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Journal articles on the topic 'Method of differential evolution'

Author: Grafiati

Published: 28 May 2022

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1

Kamiyama, Daichi, Kenichi Tamura, and Keiichiro Yasuda. "Down-hill Simplex Method Based Differential Evolution." IEEJ Transactions on Electronics, Information and Systems 130, no. 7 (2010): 1271–72. http://dx.doi.org/10.1541/ieejeiss.130.1271.

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2

Yamaguchi, Satoshi. "An Automatic Control Parameters Tuning Method for Differential Evolution." IEEJ Transactions on Electronics, Information and Systems 128, no. 11 (2008): 1696–703. http://dx.doi.org/10.1541/ieejeiss.128.1696.

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3

Phuong, Phan Thi Thu, Hoang Van Lai, and Bui Dinh Tri. "Reservoir optimization with differential evolution." Vietnam Journal of Mechanics 38, no. 1 (2016): 39–48. http://dx.doi.org/10.15625/0866-7136/38/1/6490.

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Reservoir optimization, is one of recent problems, which has been researched by several methods such as Linear Programming (LP), Non-linear Programming (NLP), Genetic Algorithm (GA), and Dynamic Programming (DP). Differential Evolution (DE), a method in GA group, is recently applied in many fields, especially water management. This method is an improved variant of GA to converge and reach to the optimal solution faster than the traditional GA. It is also capable to apply for a wide range space, to a problem with complex, discontinuous, undifferential optimal function. Furthermore, this method does not requirethe gradient information of the space but easily find the global solution by asimple algorithm. In this paper, we introduce DE, compare to LP which was considered mathematically decades ago to prove DE's accuracy, then apply DE to Pleikrong, a reservoir in Vietnam, then discuss about the results.

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4

Kim, Gwangseob, Hyungon Cho, and Jaeeung Yi. "Parameter Estimation of the Neyman-Scott Rectangular Pulse Model Using a Differential Evolution Method." Journal of Korean Society of Hazard Mitigation 12, no. 4 (2012): 187–94. http://dx.doi.org/10.9798/kosham.2012.12.4.187.

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5

Cui, Laizhong, Genghui Li, Zexuan Zhu, Zhenkun Wen, Nan Lu, and Jian Lu. "A novel differential evolution algorithm with a self-adaptation parameter control method by differential evolution." Soft Computing 22, no. 18 (2017): 6171–90. http://dx.doi.org/10.1007/s00500-017-2685-5.

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6

Chen, Yue Ping, Long Jin, Shu Ping Li, Shi Liu Song, and Yan Liang. "Evaluation of Sphericity Error Using Differential Evolution Method." Applied Mechanics and Materials 423-426 (September 2013): 2132–35. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.2132.

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The mathematical model of sphericity error under the condition of minimum zone is derived. An algorithm based on the differential evolution (DE) is proposed to evaluate the sphericity error. Its principle and realization approach are discussed to solve the minimum zone sphericity error. The proposed method was verified by an example. Compared with other methods, the results show that the proposed method makes the sphericity error evaluation more accurate.

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7

Li, Jiang. "Evaluation method based on neural network differential evolution." Cluster Computing 22, S2 (2018): 4869–75. http://dx.doi.org/10.1007/s10586-018-2409-3.

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8

Al-Obeidat, Feras, Nabil Belacel, Juan A. Carretero, and Prabhat Mahanti. "Differential Evolution for learning the classification method PROAFTN." Knowledge-Based Systems 23, no. 5 (2010): 418–26. http://dx.doi.org/10.1016/j.knosys.2010.02.003.

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9

Thuy, Ngo Thi Phuong, Rajashekhar Pendyala, Nejat Rahmanian, and Narahari Marneni. "Heat Exchanger Network Optimization by Differential Evolution Method." Applied Mechanics and Materials 564 (June 2014): 292–97. http://dx.doi.org/10.4028/www.scientific.net/amm.564.292.

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The synthesis of heat exchanger network (HEN) is a comprehensive approach to optimize energy utilization in process industry. Recent developments in HEN synthesis (HENS) present several heuristic methods, such as Simulated Annealing (SA), Genetic Algorithm (GA), and Differential Evolution (DE). In this work, DE method for synthesis and optimization of HEN has been presented. Using DE combined with the concept of super-targeting, the optimization is determined. Then DE algorithm is employed to optimize the global cost function including the constraints, such as heat balance, the temperatures of process streams. A case study has been optimized using DE, generated structure of HEN and compared with networks obtained by other methods such as pinch technology or mathematical programming. Through the result, the proposed method has been illustrated that DE is able to apply in HEN optimization, with 16.7% increase in capital cost and 56.4%, 18.9% decrease in energy, global costs respectively.

