I need to maximize an objective function using genetic algorithm but i am having errors

Question

Shehu Ibrahim Dauda 2020-7-18

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https://ww2.mathworks.cn/matlabcentral/answers/567171-i-need-to-maximize-an-objective-function-using-genetic-algorithm-but-i-am-having-errors

评论： Matt J 2020-7-20

Hello all,

I am trying to optimize the dimension of a piezoelectric cantilever beam with parameters specified with symbolic function (syms) as shown in fitness function script below. But when I run the genetic algorithm script, I am encountering the following error

"The following error occurred converting from sym to double:
               Error using symengine (line 59)
               DOUBLE cannot convert the input expression into a double array.
              If the input expression contains a symbolic variable, use VPA.
              Error in fcnvectorizer (line 13)
               y(i,:) = feval(fun,(pop(i,:)));
               Error in makeState (line 58)
                Score = fcnvectorizer(state.Population(initScoreProvided+2:end,:),FitnessFcn,1,options.SerialUserFcn);
                Error in galincon (line 17)
                state = makeState(GenomeLength,FitnessFcn,Iterate,output.problemtype,options);
                Error in ga (line 359)
                [x,fval,exitFlag,output,population,scores] = galincon(FitnessFcn,nvars, ...
                Error in GA (line 8)
                [Lbeam,width,thickbeam,thickpiezo,Lpiezo,fval] = ga(ObjFun,nvars,[],[],[],[],LB,UB);
                Caused by:
            Failure in user-supplied fitness function evaluation. GA cannot continue."

Please find attached my main GA code and the fitness function code

Thank you as I await your reply

Ibrahim

% Main code for maximizing fitness function using GA (Genetic algorithm)
ObjFun =@myfitness;
nvars = 5;
LB = [1e-3 0.5e-3 0.1e-3 0.01e-3 0.5e-3];
UB = [5e-3 2.5e-3 0.2e-3 0.05e-3 5e-3];
[Lbeam,width,thickbeam,thickpiezo,Lpiezo,fval] = ga(ObjFun,nvars,[],[],[],[],LB,UB);

%Fitness function
function Veb = myfitness(Lbeam,width,thickbeam,thickpiezo,Lpiezo)
rho = 2700;   %kg/m^3 density
Ebeam = 70e9; %Pa Young's modulus
Lf = .003;    %m length to forcing f(t)
%piezo properties
g31 = -9.5e-3;  %V*m/N voltage constant
Epiezo = 50e9;  %Pa Young's Modulus
%Parameters for optimization
syms x
syms Lbeam
syms width
syms thickbeam
syms thickpiezo
syms Lpiezo
%Natural frequencies of the beam for a clamped-free beam
Area = thickbeam*width; %m^2 Area
I = width*thickbeam^3/12; %m^4 M. A. of inertia
BNl = 1.8751;
BN = BNl/Lbeam;
wn = ((BN)^2)*sqrt((Ebeam*I)/(rho*Area));
%Mode shapes
alpha =((sin(BNl)+sinh(BNl)))/(cos(BNl)+cosh(BNl));
ModeShape =sin(BN*x)-sinh(BN*x)-(alpha*(cos(BN*x)-cosh(BN*x)));
%Harmonic forcing function
w = wn;
zeta = .03;
wd = wn*(1-zeta^2)^5;
syms t tt
Force = (.35)*sin(w*tt)*1/(rho*(thickbeam*width))*subs(ModeShape,x,Lf);
q = 1/wd*exp(-zeta*wn*t)...
*int(Force*exp(zeta*wn*tt)*sin(wd*(t-tt)),tt,0,t);
%Develop equation for voltage
before_w3 = q*ModeShape;
w3 = before_w3;
K_x_t = vpa(diff(w3,x,2),5);
Kavg = vpa((1/Lpiezo)*int(K_x_t,x,0,Lpiezo),5);
tau = 2;
%tau = 2:.01:5;
I = width*thickbeam^3/12;
Moment = Ebeam*I*Kavg;
psi = (Ebeam*thickbeam)/(Epiezo*thickpiezo);
T = thickbeam/thickpiezo;
Veb_sym= (6*g31*psi*(1+T))/(width*thickpiezo*(1+psi^2*T^2+2*psi*(2+3*T+2*T^2)))*Moment;
Veb1 = subs(Veb_sym,'t',tau);
Veb =(-Veb1);
end

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Answer 1

Matt J 2020-7-18

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/567171-i-need-to-maximize-an-objective-function-using-genetic-algorithm-but-i-am-having-errors#answer_467700

编辑：Matt J 2020-7-18

在 MATLAB Online 中打开

You should not have symbolic input/output in myfitness(). ga() is a numerical solver, so the operations in myfitness() should take numbers as input and produce numbers as output, not symbolic expressions. Also, your fitness function should have all the unknowns contained in a single input vector:

function Veb = myfitness(unknowns)
  [Lbeam,width,thickbeam,thickpiezo,Lpiezo] ...
      = deal(unknowns(1),unknowns(2), unknowns(3), unknowns(4), unknowns(5));
  
  ....
      
  Veb = .... ;
end

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Shehu Ibrahim Dauda 2020-7-20

Actually, by substituting "tau = 2:0.1:5", the fitness function will return a vector. Does genetic algorithm works on vector? if yes, please how can I make it work?

Regards

Ibrahim