Thilo Mahnig’s research while affiliated with Fraunhofer Institute Centre Schloss Birlinghoven and other places

Evolvable hardware represents an emerging field in which evolutionary design has recently produced promising results. However, the choice of effective circuit representation is inexplicit. In this paper, we compare different circuit representations for evolutionary analog circuit design. The results indicate that the design quality is better for the element-list circuit representation.

The paper represents the approach to evolutionary analogue circuit design on the base of the univariate marginal distribution algorithm. In order to generate a new population the probability distribution is used instead of reproduction operators. It allows us to control evolvability of a population on mesoscopic level. Experimental results obtained have indicated that a high mutation rate increases the success rate, although computational costs are increased too. The effective mutation rate that supplies high success rate and small computational costs is examined for different weightings of the fitness function.

For discrete optimization, the two basic search principles prevailing are stochastic local search and population based search. Local search has difficulties to get out of local optima. Here variable neighborhood search outperforms stochastic local search methods which accept worse points with a certain probability. Population based search performs best on problems with sharp gaps. It is outperformed by stochastic local search only when there are many paths to good local optima

This paper represents the following improvement of evolutionary analog circuit design on the base of the univariate marginal distribution algorithm. Experiments have indicated that the high mutation rate increases the success rate, although the computational expenses are increased as well. An effective mutation rate is considered with respect to a high success rate and small computational expenses. Experiments for analog arrays are discussed.

The approach to computer aided analog circuit design on the base of univariate algorithms was derived by analysing the mathematical principles behind recombination. A Bayesian prior used for the estimations of the probability distribution is equivalent to having mutation for the genetic algorithms. In this paper the relation between a success rate and a mutation one is considered for analog circuit design. Practical illustration of the use of this approach is demonstrated for filter design. Experiments indicate that mutation and elitism increase the performance of the algorithms and decrease the dependence of the correct choice of the population size.

UMDA(the univariate marginal distribution algorithm) was derived by analyzing the mathematical principles behind recombination. Mutation, however, was not considered. The same is true for the FDA (factorized distribution algorithm), an extension of the UMDA which can cover dependencies between variables. In this paper mutation is introduced into these algorithms by a technique called Bayesian prior. We derive theoretically an estimate how to choose the Bayesian prior. The recommended Bayesian prior turns out to be a good choice in a number of experiments. These experiments also indicate that mutation increases in many cases the performance of the algorithms and decreases the dependence on a good choice of the population size.

FDA - the Factorized Distribution Algorithm - is an evolutionary algorithm that combines mutation and recombination by using a distribution. First the distribution is estimated from a set of selected points. It is then used to generate new points for the next generation. In general a distribution defined for n binary variables has 2 n parameters. Therefore it is too expensive to compute. For additively decomposed discrete functions (ADFs) there exists an algorithm that factors the distribution into conditional and marginal distributions, each of which can be computed in polynomial time. The scaling of FDA is investigated theoretically and numerically. The scaling depends on the ADF structure and the specific assignment of function values. Difficult functions on a chain or a tree structure are optimized in about O(n p n) function evaluations. More standard genetic algorithms are not able to optimize these functions. FDA is not restricted to exact factorizations. It also works for approximate factorizations. Keywords -- evolutionary algorithms, graphical models, factorization of distributions, Boltzmann selection 1

FDA (the Factorized Distribution Algorithm) is an evolutionary algorithm that combines mutation and recombination by using a distribution. The distribution is estimated from a set of selected points. It is then used to generate new points for the next generation. FDA uses a factorization to be able to compute the distribution in polynomial time. Previously, we have shown a convergence theorem for FDA . But it is only valid using Boltzmann selection. Boltzmann selection was not used in practice because a good annealing schedule was lacking. Using a Taylor expansion of the average fitness of the Boltzmann distribution, we have developed an adaptive annealing schedule called SDS . The inverse temperature is changed inversely proportional to the standard deviation. In this work, we compare the resulting scheme to truncation selection both theoretically and experimentally with a series of test functions. We find that it behaves similar in terms of complexity, robustness and efficiency. Keywords: genetic algorithms, Boltzmann distribution, Boltzmann selection, truncation selection 1