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Trouble Replicating Optimization Algorithm - Result did not match the paper

Posted 5 months ago

Hello, right now I'm trying to replicate an optimization algorithm from a research paper, but I'm getting different results. In the paper, when the frequency parameter n is set to 20, the resulting value of T should be 1.67 and the profit TP should be 421.14. However, when I set n to 20 in Mathematica, I get T = 0.09 and TP = -1743. I tried to recheck the equation I wrote in Mathematica and recheck the parameter value as well but the result still did not match. I've been working on this for a while and I'm starting to run out of ideas. Here is the algorithm and the equation I try to follow : enter image description here enter image description here And also, here is the numerical example and the result that was written in the paper : enter image description here enter image description here Here is the code I wrote in mathematica :

Clear["Global`*"]
L = 4;
w = 0.064;
ww = 2;
R = 250;
Kf = 750;
cf = 0.1;
m = 0.2;
Kp = 500;
hp = 0.05;
Kd = 100;
h = 0.1;
g = 6.87;
q = 0.12;
a = 80;
b = 0.2;
pv = 1;
pf = 2;
pr = 5;
z = 120;
n = 20;
x = 0.9;
s = 0.2;
Tf = - (Log[1/z (g/ww - 1)]/q);

F[d_] = pr/d ((a (1 - b) (2 L d - d^2))/(2 L))^(1/(1 - b)) - (pv w)/(
    d x ww) ((a (1 - b) (2 L d - d^2))/(2 L))^(1/(1 - b)) - Kd/d - 
   Kp/(n d) - Kf/(
   n d) - (h a (1 - b))/(
    2 L d) (d + (((1 - b)/(
          2 - b)) (2^(1/(1 - b))  L^(1/(1 - b))  d^((2 - b)/(
           1 - b))) + d^((3 - b)/(1 - b)))) - 
   hp/(2 R d) ((a (1 - b) (2 L d - d^2))/(2 L))^(2/(1 - b)) - (
    hp (n - 1))/(2 d) ((a (1 - b) (2 L d - d^2))/(2 L))^(2/(
    1 - b)) (d ((a (1 - b) (2 L d - d^2))/(2 L))^(1/(1 - b)) - 1/
      R) - (cf x + m s)/(d x ww) ((a (1 - b) (2 L d - d^2))/(2 L))^(
    1/(1 - b)) (g Tf + g/q (Log[1 + z E^(-q Tf)] - Log[1 + z]));
FindMaximum[{Re@F[d], d > 0}, d]
Plot[F[d], {d, 0, 10}]

Note : I symbolize T as d and TP[T] as F[d] in Mathematica.

Does anyone have any insights into why this might be happening? Is there a step I might have missed?

Attachments:
POSTED BY: Shafa Hananta
Posted 5 months ago

Hi. I found two cases where the Mathematica code differs from the papers "code". See the attached, the changes I made are highlighted in yellow.

With the changes the T and TP values becomes close to the expected.

Attachments:
POSTED BY: Hans Milton
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