het tijdperk van complexiteit college fitness landscapes 14 november 2011 prof. dr. koen frenken...
TRANSCRIPT
Het tijdperk van complexiteit
College Fitness Landscapes
14 november 2011
Prof. Dr. Koen Frenken
School of Innovation Sciences
Topics of today
1. Problem-solving in complex technological artefacts
2. Problem-solving as analogous to Darwinian evolution: NK fitness landscapes
3. The power of decomposability: the example of the Wright brothers
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Readings
Frenken (2010) The NK-model as a model for technological evolution. Mimeo
Further reading: - H.A. Simon (1969) The Sciences of the Artificial (MIT Press)- Bradshaw, G., (1992) The airplane and the logic of invention. In
R.N. Giere (Ed.), Cognitive Models of Science. Minneapolis, MN: The University of Minnesota Press, pp. 239-250
- S.A. Kauffman (1993) Origins of Order (Oxford University Press)- K. Frenken (2006) Innovation, Evolution and Complexity Theory
(Cheltenham: Edward Elgar)
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The problem of design
• Design starts from a list of functional requirements that the artefact needs to have
• The requirements are not ‘natural’ but normative: these are decided by human beings with some purpose in mind
• Given the requirements, the designer looks for a solution that meets these functional requirements
• The main problem for the designer is not to find the optimal solution, because it takes too much time due to combinatorial complexity. The main problem is to a good solution relatively quickly
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Design space
• Think of an artefact as a system containing elements• Let N stand for the number of elements in the system, indexed
by n = 1,2,…,N
• Let An stand for the number of design variants (“alleles”) for each element
• The number of possible artefacts is called the design space and is given by all possible combinations between the design options of elements:
• For example, if each element comes in two variants (0 and 1), we have a binary design space with size 2N
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Fitness landscapes
• A fitness landscape specifies the fitness of each possible artefact in the design space
• The fitness of an artefact can be derived by the mean of the N fitness values
• The fitness of an artefact thus measures how well each element functioned on average
• One can then distinguish between systems with varying degrees of complexity as reflected in K, where K stands for the number of interdependencies in a system
• Hence, the NK-model
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NK fitness landscapes (N=3,K=0)
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NK fitness landscapes (N=3,K=2)
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NK fitness landscapes (N=3,K=1)
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Properties of NK fitness landscapes
• Search as trial-and-error a.k.a. “hill-climbing”
• Local search and the analogy with Darwinian evolution
• Local optima
• Basins of attraction
• Search distance
• Exhaustive search
• Imitation
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The power of decomposability
• In a non-decomposable system, the global optimum can be found only by exhaustive search, which requires as many trials as there exist designs
• In a decomposable system, the global optimum can be found by exhaustive search of each subsystem, which requires much less trials
• The time required to find the global optimum is bounded by the size of the largest subsystem, called the cover size
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Example of a decomposable system (N=4, K=1)
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Fintess landscape of a decomposable system (N=4, K=1)
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The example of the Wright Brothers
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The example of the Wright Brothers
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The example of the Wright Brothers
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