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Subject: optimization GA
Date: Fri, 9 May 2008 17:13:04 +0000 (UTC)
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Hi everyone,
can anyone help me to solve multiobjective problem with 
liner and nonlinear constraints and bounds in Genetic 
Algorithm toolbox.
Problem:
five design variables: x=[Ri;Ro;A;F;Z]

objective functions:

f(1)= pi*(Ro^2-Ri^2)*A*(Z+1)*Rho; % min weight
f(2)=Jz*omega/(Mh+Mf)*1000; % min time

subject to:

linear constraints:
  Aineq=[-1 0 0 0 0;0 1 0 0 0;1 -1 0 0 0;0 0 -1 0 0;...
0 0 1 0 0;0 0 0 0 1;0 0 0 0 -1;0 0 0 -1 0;0 0 0 1 0];
bineq=[-55;110;-20;-1.5;3;9;-1;0;1000];

nonlinear constraints:
where c=<0
c=[-Lmax+(Z+1)*(A+delta);prz-pmax;th-tmax;s*Ms-Mh;...
-th;prz*Vsr-pmax*Vsrmax;Vsr-Vsrmax];
                                                 
ceq=[];

where:

Rimin=55;       
Romax=110;      
deltaR=20;      
Amin=1.5;       
Amax=3;         
delta=0.5;      
Lmax=30;        
Zmax=10;        
Vsrmax=10000;  
mi=0.5;        
Rho=0.000007850;
s=1.5;          
Ms=40;         
Mf=3;           
n=250;          
pmax=1;         
Jz=55;          
tmax=15;
Fmax=1000;

and

S=pi*(Ro^2-Ri^2);                    
prz=F/S ;                           
Rsr=(2/3)*((Ro^3-Ri^3)/(Ro^2-Ri^2)); 
Vsr=(pi*Rsr*n)/30;                  
omega=(pi*n)/30;
Mh=2/3*mi*F*Z*((Ro^3-Ri^3)/(Ro^2-Ri^2));
f(2)=th=Jz*omega/(Mh+Mf)*1000;

I have tried to solve this as a single objective which is 
fine but i could only get one solution instead of pareto 
solution and when i tried to solve it as a multiobjective 
problem i didn't know how to handle the nonlinear 
constraints. If anyone know how to solve such problem 
please let me know i would be very thankful.