Optimization to minimize output

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Anand Ra
Anand Ra 2021-10-6
评论： Anand Ra 2021-10-6
Ran in:
Hello,
I am trying to optimize the lengths to minimize the power ( details in the code)
I am unable to proceed with the optimization part. ( Iam not getting the expected result of optimized power)
Any help would be greatly appreciated.
% Objective:Optimize the lengths to minimze the power using a new variable.
%Constants
k= 1;
w=1;
%Variable lengths
l1 = 3*(5)^0.5;
l2 = 5*(2)^0.5
l2 = 7.0711
l3 = sqrt(5);
v1 = sqrt(5);
v2 = 2*sqrt(2);
v3 = 2*sqrt(5);
% Expressing the l and v in terms of a b and c. Open to expressing differently
% if it helps the objective below.
a = l1*v1;
b = l2*v2;
c = l3*v3;
%Actual Power
P = (l1*v1 + l2*v2 + l3*v3)*k*w; % Power
% Objective
%To search and find the values for a, b and c to minimize power
%Considering x to represent a,b and c.
fun = @(x)(x(:,1) + x(:,2) + x(:,3)).*k.*w;
[X1, X2, X3] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?
X = [X1(:), X2(:), X3(:)];
P = fun(X);
[bestP, idx] = min(P(:))
bestP = 0
idx = 1
best_X = X(idx,:)
best_X = 1×3
0 0 0
  1 个评论
Matt J
Matt J 2021-10-6
Your post now contains the results of running the code (I took the liberty...). The answer looks correct to me.

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回答（1 个）

Walter Roberson
Walter Roberson 2021-10-6
Ran in:
% Objective:Optimize the lengths to minimze the power using a new variable.
%Constants
k= 1;
w=1;
%Variable lengths
l1 = 3*(5)^0.5;
l2 = 5*(2)^0.5
l2 = 7.0711
l3 = sqrt(5);
v1 = sqrt(5);
v2 = 2*sqrt(2);
v3 = 2*sqrt(5);
% Expressing the l and v in terms of a b and c. Open to expressing differently
% if it helps the objective below.
a = l1*v1;
b = l2*v2;
c = l3*v3;
%Actual Power
P = (l1*v1 + l2*v2 + l3*v3)*k*w; % Power
% Objective
%To search and find the values for a, b and c to minimize power
%Considering x to represent a,b and c.
fun = @(x)(x(:,1) + x(:,2) + x(:,3)).*k.*w;
[X1, X2, X3] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?
X = [X1(:), X2(:), X3(:)];
P = fun(X);
[bestP, idx] = min(P(:))
bestP = 0
idx = 1
best_X = X(idx,:)
best_X = 1×3
0 0 0
This is obviously the correct output for the formula.
k is positive. w is positive. k*w is positive. k*w is being multiplied by (x1 + x2 + x3)
To get the smallest result of a multiplication of a positive number and another number, you want the second number to be as small as possible.
Your x1, x2, x3 are all bounded by 0 below. Increasing x1 or x2 or x3 would increase the sum x1+x2+x3 . So the smallest x1+x2+x3 is at the lower bound, where x1 = x2 = x3 = 0.
So your minima is clearly at x1 = x2 = x3 = 0 with power 0 .
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Walter Roberson
Walter Roberson 2021-10-6
fun = @(x)(x(:,1) + x(:,2) + x(:,3) + x(:4) + x(5).*k.*w;
missing close bracket
has same issue as before with minima at 0
Anand Ra
Anand Ra 2021-10-6
@Walter Roberson@Matt J
I think I missed the relationship constaints. I have included that now. I am not sure how to construct the minimization part, given my relationshipo constrains
% Objective:Optimize the lengths to minimze the power using a new variable.
a = 0.1:20;
b = 0.1:20;
d = a + 0.1:20;
c = b + 0.1:20;
e = d + 0.1:20
%Constants
k= 2;
w=1;
v=1.5
%Variables
AB = sqrt(a.^2 + b.^2);
BC = sqrt( c.^2 + ((e-d)/2).^2 );
CS = sqrt( c.^2 + ((e-d)/2).^2 );
VAB = sqrt(((((a.*v).^2/(((b.^2).*4))) + (v^2)/2 )));
% VBS = sqrt(((a*v)^2/((4*b*b)) + (v^2)/2 ));
VCS = ((2*c)./(e-d)).*sqrt(AB.^2);
VBC= CS.^2 + BC.^2;
%Actual Power
%P = (AB*VAB + BC*VBC + CS*VCS)*k*w; % Power
%
% Objective
%To search and find the values for a, b, c d and eto minimize power
% Not sure how to write the function for above
% fun = @(x)(x(:,1) + x(:,2) + x(:,3) + x(:,4) + x(:,5)).*k.*w;
%
% [X1, X2, X3, X4, X5] = ndgrid(0:.1:2); % Should I give this condition in a nested loop?
%
% X = [X1(:), X2(:), X3(:), X4(:), X5(:)];
%
% P = fun(X);
% [bestP, idx] = min(P(:))
% best_X = X(idx,:)

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