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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