Optimiser returns strange values

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)

[Matt J]

Note that the optimal solution shouls be a value between ( 4 and 5) or (-1 and 0).

I don't see why the solution couldn't fall anywhere between the LB and UB that you've supplied. However, here are the results that I get.

x =

  -4.4789e-05


fval =

  -6.6980e+05

Since x falls within the bounds that you mention, I see nothing confounding about the result.

[Matt J]

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]

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.