Physical aspects of evolutionary optimization and adaptation

A model of an objective function based on polynucleotide folding is used to investigate the dynamics of evolutionary adaptation in finite populations. Binary sequences are optimized with respect to their kinetic properties through a stochastic process involving mutation and selection. The objective function consists in a mapping from the set of all binary strings with given length into a set of two-dimensional structures. These structures then encode the kinetic properties, expressed in terms of parameters of reaction probability distributions. The objective function obtained thereby represents a realistic example of a highly ``rugged landscape.'' Ensembles of molecular strings adapting to this landscape are studied by tracing their escape path from local optima and by applying multivariate analysis. Effects of small population numbers in the tail of the sequence distribution are discussed quantitatively. Close upper bounds to the number of distinct values produced by our objective function are given. The distribution of values is explored by means of simulated annealing and reveals a random scatter in the locations of optima in the space of all sequences. The genetic optimization protocol is applied to the ``traveling salesman'' problem.