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The Wiener-Hammerstein nonlinear system is made up of two dynamic linear subsystems in series with a static nonlinear subsystem, and it is widely used in electrical, mechanical, aerospace and other fields. This paper considers the parameter estimation of the Wiener-Hammerstein output error moving average (OEMA) system.

The idea of multi-population and parameter self-adaptive identification is introduced, and a multi-population self-adaptive differential evolution (MPSADE) algorithm is proposed. In order to confirm the feasibility of the above method, the differential evolution (DE), the self-adaptive differential evolution (SADE), the MPSADE and the gradient iterative (GI) algorithms are derived to identify the Wiener-Hammerstein OEMA system, respectively.

From the simulation results, the authors find that the estimation errors under the four algorithms stabilize after 120, 30, 20 and 300 iterations, respectively, and the estimation errors of the four algorithms converge to 5.0%, 3.6%, 2.7% and 7.3%, which show that all four algorithms can identify the Wiener-Hammerstein OEMA system.

Compared with DE, SADE and GI algorithm, the MPSADE algorithm not only has higher parameter estimation accuracy but also has a faster convergence speed. Finally, the input–output relationship of laser welding system is described and identified by the MPSADE algorithm. The simulation results show that the MPSADE algorithm can effectively identify parameters of the laser welding system.

Since the last few decades, Artificial Neural Networks have been the center of attraction of a large number of researchers for solving diversified problem domains. Due to its distinguishing features such as generalization ability, robustness and strong ability to tackle nonlinear problems, it appears to be more popular in financial time series modeling and prediction. In this paper, a Pi-Sigma Neural Network is designed for foretelling the future currency exchange rates in different prediction horizon. The unrevealed parameters of the network are interpreted by a hybrid learning algorithm termed as Shuffled Differential Evolution (SDE). The main motivation of this study is to integrate the partitioning and random shuffling scheme of Shuffled Frog Leaping algorithm with evolutionary steps of a Differential Evolution technique to obtain an optimal solution with an accelerated convergence rate. The efficiency of the proposed predictor model is actualized by predicting the exchange rate price of a US dollar against Swiss France (CHF) and Japanese Yen (JPY) accumulated within the same period of time.

This paper presents the application of Differential Evolution (DE), an evolutionary computation technique for the optimal design of gas transmission network. As a gas transmission system includes source of gas, delivery sites with pipeline segments and compressors, the design of efficient and economical network involves lot of parameters. In addition, there are many equality and inequality constraints to be satisfied making the problem highly non‐linear. Hence an efficient strategy is needed in searching for the global optimum. In this study, DE has been successfully applied for optimal design of gas transmission network. The results obtained are compared with those of nonlinear programming technique and branch and bound algorithm. DE is able to find an optimal solution with a cost that is less than reported in the earlier literature. The proposed strategy takes less computational time to converge when compared to the existing techniques without compromising with the accuracy of the parameter estimates.

The purpose of this paper is to present a Differential Immune Clone Clustering Algorithm (DICCA) to solve image segmentation.

DICCA combines immune clone selection and differential evolution, and two populations are used in the evolutionary process. Clone reproduction and selection, differential mutation, crossover and selection are adopted to evolve two populations, which can increase population diversity and avoid local optimum. After extracting the texture features of an image and encoding them with real numbers, DICCA is used to partition these features, and the final segmentation result is obtained.

This approach is applied to segment all sorts of images into homogeneous regions, including artificial synthetic texture images, natural images and remote sensing images, and the experimental results show the effectiveness of the proposed algorithm.

The method presented in this paper represents a new approach to solving clustering problems. The novel method applies the idea two populations are used in the evolutionary process. The proposed clustering algorithm is shown to be effective in solving image segmentation.

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.

The purpose of this paper is to compare the efficiency of four different algorithmic parallelization methods for inverse shape design flow problems.

The included algorithms are: a parallelized differential evolution algorithm; island‐model differential evolution with multiple subpopulations; Nash differential evolution with geometry decomposition using competitive Nash games; and the new Global Nash Game Coalition Algorithm (GNGCA) which combines domain and geometry decomposition into a “distributed one‐shot” method. The methods are compared using selected academic reconstruction problems using a different number of simultaneous processes.

The results demonstrate that the geometry decomposition approach can be used to improve algorithmic convergence. Additional improvements were achieved using the novel distributed one‐shot method.

This paper is a part of series of articles involving the GNGCA method. Further tests implemented for more complex problems are needed to study the efficiency of the approaches in more realistic cases.

