FOA for constrained evolutionary optimization

 

Solving PrG6f(x)

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 % Matlab Code by A. Hedar (Nov. 23, 2005).

 % Min y = (x(1)-10)^3+(x(2)-20)^3;

  % Constraints

% y(1) = -(x(1)-5)^2-(x(2)-5)^2+100

%y(2) = (x(1)-6)^2+(x(2)-5)^2-82.81;

 % Variable lower bounds
% y(3) = -x(1)+13;

% y(4) = -x(2);

 % Variable upper bounds

% y(5) = x(1)-100;

% y(6) = x(2)-100;
 

Optimal value x*=(14.095,0.84296) f*=-6961.81

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Case 1:

 

 

 

 

Clever 3D-FOA (More efficient):

Output:

 

  

 

 

Optimal value x* = (13.1708, 0.0017), f* = -7966.1

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Original 3D-FOA:  

 

 

Output:

Optimal value x*= (13.0467, 0.7330), f*= -7123.9

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Case 2:

 

% Min y = (x(1)-10)^3+(x(2)-20)^3;

 % Constraints

%  -(x(1)-5)^2-(x(2)-5)^2 + 100 <=0
%  (x(1)-6)^2+(x(2)-5)^2-82.81 <=0;

 % Variable lower bounds
%  -x(1)+13 <=0 ;
%  -x(2) <=0 ;  ;

% Variable upper bounds
%  x(1)-100 <=0 ;
%  x(2)-100 <=0 ;

%%********************

 Output:
 

 

 

 

 

 

  
Optimal value x*= (14.0989, 0.8514), f*= -6952.3

Smellbest1 =   1.0e+03 * -6.9523

 

x1Best =  14.0989

x2Best =  0.8514

g1 =     -1.7997

g2 =     -0.0140

>> 
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 PS:  After my paper was published, and I will put these programs into my blogger.

 

Jing Si Aphorism:

 

 

Willing to think,

cultivate ourselves,

and take mindful action,  

there is nothing

we cannot achieve.

 

 

 

 

 Soochow University EMA