multi-objective optimisation using GA
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Hello everyone,
I've been trying to find the minimum point that minimise a cost function using multi-objective ga method
I have attached a pdf file that has the question.
The optimal solution should be + value located between Vhigh and Vmax and the other -value is located between Vmin and Vlow.
Here's my attempt;
function z = costfunction(x)
vx1=x(1);
vx2=x(2);
A = [4/3 -4];
Vmax = 5; % Maximum temperature
Vhigh = 4; % High temperature
Vlow = 0; % Low temperature
Vmin = -1; % Minimum temperature
V0=0; % Room initial temperature
PiD = 30 ; % Discrete cost
PiC = 10 ; % Continuous cost
PiP = 50; % Penalty cost
rng default % For reproducibility
if ((vx1 >= Vmin) & (vx1 < Vlow))|((vx2 >= Vmin) & (vx2 < Vlow))
vx1=x(1);
TotalTime1 = abs(vx1)*((1)/A(1));
pvx1 = @(vx1) -vx1;
cost1 = (PiD + (PiC*(abs(vx1)/A(1)))+(PiP*(abs(integral(pvx1,0,1,...
'ArrayValued',true)))))/TotalTime1;
TotalTime2 = TotalTime1+(vx2/A(2));
pvx2 = @(vx2) -vx2;
cost2 = (PiP*abs(integral(pvx2,0,1,...
'ArrayValued',true)))/TotalTime2;
elseif (vtx > Vhigh) & (vtx <= Vmax)|(vx2 > Vhigh) & (vx2 <= Vmax)
TotalTime1 = abs(vx1*((1)/A(1)));
pvx1 = @(vx1) vx1-Vhigh;
cost1 = (PiD + (PiC*(abs(vx1)/A(1)))+(PiP*(abs(integral(pvx1,0,1,...
'ArrayValued',true)))))/TotalTime1;
TotalTime2 = TotalTime1+(vx2/A(2));
pvx2 = @(vx2) vx2-Vhigh;
cost2 = (PiP*abs(integral(pvx2,0,1,...
'ArrayValued',true)))/TotalTime2;
elseif (vx1 ==V0)|(vx2 == V0)
cost1 = 0;
cost2 = 0;
else
TotalTime1 = abs(vx1)*((1)/A(1));
cost1 = (PiD + PiC*(vx1/A(1)))/TotalTime1;
cost2 = 0;
end
z=[cost1 cost2]
vt=[vx1 vx2]
end
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