Fuzzy Pareto Dominance (FPD)

Implicite Crowding Avoidance

One of the interesting properties of the FPD relation is the implicit handling of crowding. The following movie will demonstrate this. We can see 10 points, randomly moving around in the objective space spanned by the two functions

$\,\, y_1 = x^2$
$\,\, y_2 = (1-x)^2$

with x from [0,1]. The size of each point's disc is related to the ranking value of this point within the set of all ten points. The smaller the disc, the more this point is not dominated by the other points in the set. In terms of the multi-objective GA that we will study later: the smaller the disc, the more like is this point selected for mating. It can be seen in the movie that the points become smaller, as they move apart from other points. Once two points are approaching each other, the corresponding discs increase to the maximum size.

Movie: FPD Ranking Values

< FPD.Definition | FPD.FPD | FPD.Motivation >

Page last modified on September 07, 2006, at 05:24 PM

On small computer displays, you can hide this right bar by using the 'Hide' button above.

News

Next conferences COMPSAC 2014 (Vasteras, Sweden, July 2014), INCoS-2014 (Salerno, Italy, September 2014).

New edited book "Soft Computing in Industrial Applications", V. Snasel, P. Kroemer, M. Koeppen, G. Schaefer, Springer AISC 223, July 2013.

Attach:Site/PageHeader/softflow.gif Δ Home Edit History Recent Changes
Mario Köppen Personal Synopsis c.v. Collaborators Thanks Contact Research Topics Thesis Publications By Year By Type By Topic Academic Activities Academic Services Conferences Education Open Calls (site under construction) TriadSkin 3 Powered by PmWiki	FPD Fuzzy Pareto Dominance (FPD) Implicite Crowding Avoidance One of the interesting properties of the FPD relation is the implicit handling of crowding. The following movie will demonstrate this. We can see 10 points, randomly moving around in the objective space spanned by the two functions $\,\, y_1 = x^2$ $\,\, y_2 = (1-x)^2$ with x from [0,1]. The size of each point's disc is related to the ranking value of this point within the set of all ten points. The smaller the disc, the more this point is not dominated by the other points in the set. In terms of the multi-objective GA that we will study later: the smaller the disc, the more like is this point selected for mating. It can be seen in the movie that the points become smaller, as they move apart from other points. Once two points are approaching each other, the corresponding discs increase to the maximum size. Movie: FPD Ranking Values < FPD.Definition \| FPD.FPD \| FPD.Motivation > View Edit Page History Attach File Backlinks List Group Page last modified on September 07, 2006, at 05:24 PM	On small computer displays, you can hide this right bar by using the 'Hide' button above. News Next conferences COMPSAC 2014 (Vasteras, Sweden, July 2014), INCoS-2014 (Salerno, Italy, September 2014). New edited book "Soft Computing in Industrial Applications", V. Snasel, P. Kroemer, M. Koeppen, G. Schaefer, Springer AISC 223, July 2013.
© Mario Köppen 2006-2014