Hierarchical Crossover and Probability Landscapes of Genetic Operators

The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point crossover operations. This model is solved analytically in the flat fitness case. Numerical simulations compare the way of phase space exploration of different genetic operators. In the case of a non-flat fitness landscape, numerical solutions of the evolution equations point out ways to estimate premature convergence.Comment: 11 pages, uuencoded postcript fil

Genetic Programming in Control Theory: On Evolving Programs and Solutions to Control Problems

More often than not one would encounter a problem, know that the solution has to meet some requirements, but do not how to start or how to progress towards solving it. Motivation for a computer that can solve the problem automatically without explicitly programming it is apparent, i.e. a computer that \programs itself", is greatly desired. The method of genetic programming has demonstrated its potential by evolving programs for a wide range of applications. Examples are target identi_cation [Tackett, 1993], performing optical character recognition [Andre, 1994], electronic circuit design [Koza, 1996] among many. In certain areas, GP generated designs or solutions were shown to be on par or even better than those created by human; although this is of course, not always the case. However, the power of GP is inherent that it is possible to use all tools and functions of computer programming that have ever been devised since it is evolving programs from programs themselves. This thesis applies this method to the area of control engineering. Applying genetic algorithm to this field is not new, however, but using genetic programming is relatively recent. The intention is therefore clear, to introduce another set of tools, perhaps quite unconventional but hopefully useful, to the control engineer. All the solutions presented in this thesis have been implemented using the program Matlab. Although the mathematical functions that have been used are limited and often no more than simple additions or multiplication, it should be clear that a whole arsenal of Matlab functions could be used as part of GP, depending on how the programmer formulate his/her problem. Hence besides having the basic program code to be re-usable for di_erent problems, care has been taken to allow user to be able to add additional functions easily. Designing a GP run would then consist of simply selecting or writing functions, and setting up a suitable evaluation and termination criteria. Problem solving should be automatic. Perhaps one might think that the solutions presented here are trivial, and the program might not work for other more diÆcult problems, or it may end up in a combinational explosion. This should however not to be seen as a poor re ection on the method, but rather may simply be due to bad programming practice. Therefore having said that, it should also be mentioned that there is more than enough room for improvements to the basic progra

04081 Abstracts Collection -- Theory of Evolutionary Algorithms

From 15.02.04 to 20.02.04, the Dagstuhl Seminar 04081 ``Theory of Evolutionary Algorithms\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Exploring Evolutionary Economic Geographies

Evolutionary approaches in economics have gathered increasing support over the last 25 years. Despite an impressive body of literature, economists are still far from formulating a coherent research paradigm. The multitude of approaches in evolutionary economics poses problems for the development of an evolutionary economic geography. For the most part, evolutionary economic geography imports selective concepts from evolutionary biology and economics and applies those concepts to specific problems within economic geography. We discuss a number of problems with this approach and suggest that a more powerful and appealing alternative requires the development of theoretically consistent models of evolutionary processes. This paper outlines the contours of an evolutionary model of economic dynamics where economic agents are located in different geographical spaces. We seek to show how competition between those agents, based on the core evolutionary principles of variety, selection and retention, may produce distinct economic regions sharing properties that differentiate them from competitors elsewhere. These arguments are extended to illustrate how the emergent properties of economic agents and places co-evolve and lead to different trajectories of economic development over space.evolutionary economics, economic geography, Generalized Darwinism, biological metaphors, self-organization

Adaptive evolution in static and dynamic environments

This thesis provides a framework for describing a canonical evolutionary system. Populations of individuals are envisaged as traversing a search space structured by genetic and developmental operators under the influence of selection. Selection acts on individuals' phenotypic expressions, guiding the population over an evaluation landscape, which describes an idealised evaluation surface over the phenotypic space. The corresponding valuation landscape describes evaluations over the genotypic space and may be transformed by within generation adaptive (learning) or maladaptive (fault induction) local search. Populations subjected to particular genetic and selection operators are claimed to evolve towards a region of the valuation landscape with a characteristic local ruggedness, as given by the runtime operator correlation coefficient. This corresponds to the view of evolution discovering an evolutionarily stable population, or quasi-species, held in a state of dynamic equilibrium by the operator set and evaluation function. This is demonstrated by genetic algorithm experiments using the NK landscapes and a novel, evolvable evaluation function, The Tower of Babel. In fluctuating environments of varying temporal ruggedness, different operator sets are correspondingly more or less adapted. Quantitative genetics analyses of populations in sinusoidally fluctuating conditions are shown to describe certain well known electronic filters. This observation suggests the notion of Evolutionary Signal Processing. Genetic algorithm experiments in which a population tracks a sinusoidally fluctuating optimum support this view. Using a self-adaptive mutation rate, it is possible to tune the evolutionary filter to the environmental frequency. For a time varying frequency, the mutation rate reacts accordingly. With local search, the valuation landscape is transformed through temporal smoothing. By coevolving modifier genes for individual learning and the rate at which the benefits may be directly transmitted to the next generation, the relative adaptedness of individual learning and cultural inheritance according to the rate of environmental change is demonstrated

Aggregation of variables and system decomposition: Applications to fitness landscape analysis

In this paper we present general results on aggregation of variables, specifically as it applies to decomposable (partitionable) dynamical systems. We show that a particular class of transition matrices, namely, those satisfying an equitable partitioning property, are aggregable under appropriate decomposition operators. It is also shown that equitable partitions have a natural application to the description of mutation-selection matrices (fitness landscapes) when their fitness functions have certain symmetries concordant with the neighborhood relationships in the underlying configuration space. We propose that the aggregate variable descriptions of mutation-selection systems offer a potential formal definition of units of selection and evolution