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10

Li, Xiangtao, and Minghao Yin. "Modified differential evolution with self-adaptive parameters method." Journal of Combinatorial Optimization 31, no. 2 (2014): 546–76. http://dx.doi.org/10.1007/s10878-014-9773-6.

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11

Locatelli, Marco, and Massimiliano Vasile. "(Non) convergence results for the differential evolution method." Optimization Letters 9, no. 3 (2014): 413–25. http://dx.doi.org/10.1007/s11590-014-0816-9.

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12

Lýsek, J., and J. Šťastný. "Automatic discovery of the regression model by the means of grammatical and differential evolution ." Agricultural Economics (Zemědělská ekonomika) 60, No. 12 (2014): 546–52. http://dx.doi.org/10.17221/160/2014-agricecon.

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In the contribution, there is discussed the usage of the method based on the grammatical and differential evolution for the automatic discovery of regression models for discrete datasets. The combination of these two methods enables the process to find the precise structure of the mathematical model and values for the model constants separately. The used method is described and tested on the selected regression examples. The results are reported and the obtained mathematical models are presented. The advantages of the selected approach are described and compared to the classical methods.

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13

Charilogis, Vasileios, Ioannis G. Tsoulos, Alexandros Tzallas, and Evangelos Karvounis. "Modifications for the Differential Evolution Algorithm." Symmetry 14, no. 3 (2022): 447. http://dx.doi.org/10.3390/sym14030447.

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Differential Evolution (DE) is a method of optimization used in symmetrical optimization problems and also in problems that are not even continuous, and are noisy and change over time. DE optimizes a problem with a population of candidate solutions and creates new candidate solutions per generation in combination with existing rules according to discriminatory rules. The present work proposes two variations for this method. The first significantly improves the termination of the method by proposing an asymptotic termination rule, which is based on the differentiation of the average of the function values in the population of DE. The second modification proposes a new scheme for a critical parameter of the method, which improves the method’s ability to better explore the search space of the objective function. The proposed variations have been tested on a number of problems from the current literature, and from the experimental results, it appears that the proposed modifications render the method quite robust and faster even in large-scale problems.

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14

Koguma, Yuji, and Eitaro Aiyoshi. "Search Points Distribution Analysis for Differential Evolution Based on Maximum Entropy Method." IEEJ Transactions on Electronics, Information and Systems 134, no. 9 (2014): 1341–47. http://dx.doi.org/10.1541/ieejeiss.134.1341.

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15

Wang, Dong Xia, Ai Guo Song, Xiu Lan Wen, and Feng Lin Wang. "Circularity Error Evaluation Based on Differential Evolution Algorithm." Applied Mechanics and Materials 143-144 (December 2011): 416–21. http://dx.doi.org/10.4028/www.scientific.net/amm.143-144.416.

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An algorithm based on the differential evolutionary (DE) computation is proposed to evaluate circularity error. It is a heuristic evolutionary algorithm based on population optimization .In the meantime, the suggested method is used to solve the minimum zone circularity error. Compared with other methods, the results show the presented method has very strong self-adaptive ability to environment and better global convergence. Examples proves that the proposed method is effective, convergence and robustness in the process of optimization. And this method makes the circularity error evaluation more accurate.

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16

Li, Hong-wei, Jun Wang, and Hai-tao Wang. "A New Particle Filter Based on Differential Evolution Method." Journal of Electronics & Information Technology 33, no. 7 (2011): 1639–43. http://dx.doi.org/10.3724/sp.j.1146.2010.01212.

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17

Mao Yanjie, 茅言杰, 李思坤 Li Sikun, 王向朝 Wang Xiangzhao, and 韦亚一 Wei Yayi. "Lithographic Tool-Matching Method Based on Differential Evolution Algorithm." Acta Optica Sinica 39, no. 12 (2019): 1222002. http://dx.doi.org/10.3788/aos201939.1222002.

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18

Zheng, Yu-Jun, Xin-Li Xu, Hai-Feng Ling, and Sheng-Yong Chen. "A hybrid fireworks optimization method with differential evolution operators." Neurocomputing 148 (January 2015): 75–82. http://dx.doi.org/10.1016/j.neucom.2012.08.075.

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19

Santosa, Budi, Andiek Sunarto, and Arief Rahman. "Using Differential Evolution Method to Solve Crew Rostering Problem." Applied Mathematics 01, no. 04 (2010): 316–25. http://dx.doi.org/10.4236/am.2010.14042.

