Convergence Mechanism Of Differential Evolution Algorithm And Its Application In Data Processing

Convergence theory of differential evolution(DE)is one of the important topics in the study of evolutionary algorithms.There are usually two forms on geometry:the building block principle of population individuals or the principle of population evolution in discrete space and continuous space.Based on previous studies,this thesis studies the convergence theory of the DE algorithm,the topology structure of the DE algorithm in the search space,and the quantum properties of individual populations.This thesis also studies the application of the improved DE algorithm in data processing.The specific research content is as follows:1.This thesis studies the schema sets theorem of individuals in real space about the DE algorithm.That is,let C be the generalized complete space in R,the population feature function f?(Xi)is continuous in the generalized complete space,the iterative form of the differential equation under the condition of a perturbed variable(P-?)is uniformly con-vergent.Then there are the following theorem by the real(or integer)coding of individual populations,under the action of selection,crossover and mutation operators of DE algo-rithm,the survival number of the schema setting with lower schema setting order,shorter schema setting distance and higher fitness function value shows an increasing convergence trend with the increase of population iteration number.2.This thesis explores the convergence of the DE algorithm in the Hilbert space with the parameter ? and the quantum properties of the iteration points,establishes a control con-vergence iteration scheme for higher-order differential under the condition of P-varepsilon,analyzes the three topologies that the DE algorithm contains in Hilbert space:single-point topology heterogeneity structure,branch topology heterogeneity structure,and dis-crete topology heterogeneity structure,illustrates the correlation between the uncertainty of quantum properties and topological heterogeneity of the Heisenberg uncertainty of the DE algorithm in the ?-Hilbert space on geometry.The speed resolution ?v2 of the iterative sequence convergent speed and the position resolution ?x?? of the global optimal point with the swinging range are a pair of conjugate variables of the quantum states in ?-Hilbert s-pace about eigenvalues ?i?R,corresponding to the uncertainty characteristics on quantum states,and they cannot simultaneously achieve bidirectional efficiency between convergent speed and the best point precision with any procedural improvements.3.Based on the normalization of internal and external penalty functions,this thesis estab-lishes screening criteria for mixed penalty functions,establishes a differential evolutionary integration algorithm based on mixed penalty function screening criteria,which broadens the algorithm base for efficient integration of imbalanced data,constructs a Markov process for a differential evolution ensemble algorithm based on mixed penalty function selection crite-ria,and proves the theoretical validity and evolutionary mechanism of the algorithm.After an empirical analysis of UCI machine learning data,this thesis further illustrates the effec-tiveness of the algorithm in the efficient integration and classification of imbalanced data.It provides useful ideas for studying the efficient integration of multi-modal imbalanced data.