The Evolutionary Unfolding of Complexity

We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current ``landscape'' models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher fitness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity.Comment: 28 pages, 5 figure

Self adaptation in evolutionary algorithms

Evolutionary Algorithms are search algorithms based on the Darwinian metaphor of “Natural Selection”. Typically these algorithms maintain a population of individual solutions, each of which has a fitness attached to it, which in some way reflects the quality of the solution. The searchproceeds via the iterative generation, evaluation and possible incorporation of new individuals based on the current population, using a number of parameterisedgenetic operators. In this thesis the phenomenon of Self Adaptation of the genetic operators is investigated.A new framework for classifying adaptive algorithms is proposed, based on the scope of the adaptation, and on the nature of the transition function guiding the search through the space of possible configurations of the algorithm. Mechanisms are investigated for achieving the self adaptation of recombination and mutation operators within a genetic algorithm, and means of combining them are investigated. These are shown to produce significantly better results than any of the combinations of fixed operators tested, across a range of problem types. These new operators reduce the need for the designer of an algorithm to select appropriate choices of operators and parameters, thus aiding the implementation of geneticalgorithms. The nature of the evolving search strategies are investigated and explained in terms of the known properties of the landscapes used, and it is suggested how observations of evolving strategies on unknown landscapes may be used to categorise them, and guide further changes in other facets of the genetic algorithm.This work provides a contribution towards the study of adaptation in Evolutionary Algorithms, and towards the design of robust search algorithms for “real world” problems

Deceptiveness and Neutrality - the ND family of fitness landscapes

When a considerable number of mutations have no effects on fitness values, the fitness landscape is said neutral. In order to study the interplay between neutrality, which exists in many real-world applications, and performances of metaheuristics, it is useful to design landscapes which make it possible to tune precisely neutral degree distribution. Even though many neutral landscape models have already been designed, none of them are general enough to create landscapes with specific neutral degree distributions. We propose three steps to design such landscapes: first using an algorithm we construct a landscape whose distribution roughly fits the target one, then we use a simulated annealing heuristic to bring closer the two distributions and finally we affect fitness values to each neutral network. Then using this new family of fitness landscapes we are able to highlight the interplay between deceptiveness and neutrality.Comment: Genetic And Evolutionary Computation Conference, Seatle : \'Etats-Unis d'Am\'erique (2006

Separating what is evaluated from what is selected in artificial evolution

In artificial evolution, selection and evaluation are separate and distinct steps. This distinction is rather different in natural evolution, where fitness (corresponding to evaluation) is a direct consequence of selection rather than a precursor to it. This thesis presents a new way of thinking about artificial evolution that separates evaluation and selection and consequently opens up the space of potential evolutionary algorithms beyond the limitations imposed by ignoring this distinction. In Part I of the thesis we explore how varying the level of evaluation and selection impacts evolution. Using novel genetic algorithms (GAs) we show how group level evaluation allows evolution to find solutions to problems that require niching or a division of labour amongst component parts, something that cannot be accomplished using a standard GA. One of the inspirations for testing GAs with group-level evaluation was recent research into bacterial evolution which shows in bacterial colonies, distinguishing between the individual and group is very difficult because of the symbiotic relationship between different bacteria. We find that depending on the task it sometimes makes sense to select the individual while in other cases simply selecting groups is the best choice. Finally, we present a method for evolving the group size in these types of GAs that has the benefit of avoiding the need to know the optimal division of labour ahead of time. In Part II we move away from studying the relationship between evaluation and selection to show how our novel view of evolution can be used to develop GAs that implement horizontal gene transfer which was again inspired by looking at bacterial evolution. By testing these GAs on a variety of different tasks we show how this promiscuous gene swapping is often beneficial to evolution because it can reduce the probability of the population getting stuck on a sub-optimal solution. The thesis demonstrates the benefits of of looking at artificial evolution in terms of both evaluation and selection when it comes to algorithm development, and thus provides the GA community with a new context in which they can choose different algorithms appropriate to different tasks

Simon-Ando decomposability and fitness landscapes

In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems

Adaptive scaling of evolvable systems

Neo-Darwinian evolution is an established natural inspiration for computational optimisation with a diverse range of forms. A particular feature of models such as Genetic Algorithms (GA) [18, 12] is the incremental combination of partial solutions distributed within a population of solutions. This mechanism in principle allows certain problems to be solved which would not be amenable to a simple local search. Such problems require these partial solutions, generally known as building-blocks, to be handled without disruption. The traditional means for this is a combination of a suitable chromosome ordering with a sympathetic recombination operator. More advanced algorithms attempt to adapt to accommodate these dependencies during the search. The recent approach of Estimation of Distribution Algorithms (EDA) aims to directly infer a probabilistic model of a promising population distribution from a sample of fitter solutions [23]. This model is then sampled to generate a new solution set. A symbiotic view of evolution is behind the recent development of the Compositional Search Evolutionary Algorithms (CSEA) [49, 19, 8] which build up an incremental model of variable dependencies conditional on a series of tests. Building-blocks are retained as explicit genetic structures and conditionally joined to form higher-order structures. These have been shown to be effective on special classes of hierarchical problems but are unproven on less tightly-structured problems. We propose that there exists a simple yet powerful combination of the above approaches: the persistent, adapting dependency model of a compositional pool with the expressive and compact variable weighting of probabilistic models. We review and deconstruct some of the key methods above for the purpose of determining their individual drawbacks and their common principles. By this reasoned approach we aim to arrive at a unifying framework that can adaptively scale to span a range of problem structure classes. This is implemented in a novel algorithm called the Transitional Evolutionary Algorithm (TEA). This is empirically validated in an incremental manner, verifying the various facets of the TEA and comparing it with related algorithms for an increasingly structured series of benchmark problems. This prompts some refinements to result in a simple and general algorithm that is nevertheless competitive with state-of-the-art methods