Optimization Methods

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1Optimization 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.

Equality constraints. state that functional relationships should exactly match a resource value. Example: The deflection δ(x)of a point in the component must be exactly equal to 5 mm. Then δ(x) = 5. It is very difficult to handle the equality constraints in the algorithms. In such cases, equality constraint is relaxed by

  Equality, Optimization