
tiontime;
deterministicorhill-climbingmethodswhichattempttoreachtheminimum
throughsuccessivevariationsofthedesignvariablesaccordingtothegradi-
entoftheobjectivefunction.Haug[1]andhiscollaboratorswerecertainly
pioneersforthesecomputationallyefficientmethodssufferingfromtwo
disadvantages:
theyneedtoaddtothemainCADsimulationcodeanadditionalcompu-
tationalprogramforevaluatingthesensitivityoftheobjectivefunction
ortheconstraintsversusthedesignvariables.Generally,suchfurther
calculationsrequiredeepinteractionswiththeCADprogramslimiting
thepossibilitytouse,forCAD,acommercialcodeonlyknownasa
blackbox;
theydon’tnecessarilyleadtotheglobaloptimum.