Decomposition Analysis of an Automotive Powertrain Design ...

NLP PROBLEM
FDT
Objective
Constraints
Bounds
Expressions x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
f 1 0.4 x 1
0.67
x 7
-0.67 f 1 1 1
f 2 0.4 x 2 0.67 x 8
-0.67 f 2 1 1
f 3 10 - x 1 f 3 1
f 4 x 2 f 4 1
g 1 0.1 x 1 + 0.0588 x 5 x 7 -1.0 g 1 1 1 1
g 2 0.1 x 1 + 0.1 x 2 + 0.0588 x 6 x 8 - 1.0 g 2 1 1 1 1
g 3 4x 3 x 5
-1
+2x 3
-0.71
x 5 -1 + 0.0588 x 3 -1.3 x 7 -1.0 g 3 1 1 1
g 4 -1
4x 4 x 6 + 2x4
-0.71
x 6
-1 + 0.0588 x -1.3 4 x 8 -1.0 g 4 1 1 1
g i+4 - 0.1 - x i , i = 1, ..., 8
g i+12 x i - 10, i = 1, ..., 8
PARTITIONS
PARTITIONED FDT
x 1 x 2 x 4 x 6 x 8 x 3 x 5 x 7
DP y y = (x 1 ); f(y) = (f 3 ); g(y) = (g 5 , g 13 )
f 3 1
DP 1 x 1 = (x 2 , x 4 , x 6 , x 8 ); f 1 (y,x 1 ) = (); f 1 (x 1 ) = f 2 + f 4
f 2 1 1
g 1 (y,x 1 ) = (g 2 )
f 4 1
g 1 (x 1 ) = (g 4 )
g 2 1 1 1 1
g b (x 1 ) = (g 6 , g 8 , g 10 , g 12, g 14 , g 16 , g 18 , g 20 )
g 4 1 1 1
DP 2 x 2 = (x 3 , x 5 , x 7 ); f 2 (y,x 2 ) = (f 1 ); f 2 (x 2 ) = ()
f 1 1 1
g 2 (y,x 2 ) = (g 1 ); g 2 (x 2 ) = (g 3 )
g 1 1 1 1
g b (x 2 ) = (g 7 , g 9 , g 11 , g 15 , g 17 , g 19 )
g 3 1 1 1
Figure 2. Partitioning example of an NLP problem.