Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and ob...

Differential Evolution (DE) is a powerful metaheuristic method used to numerically optimize functions or multidimensional problems not solved by traditional methods of global optimization. In turn, if boundary conditions are added, constraint handling techniques should be need. To improve DE’s performance, algorithms of local search are a good alternative. Hybridization of Differential Evolutio...

CODEQ is a new, population-based meta-heuristic algorithm that is a hybrid of concepts from chaotic search, opposition-based learning, differential evolution and quantum mechanics. CODEQ has successfully been used to solve different types of problems (e.g. constrained, integer-programming, engineering) with excellent results. In this paper, CODEQ is used to train feed-forward neural networks. T...

In this paper, a differential evolution (DE) algorithm combined with Lévy flight is proposed to solve the reliability redundancy allocation problems. The Lévy flight is incorporated to enhance the ability of global search of differential evolution algorithm. DE is used for local search mainly. The method considers the trade-off of the diversification and the intensification simultaneously. Expe...

The invariant subspace method is used to classify a class of systems of nonlinear dispersive evolution equations and determine their invariant subspaces and exact solutions. A crucial step is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that systems of evolution equations admit. A few examples of presenting exact solutions with generalized sepa...

The differential evolution algorithm for finding the global minimum of a possibly nonlinear and nondifferential continuous space function is discussed. Directory • Table of

In this paper, a novel method based on a combination of Extended Kalman Filter (EKF) with Self-adaptive Differential Evolution (SaDE) algorithm to estimate rotor position, speed and machine states for a Permanent Magnet Synchronous Motor (PMSM) is proposed. In the proposed method, as a first step SaDE algorithm is used to tune the noise covariance matrices of state noise and measurement noise i...

In this study, weight optimization of the prismatic core sandwich panel under transverse and longitudinal loadings has been independently investigated. To solve the optimization problems corresponding to the mentioned loadings, a new Improved Constrained Differential Evolution (ICDE) algorithm based on the multi-objective constraint handling method is implemented. The constraints of the problem...

reduced differential transform method (rdtm) is applied to various wave equations. to assessthe accuracy of the solutions, we compare the results with the exact solutions and variational iteration method.the results reveal that the rdtm is very effective, convenient and quite accurate to systems of nonlinearequations.

This paper describes a new method of evolution that is named Transplant Evolution (TE). None of the individuals of the transplant evolution contains genotype as in Grammatical Evolution (GE). Each individual of the transplant evolution contains the phenotype in the tree structure. Reproduction methods as crossover and mutation work with parts of phenotypes (sub-trees). The hierarchical structur...