Modifications of Flower Pollination, Teacher-Learner and Firefly Algorithms for Solving Multiextremal Optimization Problems

Abstract

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.