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Optimization Methods

1 Optimization Introduction:Inoptimizationofa design, satisfactorysolutionis ,optimizationhasbecomea partofcomputer-aideddesignactivities. Therearetwodistincttypesofoptimizational gorithmswidelyusedtoday.(a) (b) :Anaiveoptimaldesignisachievedbycomparin gafew(limiteduptotenorso) (cost,profit,etc., ) ofeachsolutionis comparedandbestsolutionis isimpossibletoapplysingleformulationproc edureforallengineeringdesignproblems,sin cetheobjectiveinadesignproblemandassocia tedtherefore,designparametersvaryproduct to ,whichthencanbesolvedusinganoptimization algorithm. Figure1 :Theformulationofanoptimizationproblembe ginswithidentifyingtheunderlyingdesignva riables,whichareprimarilyvariedduringthe optimizationprocess. A designproblemusuallyinvolvesmanydesignpa rameters, Other(notsoimportant)designparametersusu allyremainfixedorvaryin :Theconstraintsrepresentsomefunctionalre lationshipsamongthedesignvariablesandoth erdesignparameterssatisfyingcertainphysi calphenomenonandcertainresourcelimitatio ns.

shape, finite element simulation software may be necessary to compute the maximum stress. The following two types of constraints emerge from most considerations: 1. Inequality type constraints. 2. Equality type constraints.

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