MATLAB Central Newsreader - the theory behind 'gamultiobj' function

the theory behind 'gamultiobj' function

hailiang shen — Tue, 24 Feb 2009 15:47:37 -0500

Hi everyone,
Can any one tell me the theory behind the 'gamultiobj' function? Is it using the NSGA-II algorithm? I see Deb(2002) is referenced.
Thanks,
Hailiang

Re: the theory behind 'gamultiobj' function

Alan Weiss — Tue, 24 Feb 2009 15:57:06 -0500

hailiang shen wrote:
> Hi everyone,
> Can any one tell me the theory behind the 'gamultiobj' function? Is it using the NSGA-II algorithm? I see Deb(2002) is referenced.
> Thanks,
> Hailiang

From the MATLAB demo "Multiobjective Genetic Algorithm Options":
http://www.mathworks.com/products/gads/demos.html?file=/products/demos/shipping/gads/gamultiobjoptionsdemo.html

"The multiobjective GA function GAMULTIOBJ uses a controlled elitist
genetic algorithm (a variant of NSGA-II [1])"

Sorry this isn't so obvious in the documentation, it's on my "to-do" list.

Alan Weiss
MATLAB mathematical toolbox documentation

Re: the theory behind 'gamultiobj' function

hailiang shen — Tue, 24 Feb 2009 17:02:42 -0500

Thanks Alan for the reply.
In NSGA-II, it firstly selects the individuals with the best rank from fronts (first 1 then 2, etc. ). Suppose the population size is 100, the number of the individuals in fronts with rank <= 10 is 97, and the number of individuals in the 11th front is 5. We will select the 3 individuals with the bigger distance.

In 'gamultiobj', do you i) first take the best rank? e.g. select 10 individuals with the best rank. and then ii) take the bigger distance? How do you calculate the distance in the subsequent fronts.

Hailiang

Re: the theory behind 'gamultiobj' function

Alan Weiss — Tue, 24 Feb 2009 20:02:32 -0500

hailiang shen wrote:
> Thanks Alan for the reply.
> In NSGA-II, it firstly selects the individuals with the best rank from fronts (first 1 then 2, etc. ). Suppose the population size is 100, the number of the individuals in fronts with rank <= 10 is 97, and the number of individuals in the 11th front is 5. We will select the 3 individuals with the bigger distance.
>
> In 'gamultiobj', do you i) first take the best rank? e.g. select 10 individuals with the best rank. and then ii) take the bigger distance? How do you calculate the distance in the subsequent fronts.
>
> Hailiang

Hailiang, if you want to understand all the gory details of the
implementation, then I suggest you look at the code. All the code is
M-files, you can look at the files with, say, edit gamultiobj.m. When
you come across a subroutine you want to examine, select it and press
control-D.

Alan Weiss
MATLAB mathematical toolbox documentation