Max-Planck-Institut für Physik komplexer
Systeme
International Workshop on
Biological Evolution and Statistical
Physics
May 10-14, 2000
The Structure of Fitness Landscapes
Peter F. Stadler
Institute for Theoretical
Chemistry and Structural Biology
Währingerstr. 17, A-1090 Vienna
studla@tbi.univie.ac.at
Landscapes are an important concept in molecular evolution,
the physics of disordered systems, and combinatorial optimization. We understand
a landscape as a real-valued function of a usually very large set of configurations:
RNA sequences, spin configurations, or Travelling Salesman tours, together
with a notion of ``nearness'' among configurations, which is derived e.g.
from the genetic operators or search rules.
In order to understand the qualitative differences between relatively
simple spin glasses or combinatorial optimization problems and realistic
biological fitness landscape models, aggregate measures of ruggedness and
neutrality are considered. Ruggedness, sometimes measured in terms of local
optima or adaptive walks, is most easily quantified by means of correlation
functions. Neutrality, albeit seemingly just the absence of ruggedness,
turns out to be an independent property of landscapes.
A Fourier transform-like formalism can be used to extract global information
on a landscape and to compare different cost functions on the same configuration
space or the same cost function as seen by different search operators.
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