It is possible to find out several authors in the literature that have used the schema theorem to solve or justify some optimization problem. However, in general, it is also possible to realize that even the generalization of the schema theorem (proposed by Goldberg, 2002) is not sufficient to demonstrate, for instance, the superiority of genetic algorithms over other evolutionary algorithms. Indeed, one of the main reasons consists on the disruption of the building blocks caused by crossover operators.
In this sense, what do you think about that?
Conference Paper Variable Selection for Multivariate Calibration in Chemometr...
There you are
http://link.springer.com/article/10.1023/A:1011552313821#page-1
http://www.mitpressjournals.org/doi/abs/10.1162/106365603766646825#.Vt2Hu_mLSUk
http://link.springer.com/article/10.1007/s10489-015-0696-4 (recent publication)
Patricia
Dear Patricia,
I appreciate the links you sent me. However, all of them are related to Genetic Programming. I would like to read a paper restricted to only Genetic Algorithms (or evolutionary strategies).
I believe you want to look at the paper by Nix and Vose, which gets rid of the inequality in the schema theorem. Their Markov model provides a precise description of a GA. Here is how we used it.
https://www.researchgate.net/publication/2713452_Using_Markov_chains_to_analyze_GAFOs
Providing proofs of the "superiority of genetic algorithms over other evolutionary algorithms" is unlikely, if you examine the No Free Lunch Theorems of Wolpert and Macready. Instead, it is best to think of matching algorithms to problems. As far as I know this is still a significant problem.
Also of interest (w/r schema analysis) is
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.1448
Crossover can provide disruption and construction of building blocks.
The Nix and Vose formulation covers it all. One downside is that examining the resulting Markov chain can be more expensive than running the GA itself, due to the huge number of states.
Article Using Markov chains to analyze GAFOs
Dear William,
thank you for sending me these links. I was not able to access the last one, but I think that the first paper may be useful for me.
Sorry - you are right, the link doesn't work. Try this one:
http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA294072
I don't think this is directly related. But, you may be interested in this paper:
http://www.sciencedirect.com/science/article/pii/S0096300307009897
Dear Zong Woo Geem,
I appreciate for sending me this link, but your paper indeed is not related with my issue.
- Badges
- Science topic
- Similar topics
- Engineering
- Modeling