I am trying to optimise a cost function that consists of three parameters (A,B,C) using weighted sum approach for the selection of optimal technique out of three techniques. Parameter A unit is in percentage while parameter B and C unit is milliseconds. Parameter A is beneficial attribute, while B and C are non-beneficial attributes.
min(cost)=Aw1+Bw2+Cw3
The following data, normalised by considering beneficial and non-beneficial attributes. I am trying to minimise the cost of the function of t weighted sum approach that provides the best technique out of three technique with supplied user weights. However, I noticed that for better input the cost function is higher for instance for 4.466916 the normalised value is 1 and for 24.2542 it's 1 in below data
Parameter B Min
4.466916 27.07074 24.57503 4.466916
24.2542 27.07074 25.95272 24.2542
Normalised data after applying formula xmin/x
1 0.165009 0.181766
1 0.895956 0.934553
Below is the data of Parameter A data which consists of data of three techniques T1,T2,T3
T1 T2 T3 Max
0.6233 0.8253 0.8324 0.8324
0.8063 0.8253 0.8311 0.8311
Normalised data after applying formula x=x/xmax
0.748799 0.991444 1
0.97016 0.993021 1
However, for above data I am trying to understand and couldn't understand that for better input the cost function is higher which should be minimum for instance for 4.466916 the normalised value is 1 and for 24.2542 which is not a better input its one. Would anyone please me in understand this
