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In this paper, a newly proposed hybridization algorithm namely constriction coefficient-based particle swarm optimization and gravitational search algorithm (CPSOGSA) has been employed for training MLP to overcome sensitivity to initialization, premature convergence, and stagnation in local optima problems of MLP.

In this study, the exploration of the search space is carried out by gravitational search algorithm (GSA) and optimization of candidate solutions, i.e. exploitation is performed by particle swarm optimization (PSO). For training the multi-layer perceptron (MLP), CPSOGSA uses sigmoid fitness function for finding the proper combination of connection weights and neural biases to minimize the error. Secondly, a matrix encoding strategy is utilized for providing one to one correspondence between weights and biases of MLP and agents of CPSOGSA.

The experimental findings convey that CPSOGSA is a better MLP trainer as compared to other stochastic algorithms because it provides superior results in terms of resolving stagnation in local optima and convergence speed problems. Besides, it gives the best results for breast cancer, heart, sine function and sigmoid function datasets as compared to other participating algorithms. Moreover, CPSOGSA also provides very competitive results for other datasets.

The CPSOGSA performed effectively in overcoming stagnation in local optima problem and increasing the overall convergence speed of MLP. Basically, CPSOGSA is a hybrid optimization algorithm which has powerful characteristics of global exploration capability and high local exploitation power. In the research literature, a little work is available where CPSO and GSA have been utilized for training MLP. The only related research paper was given by Mirjalili et al., in 2012. They have used standard PSO and GSA for training simple FNNs. However, the work employed only three datasets and used the MSE performance metric for evaluating the efficiency of the algorithms. In this paper, eight different standard datasets and five performance metrics have been utilized for investigating the efficiency of CPSOGSA in training MLPs. In addition, a non-parametric pair-wise statistical test namely the Wilcoxon rank-sum test has been carried out at a 5% significance level to statistically validate the simulation results. Besides, eight state-of-the-art meta-heuristic algorithms were employed for comparative analysis of the experimental results to further raise the authenticity of the experimental setup.

An analytical theory based on a perturbation approach is presented to model planar resistors with a stochastic edge. The theoretical analysis is confirmed by Monte Carlo simulations.

The paper aims to compare and clarify the differences and between the two well-known decomposition spectral techniques; the Winer–Chaos expansion (WCE) and the Winer–Hermite expansion (WHE). The details of the two decompositions are outlined. The difficulties arise when using the two techniques are also mentioned along with the convergence orders. The reader can also find a collection of references to understand the two decompositions with their origins. The geometrical Brownian motion is considered as an example for an important process with exact solution for the sake of comparison. The two decompositions are found practical in analysing the SDEs. The WCE is, in general, simpler, while WHE is more efficient as it is the limit of WCE when using infinite number of random variables. The Burgers turbulence is considered as a nonlinear example and WHE is shown to be more efficient in detecting the turbulence. In general, WHE is more efficient especially in case of nonlinear and/or non-Gaussian processes.

The paper outlined the technical and literature review of the WCE and WHE techniques. Linear and nonlinear processes are compared to outline the comparison along with the convergence of both techniques.

The paper shows that both decompositions are practical in solving the stochastic differential equations. The WCE is found simpler and WHE is the limit when using infinite number of random variables in WCE. The WHE is more efficient especially in case of nonlinear problems.

Applicable for SDEs with square integrable processes and coefficients satisfying Lipschitz conditions.

This paper fulfils a comparison required by the researchers in the stochastic analysis area. It also introduces a simple efficient technique to model the flow turbulence in the physical domain.

Impedance data obtained by electrochemical impedance spectroscopy (EIS) are fitted to a relevant electrical equivalent circuit to evaluate parameters directly related to the resistance and the durability of metal–coating systems. The purpose of this study is to present a novel and more efficient computational strategy for the modelling of EIS measurements using the Differential Evolution paradigm.

An alternative method to non-linear regression algorithms for the analysis of measured data in terms of equivalent circuit parameters is provided by evolutionary algorithms, particularly the Differential Evolution (DE) algorithms (standard DE and a representative of the self-adaptive DE paradigm were used).

The results obtained with DE algorithms were compared with those yielding from commercial fitting software, achieving a more accurate solution, and a better parameter identification, in all the cases treated. Further, an enhanced fitting power for the modelling of metal–coating systems was obtained.

The great potential of the developed tool has been demonstrated in the analysis of the evolution of EIS spectra due to progressive degradation of metal–coating systems. Open codes of the different differential algorithms used are included, and also, examples tackled in the document are open. It allows the complete use, or improvement, of the developed tool by researchers.

Feature selection is an important step for data pre-processing specially in the case of high dimensional data set. Performance of the data model is reduced if the model is trained with high dimensional data set, and it results in poor classification accuracy. Therefore, before training the model an important step to apply is the feature selection on the dataset to improve the performance and classification accuracy.

A novel optimization approach that hybridizes binary particle swarm optimization (BPSO) and differential evolution (DE) for fine tuning of SVM classifier is presented. The name of the implemented classifier is given as DEPSOSVM.

