How to solve a cubic equation using Genetic Algorithms?

Hello there,

I want to write a code in matlab that finds a real solution for the equation x^3+x^2+x+7=0 , -5<x<5, using Genetic Algorithms.

How can I implement that with code?

Answer 1

[Stephan]

start here:

https://de.mathworks.com/help/gads/ga.html?searchHighlight=ga&s_tid=srchtitle#mw_a07ddf7d-face-4243-a656-f1528b592de0

Answer 2

[Walter Roberson]

f = @(x) x.^4-2*x.^3+3*x.^2+x-4

f = function_handle with value:
    @(x)x.^4-2*x.^3+3*x.^2+x-4

target = 5;
residue = @(x) (f(x)-target).^2

residue = function_handle with value:
    @(x)(f(x)-target).^2

[bestx, fval] = ga(residue, 1)

Optimization terminated: average change in the fitness value less than options.FunctionTolerance.

bestx = -1.1833

fval = 0.5017

roots([1, -2, 3, 1, -4-target])

ans = 
   0.7541 + 1.9406i
   0.7541 - 1.9406i
   1.7076 + 0.0000i
  -1.2159 + 0.0000i

[Nick]

So what fitness function should I use for the x^3+x^2+x+7=0 equation?

[Walter Roberson]

One that computed the left hand side of that polynomial, with the target set to the constant that is the right hand side of the equation.

... you are obviously answering homework, so I deliberately showed you how to do it for a different polynomial, so that you would have to do at least minimal study of the technique instead of just copying what I posted.