Subsequently, an objective (i.e., desirability) function d i was calculated for each
response y i individually, based on the user-defined constraints as lower acceptable
response L i and the upper acceptable response U i .
d i y i
ð Þ ¼
0
i fy i < L i
y i À L i
ð
Þ
U i À L i
ð
Þ
if L i < y i < U i
1
i fy i > U i
2
6
6
4
3
7
7
5
ð18Þ
d i (y i ) is 0 if the optimization criteria is not fulfilled, and d i (y i ) tend toward 1 if the
optimization is highly desirable. The multidimensional optimization problem is
Max. X v
Max. AnƟbody
Max. Lactate
Max. Ammonium
6
8
10
12
14
16
X
v
l
m
s
l
l
e
c
[
-1
]
10
15
20
25
30
35
c
Lac [mmol l -1
]
40
0
2
4
6
8
10
Amm [mmol l -1
]
12
0
100
200
300
400
500
c
mAb
l
m
s
l
l
e
c
[
-1
]
Fig. 9 Different shapes of the response surface plots for X v , c Lac , c mAb , and c Amm with different
individual optimum. The user-defined constraints for medium optimization were marked red
52
K. B. Kuchemüller et al.