Week 4.1 - Genetic Algorithm

theory:- genetic algorithm 

• Genetic algorithm is an optimization tool in matlab that is used to find the minimum value of a function.
• A genetic algorithm works with the fitness function. This function evaluates the fitness of the individuals. Fitness function defines the eligibility criteria for selection of the fruitful candidates.
• It is based on the evolution process in which the eligible candidates are selected, then these fit candidates undergo mutation during their lifetime in the generation. 
• These points run through fitness functions in order to select the better candidates,here local maxima are chosen.
• The new set undergo mutation.This initial population keeps on increasing and repeating for the next 100 generation default.The generation are interchanged into the better candidates for the next upcoming generations.
• syntax :- [x, fval] = ga(fun,nvars,A,b,[],[],lb,ub,option)
• x-an array which stores the point generated by ga at which local and global minima can be found.
• fval-stores local minima
• fun-fitness function
• A,b-inequality
• lb-lower bond
• ub-upper bond
• options-structure data type.
• code:fitness function

function [f] = stalagmite(input_vector)

x = input_vector(1);
y = input_vector(2);

t1=(sin((5.1*pi*a)+0.5))^6;
t2=(sin((5.1*pi*b)+0.5))^6;
t3=exp(-4*log(2)*((a-0.0667)^2)/0.64);
t4=exp(-4*log(2)*((b-0.0667)^2)/0.64);

[f]=(t1*t2*t3*t4);
end

• stalgmite function:-

Stalagmite functon is a methametical function model which helps to generate  local minima and maxima.It is a 3D function and the way the function is designed is that it has a lot of local maxima or minima and one global maxima and minima .

for i=1:length(xx)
for j=1:length(yy)
input_vector(1)=xx(i,j);
input_vector(2)=yy(i,j);
f(i.j)=stalagmite(input_vector);
end
end