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I have calculated data from a computer simulation for a wireless network as shown below, here P is an algorithm tuning parameter, 'C' and 'D' are % decrease in collisions and % decrease in delay respectively. Frame lenght is 20%.

P   C   D    Frame Lenght
0.3 184 249   20%
0.4 137 241   20% 
0.5 168 230   20%
0.6 221 210   20%
0.7 148 219   20%
0.8 80  219   20%

I need to derive a cost function to provide an output (value of 'P') based on 'C', 'D' and Frame Length. The value of 'P' should be such that max % decrease in 'C' and 'D' is obtained, but 'C' has priority. In this case 'P'=0.6 should be the output of the cost function. I also need to perform simulations by varying Frame length like 40% and 80% to obtain optimum value of 'P' from cost function that provides high %decrease in 'C' . Therefore is it also possible to use Frame length in cost function. Can any one tell how can I derive cost function for 'P'.

user308606
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  • What does it mean to provide an output value of $P$ based on $C$ and $D$? Without a specified function relating $(P, C, D)$, it seems that any curve interpolating these points is a satisfactory answer. What is the problem you're trying to solve, and how does "deriving a cost function" help you solve it? – Sycorax Jan 18 '21 at 20:49
  • It will let me know what value of parameter 'P' is optimum to use in the algorithm. The function of (P, C, D) will be desired cost function, if it can be derived from the tabular data shared. – user308606 Jan 19 '21 at 14:45
  • Trying to infer a function given some observed values and then find an optimal value (maximum or minimum) of that function is called *black-box optimization*. The linked threads will get you started. – Sycorax Jan 19 '21 at 15:18

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