A General Theory of Optimization - Revision history

Delgadoj at 19:13, 10 June 2007

2007-06-10T19:13:35Z

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	==Motivation==		==Motivation==

	I have been Raking my brain on this fascinating problem for a couple of month now and I think I have some ideas of how it might be solvable. However it is a really complex issue and I am definitely not an expert of most disciplines that are involved in analyzing this problem. So if anyone with experience in evolution, search or algorithms, social systems, information theory, computation, neural networks, Boolean networks, etc. would like to work on this problem with me it would be great. Also let me know if you have any ideas or sugestion. [http://www.santafe.edu/events/workshops/index.php/Jose_Delgado jd]		I have been Raking my brain on this fascinating problem for a couple of month now and I think I have some ideas of how it might be solvable. However it is a really complex issue and I am definitely not an expert of most disciplines that are involved in analyzing this problem. So if anyone with experience in evolution, search or algorithms, social systems, information theory, computation, neural networks, mathematics, Boolean networks, etc. would like to work on this problem with me it would be great. Also let me know if you have any ideas or sugestion. [http://www.santafe.edu/events/workshops/index.php/Jose_Delgado jd]

Delgadoj at 19:03, 10 June 2007

2007-06-10T19:03:06Z

← Older revision		Revision as of 19:03, 10 June 2007
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	==References==		==References==
			# [http://ic.arc.nasa.gov/people/dhw/papers/78.pdf Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for Optimization," IEEE Transactions on Evolutionary Computation 1, 67].
			# [http://ase.arc.nasa.gov/publications/pdf/0995.pdf Wolpert, D.H., and Macready, W.G. (2005) "Coevolutionary free lunches," IEEE Transactions on Evolutionary Computation, 9(6): 721-735]
			# Scott E. Page, The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies, Princeton University Press (2007) pp. 60-61 (a very basic an easy to understand explaination of NFL theorem)

Delgadoj at 18:52, 10 June 2007

2007-06-10T18:52:17Z

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	==Concept==		==Concept==

			Analyzing the similarities and differences between multiple optimization systems in both nature and computation and determining if there are basic fundamental principles that can be framed and used to achieve predictive value.


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	If you are familiar with the evolution of social systems, or the way neural representations compete in the hidden layer of a neural network, or the evolution of ideas, trends or memes, you might have noticed that there is something utterly “Darwinian” about them. The problem is that no-one has been able to develop a unified framework that would allows for the analysis of all of those systems and provide predictive value about how exactly optimizers would perform under different varieties of problems.		If you are familiar with the evolution of social systems, or the way neural representations compete in the hidden layer of a neural network, or the evolution of ideas, trends or memes, you might have noticed that there is something utterly “Darwinian” about them. The problem is that no-one has been able to develop a unified framework that would allows for the analysis of all of those systems and provide predictive value about how exactly optimizers would perform under different varieties of problems.



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	I have been Raking my brain on this fascinating problem for a couple of month now and I think I have some ideas of how it might be solvable. However it is a really complex issue and I am definitely not an expert of most disciplines that are involved in analyzing this problem. So if anyone with experience in evolution, search or algorithms, social systems, information theory, computation, neural networks, Boolean networks, etc. would like to work on this problem with me it would be great. Also let me know if you have any ideas or sugestion. [http://www.santafe.edu/events/workshops/index.php/Jose_Delgado jd]		I have been Raking my brain on this fascinating problem for a couple of month now and I think I have some ideas of how it might be solvable. However it is a really complex issue and I am definitely not an expert of most disciplines that are involved in analyzing this problem. So if anyone with experience in evolution, search or algorithms, social systems, information theory, computation, neural networks, Boolean networks, etc. would like to work on this problem with me it would be great. Also let me know if you have any ideas or sugestion. [http://www.santafe.edu/events/workshops/index.php/Jose_Delgado jd]


	==References==		==References==

Delgadoj at 18:44, 10 June 2007

2007-06-10T18:44:00Z

New page

{{CSSS 2007 Santa Fe}}
==Concept==

==Framing the question==
Many systems in nature can by analyze as optimizers. Biological evolution creates variations that are more optimal for a given niche. The brain takes sensory inputs and selects motor outputs that would benefit the organism. Corporations are constantly changing paradigms in order to maximize revenue, etc. the question is whether all of these systems work based on the similar principles and whether we can understand such basic mechanisms enough to determine what the best optimized is for every environment. In a sense, how to optimize optimizers.

If you are familiar with the evolution of social systems, or the way neural representations compete in the hidden layer of a neural network, or the evolution of ideas, trends or memes, you might have noticed that there is something utterly “Darwinian” about them. The problem is that no-one has been able to develop a unified framework that would allows for the analysis of all of those systems and provide predictive value about how exactly optimizers would perform under different varieties of problems.

==Background==

No Free Lunch Theorem:

In 1995 David H. Wolpert and William G. Macready developed the [http://en.wikipedia.org/wiki/No_free_lunch_theorem “No Free Lunch” Theorem]. In a simplified manner this theorem states that over the set of all mathematically possible problems, all optimization algorithms should perform in average the same. In general that if one heuristic or algorithm performs better than average in a set of problems, then it must necessarily perform worse than average in at least another set of mathematically possible problems. (notice that some limitations of conditions were made in order to make the theorem solvable, so there is dispute about exactly how generalizable the theorem is).

In general the theorem seems fairly intuitive. Just because a heuristic or optimized is capable of solving a problem it does not follow that it will perform as well on all problems. In that case, one would expect that a feed forward neural network, a Bayesian network, evolutionary algorithms, etc, would tend to perform better or worse depending on the specific characteristics of the problem.

==Motivation==

I have been Raking my brain on this fascinating problem for a couple of month now and I think I have some ideas of how it might be solvable. However it is a really complex issue and I am definitely not an expert of most disciplines that are involved in analyzing this problem. So if anyone with experience in evolution, search or algorithms, social systems, information theory, computation, neural networks, Boolean networks, etc. would like to work on this problem with me it would be great. Also let me know if you have any ideas or sugestion. [http://www.santafe.edu/events/workshops/index.php/Jose_Delgado jd]

==References==