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 30/09/09 PAGE 1 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) 30/09/09 PAGE 2 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 30/09/09 PAGE 3 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 16-09-09 PAGE 4 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 30/09/09 PAGE 5 NK fitness landscapes (N=3,K=0) 16-09-09 PAGE 6 NK fitness landscapes (N=3,K=2) 16-09-09 PAGE 7 NK fitness landscapes (N=3,K=1) / name of department 16-09-09 PAGE 8 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 30/09/09 PAGE 9 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 30/09/09 PAGE 10 Example of a decomposable system (N=4, K=1) 30/09/09 PAGE 11 Fintess landscape of a decomposable system (N=4, K=1) 30/09/09 PAGE 12 The example of the Wright Brothers PAGE 13 The example of the Wright Brothers PAGE 14 The example of the Wright Brothers PAGE 15

Download
# NK fitness landscapes