Трансмерная гибридизация эволюционных алгоритмов многокритериальной оптимизации управления

Abstract

The paper presents a hybrid evolutionary algorithm for multicriteria synthesis of the optimal control law for a dynamic system based on the trans-dimensional search models. The developed trans-dimensional search model belongs to the class of sequential hybridization models of the preprocessor/processor type and implies the combined use of the evolutionary algorithms of finite-dimensional and infinite-dimensional multi-objective optimization implementing the stages of global approximate and local refinement search for the optimal solutions. A finite-dimensional model of the global multi-criteria optimization is implemented using an evolutionary algorithm of the multi-criteria optimization in regard to the polyhedral dominance cone. Introduction of the uncertainty intervals of the vector indicator components weight coefficients in constructing the dominance polyhedral cone makes it possible to reduce the Pareto set uncertainty by highlighting a subset of solutions in it that are having a higher degree of balancing values for various components of the efficiency vector indicator. Evolutionary algorithm of the infinite-dimensional multi-objective optimization is a generalization of the Zoytendijk’s methods of possible directions for the class of infinite-dimensional multi-objective optimization problems and is used at the search stage. The paper provides results of a comparative analysis of various hybrid trans-dimensional models efficiency in the evolutionary search on the example of solving the problem of multicriteria synthesis of the optimal law for a bioreactor program control. Results of the computational experiments show that trans-dimensional hybridization of the evolutionary algorithms for the finite-dimensional and infinite-dimensional multicriteria control optimization provides a synergistic effect. This effect is expressed in significant increase in the accuracy of solving the problem of multicriteria control optimization in comparison with the known hybrid metaheuristic control optimization algorithms making it possible to resolve contradiction between the finite-dimensional global search model and the infinite-dimensional initial problem formulation