This approach is evaluated using 20 UCI benchmark text data classification data set. Further, the performance of the proposed technique is also evaluated on UCI benchmark image data set of cancer images. From the results, it can be observed that the proposed DEPSOSVM techniques have significant improvement in performance over other algorithms in the literature for feature selection. The proposed technique shows better classification accuracy as well.

The proposed approach is different from the previous work, as in all the previous work DE/(rand/1) mutation strategy is used whereas in this study DE/(rand/2) is used and the mutation strategy with BPSO is updated. Another difference is on the crossover approach in our case as we have used a novel approach of comparing best particle with sigmoid function. The core contribution of this paper is to hybridize DE with BPSO combined with SVM classifier (DEPSOSVM) to handle the feature selection problems.

This paper aims to show a complete optimization tool that can be used for the design of coaxial magnetic gears. In the first part, the paper deals with the semi-analytic modelling of these machines and also discusses how to reduce the computational efforts. In the second part, an optimization algorithm is adopted for finding the Pareto optimal geometries.

The machine is subdivided into a set of domains according to their physical and geometrical properties, and the potential distribution is found semi-analytically in them under some simplifying hypothesis. A loss estimation is performed for both ferromagnetic and permanent magnet regions. A stochastic differential evolution (DE) algorithm for multi-objective constrained problems is then applied.

It is shown that the presented design tool gives results in accordance to finite element method (FEM)-based analysis keeping the advantages of robustness and simplicity of the analytical methods. The DE-based strategy performs well on the magnetic gear optimization problem.

The proposed tool appears to be a good starting point when designing coaxial magnetic gears. The optimal Pareto points can be used as initial seeds of FEM-based optimizations, resulting in a cheaper computational method with respect to a full FEM optimization.

This paper takes inspiration from recent works on magnetic gear modelling and completes the design procedure with a suitable efficiency estimation. The paper also shows how to use mature optimization strategies to solve the constrained multi-objective magnetic gear design problem.

The purpose of this paper is to present an improved approach to reactive power planning in electric power systems (EPS). It is based on minimization of a transmission network's active power losses. Several operating conditions have to be fulfilled to ensure stable operation of an EPS with minimal power losses. Some new limitations such as voltage instability detection and generator capability curve limit have been added to the existing method in order to improve the reliability of reactive power planning. The proposed method was tested on a model of the Slovenian power system. The results show the achievement of significant reduction in active power losses, while maintaining adequate EPS security.

Optimal voltage profile has to be found in order to determine minimal possible active power losses of EPS. The objective function, used to find the optimal voltage profile, has integer and floating point variables and is non‐differentiable with several local minima. Additionally, to ensure secure operation of EPS, several equality and inequality boundaries and limitations have to be applied. Differential evolution (DE) was used to solve the optimization problem.

Corresponding reactive power planning can significantly reduce active power losses in EPS. However, such planning can affect the security of EPS, therefore, several additional constrains have to be considered. The presented constrains considerably improve the operational security of EPS.

DE was used to solve the minimization problem. Although this method has proven to be fast and reliable, it is theoretically possible that the obtained solution is not global minimum.

Novel approach to voltage security constrained reactive power planning with additional nonlinear constrains, such as generator capability curves and voltage instability detection.

The purpose of this paper is to improve the existing differential evolution (DE) mutation operator so as to accelerate its convergence.

A new general donor form for mutation operation in DE is presented, which defines a donor as a convex combination of the triplet of individuals selected for a mutation. Three new donor schemes from that form are deduced.

The three donor schemes were empirically compared with the original DE version and three existing variants of DE by using a suite of nine well‐known test functions, and were also demonstrated by a practical application case – training a neural network to approximate aerodynamic data. The obtained numerical simulation results suggested that these modifications to the mutation operator could improve the DE's convergence performance in both the convergence rate and the convergence reliability.

Further research is still needed for adequately explaining why it was possible to simultaneously improve both the convergence rate and the convergence reliability of DE to that extent despite the well‐known “No Free Lunch” theorem. Also further research is considered necessary for outlining more distinctively the particular class of problems, where the current observations can be generalized.

More complicated engineering problems could be solved sub‐optimally, whereas their real optimal solution may never be reached subject to the current computer capability.

Though DE has demonstrated a considerably better convergence performance than the other evolutionary algorithms (EAs), its convergence rate is still far from what is hoped for by scientists. On the one hand, a higher convergence rate is always expected for any optimization method used in seeking the global optimum of a non‐linear objective function. On the other hand, since all EAs, including DE, work with a population of solutions rather than a single solution, many evaluations of candidate solutions are required in the optimization process. If evaluation of candidate solutions is too time‐consuming, the overall optimization cost may become too expensive. One often has to limit the algorithm to operate within an acceptable time, which maybe is not enough to find the global optimum (optima), but enough to obtain a sub‐optimal solution. Therefore, it is continuously necessary to investigate the new strategies to improve the current DE algorithm.