Модификация алгоритма роя частиц на основе метода анализа иерархий

Станислав Анатольевич Королев; Дмитрий Владимирович Майков

doi:10.17308/sait.2019.4/2679

Authors

Stanislav Anatolevich Korolev Izhevsk State Technical University
Dmitriy Vladimirovich Maikov Izhevsk Trade and Economic College

DOI:

https://doi.org/10.17308/sait.2019.4/2679

Keywords:

optimization problem, particle swarm optimization algorithm, genetic algorithm, analytic hierarchy process, leader training, conjugate gradient method, embedment hybridization, sequential hybridization, coalgorithmic hybridization

Abstract

There are problems of mathematical modeling, the solution of which necessitates finding the maximum or minimum point of some function of many variables. For example, this is training artificial neural networks, identifying the parameters of mathematical models from experimental data, and finding the optimal control for these models. To quickly find the extremum point, a lot of population optimization algorithms have been developed (particle swarm optimization (PSO), genetic algorithm and others). A modification of the particle swarm optimization algorithm based on the hierarchy analysis method is proposed. The scheme of the developed algorithm is inspired by the behavior of freshwater hydras; therefore, the authors propose to call it the H-algorithm. Successive and parallel (co-algorithmic) hybridization of the developed algorithm with the genetic algorithm using real coding (RGA) is performed. For the considered algorithms, a high-level hybridization by embedding is implemented, in which a local search is carried out in the vicinity of an agent with the best value of the objective function using the conjugate gradient method (leader training). Comparison of the effectiveness of the considered methods was per-formed on the example of various multi-extreme test functions (the function of Rosenbrock, Davis, Ackley, Rastrigin). PSO, RGA and H-algorithm for different test functions showed different, but on average the same convergence rate. Leader training significantly increased the convergence rate of all algorithms. The best results in convergence rate were shown by parallel and serial hybridization of the RGA and the H-algorithm.

Author Biographies

Stanislav Anatolevich Korolev, Izhevsk State Technical University

Candidate of Physics and Mathematics, Associate Professor, Department of Software for Information Systems, Kalashnikov Izhevsk State Technical
Dmitriy Vladimirovich Maikov, Izhevsk Trade and Economic College

mathematics teacher, Izhevsk Trade and Economic College

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