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20

Yamaguchi, Satoshi. "An automatic control parameter tuning method for differential evolution." Electrical Engineering in Japan 174, no. 3 (2010): 25–33. http://dx.doi.org/10.1002/eej.21047.

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21

Fokas, A. S. "A new transform method for evolution partial differential equations." IMA Journal of Applied Mathematics 67, no. 6 (2002): 559–90. http://dx.doi.org/10.1093/imamat/67.6.559.

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22

Xie, Wei-Cheng, and Xiu-Fen Zou. "A triangulation-based hole patching method using differential evolution." Computer-Aided Design 45, no. 12 (2013): 1651–64. http://dx.doi.org/10.1016/j.cad.2013.08.003.

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23

Mex, L., Carlos A. Cruz-Villar, and F. Peñuñuri. "Closed-Form Solutions to Differential Equations via Differential Evolution." Discrete Dynamics in Nature and Society 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/910316.

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We focus on solving ordinary differential equations using the evolutionary algorithm known as differential evolution (DE). The main purpose is to obtain a closed-form solution to differential equations. To solve the problem at hand, three steps are proposed. First, the problem is stated as an optimization problem where the independent variables areelementaryfunctions. Second, as the domain of DE is real numbers, we propose a grammar that assigns numbers to functions. Third, to avoid truncation and subtractive cancellation errors, to increase the efficiency of the calculation of derivatives, the dual numbers are used to obtain derivatives of functions. Some examples validating the effectiveness and efficiency of our method are presented.

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24

Jena, Prabir Kumar, Dhirendra Nath Thatoi, and Dayal R. Parhi. "Differential Evolution: An Inverse Approach for Crack Detection." Advances in Acoustics and Vibration 2013 (November 13, 2013): 1–10. http://dx.doi.org/10.1155/2013/321931.

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This paper presents a damage detection technique combining analytical and experimental investigations on a cantilever aluminium alloy beam with a transverse surface crack. Firstly, the first three natural frequencies were determined using analytical methods based on strain energy release rate. Secondly, an experimental method was adopted to validate the theoretical findings. The damage location and severity assessment is the third stage and is formulated as a constrained optimisation problem and solved using the proposed differential evolution (DE) algorithm based on the measured and calculated first three natural frequencies as inputs. Numerical simulation studies indicate that the proposed method is robust and can be used effectively in structural health monitoring (SHM) applications.

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25

Zhang, Xin, and Xiu Zhang. "Improving differential evolution by differential vector archive and hybrid repair method for global optimization." Soft Computing 21, no. 23 (2016): 7107–16. http://dx.doi.org/10.1007/s00500-016-2253-4.

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26

Kukushkin, Maksim V. "Evolution Equations in Hilbert Spaces via the Lacunae Method." Fractal and Fractional 6, no. 5 (2022): 229. http://dx.doi.org/10.3390/fractalfract6050229.

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In this paper, we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and uniqueness theorem and find a solution in the form of a series on the root vectors of the right-hand side. We consider fractional differential equations of various kinds as an application. Such operators as the Riemann-Liouville fractional differential operator, the Riesz potential, the difference operator have been involved.

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27

Al-Jadir, Ibraheem, Kok Wai Wong, Chun Che Fung, and Hong Xie. "Unsupervised Text Feature Selection Using Memetic Dichotomous Differential Evolution." Algorithms 13, no. 6 (2020): 131. http://dx.doi.org/10.3390/a13060131.

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Feature Selection (FS) methods have been studied extensively in the literature, and there are a crucial component in machine learning techniques. However, unsupervised text feature selection has not been well studied in document clustering problems. Feature selection could be modelled as an optimization problem due to the large number of possible solutions that might be valid. In this paper, a memetic method that combines Differential Evolution (DE) with Simulated Annealing (SA) for unsupervised FS was proposed. Due to the use of only two values indicating the existence or absence of the feature, a binary version of differential evolution is used. A dichotomous DE was used for the purpose of the binary version, and the proposed method is named Dichotomous Differential Evolution Simulated Annealing (DDESA). This method uses dichotomous mutation instead of using the standard mutation DE to be more effective for binary purposes. The Mean Absolute Distance (MAD) filter was used as the feature subset internal evaluation measure in this paper. The proposed method was compared with other state-of-the-art methods including the standard DE combined with SA, which is named DESA in this paper, using five benchmark datasets. The F-micro, F-macro (F-scores) and Average Distance of Document to Cluster (ADDC) measures were utilized as the evaluation measures. The Reduction Rate (RR) was also used as an evaluation measure. Test results showed that the proposed DDESA outperformed the other tested methods in performing the unsupervised text feature selection.