Monitoring and diagnosis of fault cases for squirrel cage induction motors can be implemented using the multiple coupled circuit model. However, the identification of the associated model parameters for a specific machine is problematic. Up to now, the main options are measurement and test procedures or the use of finite element method analyses. However, these approaches are very costly and not suitable for use in an industrial application. The purpose of this paper is a practical parameter identification based on optimization methods and a comparison of different algorithms for this task.

Population-based metaheuristics are used to determine the parameters for the multiple coupled circuit model. For this purpose, a search space for the required parameters is defined without an elaborate analytical approach. Subsequently, a genetic algorithm, the differential evolution algorithm and particle swarm optimization are tested and compared. The algorithms use the weighted mean squared error (MSE) between the real measured data of stator currents as well as speed and the simulation results of the model as a fitness function.

The results of the parameter identification show that the applied methodology generally works and all three optimization algorithms fulfill the task. The differential evolution algorithm performs best, with a weighted MSE of 2.62, the lowest error after 1,000 simulations. In addition, this algorithm achieves the lowest overall error of all algorithms after only 740 simulations. The determined parameters do not completely match the parameters of the real machine, but still result in a very good reproduction of the dynamic behavior of the induction motor with squirrel cage.

The value of the presented method lies in the application of condition-based maintenance of electric drives in the industry, which is performed based on the multiple coupled circuit model. With a parameterized model, various healthy as well as faulty states can be calculated and thus, in the future, monitoring and diagnosis of faults of the respective motor can be performed. Essential for this, however, are the parameters adapted to the respective machine. With the described method, an automated parameter identification can be realized without great effort as a basis for an intelligent and condition-oriented maintenance.

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.

The purpose of this paper is to propose a multi-objective differential evolution algorithm named as MOMR-DE to resolve multicast routing problem. In mobile ad hoc network (MANET), multicast routing is a non-deterministic polynomial -complete problem that deals with the various objectives and constraints. Quality of service (QoS) in the multicast routing problem mainly depends on cost, delay, jitter and bandwidth. So the cost, delay, jitter and bandwidth are always considered as multi-objective for designing multicast routing protocols. However, mobile node battery energy is finite and the network lifetime depends on node battery energy. If the battery power consumption is high in any one of the nodes, the chances of network’s life reduction due to path breaks are also more. On the other hand, node’s battery energy had to be consumed to guarantee high-level QoS in multicast routing to transmit correct data anywhere and at any time. Hence, the network lifetime should be considered as one objective of the multi-objective in the multicast routing problem.

Recently, many metaheuristic algorithms formulate the multicast routing problem as a single-objective problem, although it obviously is a multi-objective optimization problem. In the MOMR-DE, the network lifetime, cost, delay, jitter and bandwidth are considered as five objectives. Furthermore, three QoS constraints which are maximum allowed delay, maximum allowed jitter and minimum requested bandwidth are included. In addition, we modify the crossover and mutation operators to build the shortest-path multicast tree to maximize network lifetime and bandwidth, minimize cost, delay and jitter.

Two sets of experiments are conducted and compared with other algorithms for these problems. The simulation results show that our proposed method is capable of achieving faster convergence and is more preferable for multicast routing in MANET.

In MANET, most metaheuristic algorithms formulate the multicast routing problem as a single-objective problem. However, this paper proposes a multi-objective differential evolution algorithm to resolve multicast routing problem, and the proposed algorithm is capable of achieving faster convergence and more preferable for multicast routing.

The purpose of this paper is to reduce the computational burden and improve the precision of the parameter optimization in the convection-diffusion equation, a new algorithm, the refined gray-encoded evolution algorithm (RGEA), is proposed.

In the new algorithm, the differential evolution algorithm (DEA) is introduced to refine the solutions and to improve the search efficiency in the evolution process; the rapid cycle operation is also introduced to accelerate the convergence rate. The authors apply this algorithm to parameter optimization in convection-diffusion equations.

Two cases for parameter optimization in convection-diffusion equations are studied by using the new algorithm. The results indicate that the sum of absolute errors by the RGEA decreases from 74.14 to 99.29 percent and from 99.32 to 99.98 percent, respectively, compared to those by the gray-encoded genetic algorithm (GGA) and the DEA. And the RGEA has a faster convergent speed than does the GGA or DEA.

A more complete convergence analysis of the method is under investigation. The authors will also explore the possibility of adapting the method to identify the initial condition and boundary condition in high-dimension convection-diffusion equations.

This paper will have an important impact on the applications of the parameter optimization in the field of environmental flow analysis.

This paper will have an important significance for a sustainable social development.

The authors establish a new RGEA algorithm for parameter optimization in solving convection-diffusion equations. The application results make a valuable contribution to the parameter optimization in the field of environmental flow analysis.