The paper presents an approach to the numerical investigation of the problems of finding a global optimum of multiextremal functions, based on the use of bioinspired and local search methods. Three combined non-convex optimization algorithms are proposed and implemented. As globalized bioinspired methods, differential evolution, harmony search, and firefly methods are used. For local descents, we used the L-BFGS method. The numerical study of modifications of the implemented approach has been carried out using known non-convex test functions. The developed algorithms have been applied to investigate the problem of the optimal orientation of the aircraft in space. The obtained numerical results allowed us to demonstrate the efficiency of the proposed algorithms.

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The article offers a possible treatment for the numerical research of tasks which require searching for an absolute optimum. This approach is established by employing both globalized nature-inspired methods as well as local descent methods for exploration and exploitation. Three hybrid nonconvex minimization algorithms are developed and implemented. Modifications of flower pollination, teacher-learner, and firefly algorithms are used as nature-inspired methods for global searching. The modified trust region method based on the main diagonal approximation of the Hessian matrix is applied for local refinement. We have performed the numerical comparison of variants of the realized approach employing a representative collection of multimodal objective functions. The implemented nonconvex optimization methods have been used to solve the applied problems. These tasks utilize an optimization of the low-energy metal Sutton-Chen clusters potentials with a very large number of atoms and the parametric identification of the nonlinear dynamic model. The results of this research confirms the performance of the suggested algorithms.

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Аннотация. В статье рассматривается разработанный авторами пакет программ (ПП) MEOPT для численного исследования невыпуклых задач параметрической идентификации динамических моделей. В состав программного обеспечения входят библиотеки алгоритмов оптимизации и тестовых задач, инструментальные и сервисные модули, метакомпоненты. Реализованные библиотеки оптимизационных алгоритмов включают методы многомерной и одномерной невыпуклой оптимизации. Программное обеспечение создано на языке Си с применением компилятора GCC, поддерживает работу в операционных системах Windows, Linux и MacOS. На сегодняшний день завершены прототипы основных модулей ПП. Выполнено техническое тестирование первой версии программного обеспечения.