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Optimization Methods - Mechanical Engineering at IIT …

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.

problem parameters. The common engineering objectives involve minimization of overall cost of manufacturing or minimization of overall weight of a component or maximization of total life of a product or others. Although most of the objectives can be quantified (expressed in mathematical form), there are some objectives (such as

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