Abstract
The study of complex adaptive systems is among the key modern tasks in science. Such systems show radically different behaviours at different scales and in different environments, and mathematical modelling of such emergent behaviour is very difficult, even at the conceptual level. We require a new methodology to study and understand complex, emergent macroscopic phenomena. Coarse graining, a technique that originated in statistical physics, involves taking a system with many microscopic degrees of freedom and finding an appropriate subset of collective variables that offer a compact, computationally feasible description of the system, in terms of which the dynamics looks “natural”. This paper presents the key ideas of the approach and shows how it can be applied to evolutionary dynamics.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-642-37577-4_18
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- 1.
In OneMax, fitness is the number of 1s in a bit string and the objective is to maximise that number.
- 2.
Naturally, we would like to have an explicit form for λ(y, z, n, x). It exists, but for now we will not look at it.
- 3.
As a result, we cannot use the multinomial distribution to predict the future over multiple generations.
- 4.
This is Michael Vose’s model for a genetic algorithm [2].
- 5.
For ℓ = 2 there is only one valid crossover point (n = 1).
- 6.
Note that \(\alpha (s_{1}s_{2}\cdots s_{\ell})\) becomes particularly simple when all s i = ∗ except one. In that case it is easy to verify that \(\alpha (s_{1}s_{2}\cdots s_{\ell}) = p(s_{1}s_{2}\cdots s_{\ell})\).
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Poli, R., Stephens, C.R. (2014). Taming the Complexity of Natural and Artificial Evolutionary Dynamics. In: Cagnoni, S., Mirolli, M., Villani, M. (eds) Evolution, Complexity and Artificial Life. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37577-4_2
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DOI: https://doi.org/10.1007/978-3-642-37577-4_2
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