Summary. The issue of setting the values of various parameters of an evolutionary algorithm is crucial for good performance. In this paper we discuss how to do this, beginning with the issue of whether these values are best set in advance or are best changed during evolution. We provide a classification of different approaches based on a number of complementary features, and pay special attention to setting parameters on-the-fly. This has the potential of adjusting the algorithm to the problem while solving the problem. This paper is intended to present a survey rather than a set of prescriptive details for implementing an EA for a particular type of problem. For this reason we have chosen to interleave a number of examples throughout the text. Thus we hope to both clarify the points we wish to raise as we present them, and also to give the reader a feel for some of the many possibilities available for controlling different parameters. 1

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The optimization of a single bit string by means of iterated mutation and selection of the best (a (1+1)-Genetic Algorithm) is discussed with respect to three simple tness functions: The counting ones problem, a standard binary encoded integer, and a Gray coded integer optimization problem. A mutation rate schedule that is optimal with respect to the success probabilityofmutation is presented for each of the objective functions, and it turns out that the standard binary code can hamper the search process even in case of unimodal objective functions. While normally a mutation rate of 1=l (where l denotes the bit string length) is recommendable, our results indicate that a variation of the mutation rate is useful in cases where the tness function is a multimodal pseudoboolean function, where multimodality may be caused by the objective function as well as the encoding mechanism.

This paper will look at an evolutionary approach to robotics; partly at pragmatic issues, but primarily at theoretical issues associated with the evolutionary algorithms which are appropriate. Genetic Algorithms are not suitable in their usual form for the evolution of cognitive structures, which must be in an incremental fashion. SAGA -- Species Adaptation Genetic Algorithms -- is a conceptual framework for extending GAs to variable length genotypes, where evolution allows a species of individuals to evolve from simple to more complex. In the context of species evolution the metaphor of hill-crawling as opposed to hill-climbing is introduced,

This paper proposes using fuzzy logic techniques to dynamically control parameter settings of genetic algorithms (GAs). We describe the Dynamic Parametric GA: a GA that uses a fuzzy knowledge-based system to control GA parameters. We then introduce a technique for automatically designing and tuning the fuzzy knowledgebase system using GAs. Results from initial experiments show a performance improvement over a simple static GA. One Dynamic Parametric GA system designed by our automatic method demonstrated improvement on an application not included in the design phase, which may indicate the general applicabilityof the Dynamic Parametric GA to a wide range of applications.

Abstract � Adaptation of parameters and operators is one of the most important and promising areas of research in evolutionary computation � it tunes the algorithm to the problem while solving the problem. In this paper we develop a classi�cation of adaptation on the basis of the mechanisms used � and the level at which adaptation operates within the evolutionary algorithm. The classi�cation covers all forms of adaptation in evolutionary computation and suggests fur� ther research. I.

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. Exploration and exploitation are the two cornerstones of problem solving by search. The common opinion about evolutionary algorithms is that they explore the search space by the (genetic) search operators, while exploitation is done by selection. This opinion is, however, questionable. In this paper we give a survey of different operators, review existing viewpoints on exploration and exploitation, and point out some discrepancies between and problems with current views. 1. Introduction Evolutionary algorithms (EA) belong to the family of stochastic generate-and-test search algorithms [28]. There are different types of EAs, the most common classification distinguishes Genetic Algorithms (GA), Evolution Strategies (ES) and Evolutionary Programming (EP), [4]. A fourth type of EA, Genetic Programming (GP) has grown out of GAs and is often seen as a sub-class of them. Besides the different historical roots and philosophy there are also technical differences between the three mai...

This paper introduces the notions of `quasi-species' and `error threshold' from molecular evolutionary biology. The error threshold is a critical mutation rate beyond which the effect of selection on the population changes drastically. We reproduce, using GAs --- and hence finite populations --- some interesting results obtained with an analytical model --- using infinite populations --- from the evolutionary biology literature. A reformulation of a previous analytical expression , which explicitly indicates the extent of the reduction in the error threshold as we move from infinite to finite populations, is derived. Error thresholds are shown to be lower for finite populations. Moreover, as in the infinite case, for low mutation rates recombination can reduce the diversity of the population and enhance overall fitness. For high mutation rates, however, recombination can push the population over the error threshold, and thereby cause a loss of genetic information. These results may be ...

. The error threshold --- a notion from molecular evolution --- is the critical mutation rate beyond which structures obtained by the evolutionary process are destroyed more frequently than selection can reproduce them. We argue that this notion is closely related to the more familiar notion of optimal mutation rates in Evolutionary Algorithms (EAs). This correspondence has been intuitively perceived before ([9], [11]). However, no previous study, to our knowledge, has been aimed at explicitly testing the hypothesis of such a relationship. Here we propose a methodology for doing so. Results on a restricted range of fitness landscapes suggest that these two notions are indeed correlated. There is not, however, a critically precise optimal mutation rate but rather a range of values producing similar near-optimal performance. When recombination is used, both error thresholds and optimal mutation ranges are lower than in the asexual case. This knowledge may have both theoretical relevance ...