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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)
/ name of department PAGE 916-09-09
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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