Optimiser returns strange values

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Hamzah Faraj 2020-7-20

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关闭： MATLAB Answer Bot 2021-8-20

task1.pdf

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Hello,

I have been trying to minimse a function using the genatic algorithms (GA).

When I run the optimizer, it returns strange values.

It'd be very appreciated if someone can help me finding and solving the issue.

Note that the optimal value of V(t) should be either between ( 4 and 5) or (-1 and 0).

** Attached a file that explains the problem.

function z = costfunctiontest(x)
Vt = x;
A = [4/3, -4];
Vmax  = 5;           % Maximum temperature        [°C]
Vhigh = 4;           % High temperature           [°C]
Vlow  = 0;           % Low temperature            [°C]
Vmin  = -1;          % Minimum temperature        [°C]
PiD = 30 ;           % Discrete cost              [£]
PiC = 10 ;           % Continuous cost            [£/h]
PiP = 50;            % Penalty cost               [£/h]
ContinuousTime = Vt/A(1);
TotalTime= Vt*((1/A(1))-(1/A(2)));
if ((Vt > Vhigh) & (Vt <= Vmax))
pvt = @(t) abs(Vt-Vhigh); 
cost = (PiD + PiC*ContinuousTime + PiP*integral(pvt,0,TotalTime,'ArrayValued',true)) / TotalTime;
elseif ((Vt >= Vlow) & (Vt <= Vhigh))
cost = (PiD + PiC*ContinuousTime)/TotalTime;
else
pvt = @(t) abs(Vlow-Vt); 
cost = (PiD + PiC*ContinuousTime + PiP*integral(pvt,0,TotalTime,'ArrayValued',true)) / TotalTime;
end
z=cost;
end

%% main code for minimising the fitness function using GA 
ObjFcn = @costfunctiontest;
nvars = 1;
LB = [-1];
UB = [5];
[x,fval] = ga(ObjFcn,nvars,[],[],[],[],LB,UB)

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Matt J 2020-7-20

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Also, ga is a bit excessive for a 1-variable problem. It would be quicker just to use fminbnd over the 2 intervals of interest:

K>> [x,fval] = fminbnd(ObjFcn,-1,0)
x =
  -6.6107e-05
fval =
  -4.5380e+05
K>> [x,fval] = fminbnd(ObjFcn,4,5)
x =
    4.0001
fval =
   15.0032

Hamzah Faraj 2020-7-20

Thanks Matt J for your comments. In fact, the value of x in (4,5] should be equal to the value of x in [-1,0). In addition, fval cannot be a negative value as it’s a cost.

I really appreciate your help and the way you explained the difference between ga and Fminbnd.

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