46 research outputs found

    Markov chain models of genetic algorithms

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    Using Markov chain model to compare a steady-state and a generational GA

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    Logic-based machine learning using a bounded hypothesis space: the lattice structure, refinement operators and a genetic algorithm approach

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    Rich representation inherited from computational logic makes logic-based machine learning a competent method for application domains involving relational background knowledge and structured data. There is however a trade-off between the expressive power of the representation and the computational costs. Inductive Logic Programming (ILP) systems employ different kind of biases and heuristics to cope with the complexity of the search, which otherwise is intractable. Searching the hypothesis space bounded below by a bottom clause is the basis of several state-of-the-art ILP systems (e.g. Progol and Aleph). However, the structure of the search space and the properties of the refinement operators for theses systems have not been previously characterised. The contributions of this thesis can be summarised as follows: (i) characterising the properties, structure and morphisms of bounded subsumption lattice (ii) analysis of bounded refinement operators and stochastic refinement and (iii) implementation and empirical evaluation of stochastic search algorithms and in particular a Genetic Algorithm (GA) approach for bounded subsumption. In this thesis we introduce the concept of bounded subsumption and study the lattice and cover structure of bounded subsumption. We show the morphisms between the lattice of bounded subsumption, an atomic lattice and the lattice of partitions. We also show that ideal refinement operators exist for bounded subsumption and that, by contrast with general subsumption, efficient least and minimal generalisation operators can be designed for bounded subsumption. In this thesis we also show how refinement operators can be adapted for a stochastic search and give an analysis of refinement operators within the framework of stochastic refinement search. We also discuss genetic search for learning first-order clauses and describe a framework for genetic and stochastic refinement search for bounded subsumption. on. Finally, ILP algorithms and implementations which are based on this framework are described and evaluated.Open Acces

    Group Properties of Crossover and Mutation

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    It is supposed that the finite search space Ω has certain symmetries that can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries, then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of Ω are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on Ω to induce a group structure on Ω itself

    State Aggregation and Population Dynamics in Linear Systems

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    We consider complex systems that are composed of many interacting elements, evolving under some dynamics. We are interested in characterizing the ways in which these elements may be grouped into higher-level, macroscopic states in a way that is compatible with those dynamics. Such groupings may then be thought of as naturally emergent properties of the system. We formalize this idea and, in the case that the dynamics are linear, prove necessary and sufficient conditions for this to happen. In cases where there is an underlying symmetry among the components of the system, group theory may be used to provide a strong sufficient condition. These observations are illustrated with some artificial life examples

    Efficient Simulation Of A Simple Evolutionary System

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    An infinite population model is considered for diploid evolution under the influence of crossing over and mutation. The evolution equations show how Vose’s haploid model for Genetic Algorithms extends to the diploid case, thereby making feasible simulations which otherwise would require excessive resources. This is illustrated through computations confirming the convergence of finite diploid population short-term behaviour to the behaviour predicted by the infinite diploid model. The results show the distance between finite and infinite population evolutionary trajectories can decrease in practice like the reciprocal of the square root of population size. Under necessary and sufficient conditions (NS) concerning mutation and crossover, infinite populations show oscillating behavior. We explore whether finite populations can also exhibit oscillation or approximate oscillation. Simulation results confirm that approximate finite population oscillation is possible when NS are satisfied. We also investigate the robustness of finite population oscillation. We show that when the part of NS concerning mutation is violated, the Markov chain which models finite population evolution is regular, and perfect oscillation should not occur. However, our simulation results show finite population approximate oscillation can occur even though the Markov chain is regular. Finite populations can also exhibit approximate oscillating behavior when the part of NS concerning crossover is violated
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