multi-objective optimisation using GA

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Hamzah Faraj 2020-12-2

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https://ww2.mathworks.cn/matlabcentral/answers/673873-multi-objective-optimisation-using-ga

编辑： Hamzah Faraj 2020-12-2

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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
 