Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures

In this work, we propose a high-order algorithm based on the asymptotic numerical method (ANM) for the nonlinear elastic computation of helical structures without neglecting any nonlinear term. The nonlinearity considered in the following study will be a geometric type, and the kinematics adopted in this numerical modeling takes into account the hypotheses of Timoshenko and de Saint-Venant. The finite element used in the discretization of the middle line of this structure is curvilinear with twelve degrees of freedom. Using a simple example, we show the efficiency of the algorithm which was carried out in this context and which resides in the reduction of the number of inversions of the tangent matrix compared to the incremental iterative algorithm of Newton-Raphson.

New collocation path-following approach for the optimal shape parameter using Kernel method

The goal of this work is to develop a numerical method combining Radial Basic Functions (RBF) kernel and a high order algorithm based on Taylor series and homotopy continuation method. The local RBF approximation applied in strong form allows us to overcome the difficulties of numerical integration and to treat problems of large deformations. Furthermore, the high order algorithm enables to transform the nonlinear problem to a set of linear problems. Determining the optimal value of the shape parameter in RBF kernel is still an outstanding research topic. This optimal value depends on density and distribution of points and the considered problem for e.g. boundary value problems, integral equations, delay-differential equations etc. These have been extensively attempts in literature which end up choosing this optimal value by tests and error or some other ad-hoc means. Our contribution in this paper is to suggest a new strategy using radial basis functions kernel with an automatic reasonable choice of the shape parameter in the nonlinear case which depends on the accuracy and stability of the results. The computational experiments tested on some examples in structural analysis are performed and the comparison with respect to the state of art algorithms from the literature is given.