optimization using genetic algorithm using two variable

I am new to use GA, I want to implement genetic algorithm to find out the optimize variables for the maxiamum value of my Power function ,which is calculted by solving a differential equation but when I run my GA code then it gives only initial value (lower bond value) for the optimize variables. I here write my fitness function and GA function.please anyone suggest the possible mistakes in my GA code. Thanks

% fitness function

function [Fitness_fun] = tribo1(X)

R = X(1);

d = X(2);

sigma = 15e-5;

S = 22.5e-4;

epslno = 8.854e-12;

epslnr=3.4;

Ao = 5e-3;

f = 3.3;

w = 2*pi*f;

thita = 1.5*pi;

h=1e-5;

x = 0:h:0.8;

y = zeros(1,length(x));

I = zeros(1,length(x));

I(1)=0;

y(1)=0;

F_xy = @(t,Q) ((sigma/(epslno*R))*(Ao*sin(w*t+thita)+Ao)...

-Q*((d/epslnr)+Ao*sin(w*t+thita)+Ao)/(S*epslno*R));

for i=1:(length(x)-1)

k_1 = F_xy(x(i),y(i));

k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);

k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));

k_4 = F_xy((x(i)+h),(y(i)+k_3*h));

y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;

I(i+1)=((sigma/(epslno*R))*(Ao*sin(w*x(i+1)+thita)+Ao)...

-y(i+1)*((d/epslnr)+Ao*sin(w*x(i+1)+thita)+Ao)/(S*epslno*R));

end

V=I*R;

P=V.*I;

[Power_IND]=max(P);

Fitness_fun=1/(1+Power_IND);

end

%%

% GA code-

clc

format long g

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

%GA Inputs

rng default

FitnessFunction = @tribo1;

numberOfVariables = 2;

lb = [10e6 50e-6];

ub = [10e13 550e-6];

Aeq = [];

beq = [];

A = [];

b = [];

Ini_Popu = [10e6 50e-6];

NonLinFunction=[];

options = gaoptimset('PlotFcns',{@gaplotbestf,@gaplotbestindiv,@gaplotstopping,@gaplotselection},...

'PopulationSize',50,...

'Generations',10000,...

'EliteCount',2,...

'CrossoverFraction',0.8,...

'ParetoFraction',0.035,...

'MigrationDirection','forward',...

'MigrationInterval',20,...

'MigrationFraction',0.2,...

'TimeLimit',Inf,...

'StallGenLimit',100,...

'FitnessLimit',-Inf,...

'TolFun',1e-50,...

'TolCon',1e-12,...

'InitialPopulation',Ini_Popu,...

'PenaltyFactor',100);

options

[x,Fval,exitFlag,Output,population,scores] = ...

ga(FitnessFunction,numberOfVariables,A,b,Aeq,beq,lb,ub,NonLinFunction,[],options); %NonLinFunction

fprintf('The number of generations was : %d\n', Output.generations);

fprintf('The number of function evaluations was : %d\n', Output.funccount);

fprintf('The best function value found was : %g\n', Fval);

exitFlag

population

scores

min(scores)

x

Answer 1

[Alan Weiss]

You might want to try to copy the coding techniques in Optimize an ODE in Parallel.

Alan Weiss

MATLAB mathematical toolbox documentation