![Page 1: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/1.jpg)
Het tijdperk van complexiteit
College Fitness Landscapes
14 november 2011
Prof. Dr. Koen Frenken
School of Innovation Sciences
![Page 2: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/2.jpg)
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
PAGE 230/09/09
![Page 3: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/3.jpg)
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)
PAGE 330/09/09
![Page 4: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/4.jpg)
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
PAGE 430/09/09
![Page 5: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/5.jpg)
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
PAGE 516-09-09
![Page 6: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/6.jpg)
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
PAGE 630/09/09
![Page 7: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/7.jpg)
NK fitness landscapes (N=3,K=0)
PAGE 716-09-09
![Page 8: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/8.jpg)
NK fitness landscapes (N=3,K=2)
PAGE 816-09-09
![Page 9: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/9.jpg)
NK fitness landscapes (N=3,K=1)
/ name of department PAGE 916-09-09
![Page 10: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/10.jpg)
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
PAGE 1030/09/09
![Page 11: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/11.jpg)
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
PAGE 1130/09/09
![Page 12: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/12.jpg)
Example of a decomposable system (N=4, K=1)
PAGE 1230/09/09
![Page 13: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/13.jpg)
Fintess landscape of a decomposable system (N=4, K=1)
PAGE 1330/09/09
![Page 14: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/14.jpg)
The example of the Wright Brothers
PAGE 14
![Page 15: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/15.jpg)
The example of the Wright Brothers
PAGE 15
![Page 16: Het tijdperk van complexiteit College Fitness Landscapes 14 november 2011 Prof. Dr. Koen Frenken School of Innovation Sciences](https://reader035.vdocuments.mx/reader035/viewer/2022062517/56649f085503460f94c1d4bc/html5/thumbnails/16.jpg)
The example of the Wright Brothers
PAGE 16