Various types of design optima
Various types of design optima
Design Definition Sharp Vs constraints -0 contours shallow V- bad side of constraints -0 contours band pol Near-orthogonal intersection Objective defines a design point Tangential definition identifies Constraint descent a band of of designs
Design Definition: Sharp vs. constraints - 0 contours Shallow - bad side of 1 2 constraints - 0 contours 1 2 band point X X Constraint descent Objective • Near-orthogonal intersection defines a design point • Tangential definition identifies a band of of designs X
Multiobjective Optimization both trade off both Q=1/quality performance comfort pareto-frontier 2 esign& manufacturing sophistication pareto-optimum V&w R&R OLLS ROYCI BEETLE
Multiobjective Optimization trade- both Q = 1/(quality & f1 off both performance & f2 comfort) $ 1 4 $ 4 pareto-frontier 3 2 3 2 design & manufacturing sophistication 1 Q pareto-optimum V&W R&R
A Few Pareto-Optimization Techniques · Reduce to a single objective:F=∑Wf where ws are judgmental weighting factors · ptimize for f1;Getf1; Set a floor f,>=fi: Optimize for f2; get f2 Keep floor f, add floor f2 Optimize for f3 Repeat in this pattern to exhaust all fs: The order of fs matters and is judgmental Optimize for each f; independently; Get n optimal designs; Find a compromise design equidistant from all the above Pareto-optimization intrinsically depends on judgmental preferences
A Few Pareto-Optimization Techniques • Reduce to a single objective: F = Σ wi f i i where w‘s are judgmental weighting factors • Optimize for f1; Get f*1;; •Set a floor f1 >= f*i ; Optimize for f2; get f2 ; • Keep floor f1, add floor f2 ; Optimize for f3 ; • Repeat in this pattern to exhaust all f‘s; • The order of f‘s matters and is judgmental • Optimize for each f independently; Get n optimal designs; i Find a compromise design equidistant from all the above. • Pareto-optimization intrinsically depends on judgmental preferences
Imparting Attributes by Optimization Changing w, in F=2,, f, modifies the design within broad range EXample two objectives setting W, =1; W2=0 produces design whose F=f setting W,=0; W2= 1 produces design whose F setting W, =0.5 W2=0.5 produces design whose F is in between Using w, as control, optimization serves as a tool to steer the design toward a desired behavior or having pre-determined, desired attributes
Imparting Attributes by Optimization • Changing wi in F = Σi wi fi modifies the design within broad range • Example: Two objectives • setting w1 = 1; w2 = 0 produces design whose F = f1 • setting w1 = 0; w2 = 1 produces design whose F = f2 • setting w1 = 0.5; w2 = 0.5 produces design whose F is in between. • Using w as control, optimization serves as a tool i to —steer“ the design toward a desired behavior or having pre-determined, desired attributes