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28

SIRENDAOREJI and SUN JIONG. "AUXILIARY EQUATION METHOD AND ITS APPLICATIONS TO NONLINEAR EVOLUTION EQUATIONS." International Journal of Modern Physics C 14, no. 08 (2003): 1075–85. http://dx.doi.org/10.1142/s0129183103005200.

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By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.

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29

Arora, Geeta, and Pratiksha. "A Cumulative Study on Differential Transform Method." International Journal of Mathematical, Engineering and Management Sciences 4, no. 1 (2019): 170–81. http://dx.doi.org/10.33889/ijmems.2019.4.1-015.

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Many real-world phenomena when modelled as a differential equation don't generally have exact solutions, so their numerical or analytic solutions are sought after. Differential transform method (DTM) is one of the analytical methods that gives the solution in the form of a power series. In this paper, a cumulative study is done on DTM and its evolution as an effective method to solve the gamut of differential equations.

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30

Chen, Lin, Rong Sheng Lu, Yan Qiong Shi, and Jian Sheng Tian. "A Differential Evolution Stereo Matching Method in Digital Image Correlation." Key Engineering Materials 625 (August 2014): 297–304. http://dx.doi.org/10.4028/www.scientific.net/kem.625.297.

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Stereo matching is widely used in three-dimensional (3D) reconstruction, stereo machine vision and digital image correlation. The aim of stereo matching process is to solve the well-known correspondence problem, which tries to match points or features from one image with the same points or features in another image from the same 3D scene. There are two basic ways, correlation-based and feature-based, are used to find the correspondences between two images. The correlation-based way is to determine if one location in one image looks/seems like another in another image, and the feature-based way to find if a subset of features in one image is similar in the another image. In stereo matching, a simple algorithm is to compare small patches between two rectified images by correlation search. For the pair images acquired from two cameras inevitably exists some rotation transformation, the algorithm first runs a preprocessing step to rectify the images with the epipolar rectification to simplify the problem of finding matching points between images. The epipolar rectification is to determine a transformation of each image plane such that pairs of conjugate epipolar lines become collinear and parallel to one of the image axes. It will lead the loss of gray information of images. The effect is dependent on the amount of angle. When the angle is big enough, the correlation search may yield error results because of retrograded correlation effect. In order to solve the problem, the paper presents an improved stereo matching algorithm with differential evolution to solve the correspondence problem. Our method doesn’t need to runs the preprocessing step to rectify the images with the epipolar rectification. It uses a differential evolution algorithm to minimize the correlation function which contains the angle information after acquiring the epipoar geometry constraint of two image pairs. Then it utilizes a flood-fill algorithm to search correspondence sub-region in the area around the epipolar line. The flood-fill algorithm can overcome the problem of the traditional row-column scanning search method, which will encounter boundary barrier where exists concave polygons or cavities. The Experimental results show that the proposed method can be easily implemented in stereo matching without loss of information of image features with large rotation angle transformation. In the paper, we will introduce the stereo matching principle and its algorithms, including the differential evolution algorithm for finding the correspondences with large rotation transformation between stereo image pairs and the flood-fill traversal strategy for matching large area with complex concave polygons or cavities. In the end of the paper, some experimental results will be given to illustrate the method effectiveness. Keywords: digital image correlation, stereo matching algorithm, epipolar geometry, flood fill algorithm, differential evolution, rotation angle

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31

Gajawada, Satish. "Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution." International Journal of Software Engineering & Applications 3, no. 4 (2012): 77–85. http://dx.doi.org/10.5121/ijsea.2012.3406.

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32

Alotto, Piergiorgio. "A hybrid multiobjective differential evolution method for electromagnetic device optimization." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 30, no. 6 (2011): 1815–28. http://dx.doi.org/10.1108/03321641111168129.

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33

Zhang, Yun, Meng Li, and Yang Hu. "Model-based Balancing Method of Rotors using Differential Evolution Algorithm." IOP Conference Series: Materials Science and Engineering 751 (February 7, 2020): 012046. http://dx.doi.org/10.1088/1757-899x/751/1/012046.

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34

Zubelevich, O. "Majorant Method for the Evolution Differential Equations in Sequence Spaces." Mathematical Notes 103, no. 3-4 (2018): 565–82. http://dx.doi.org/10.1134/s0001434618030239.

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35

Gong, Wenyin, Zhihua Cai, and Liangxiao Jiang. "Enhancing the performance of differential evolution using orthogonal design method." Applied Mathematics and Computation 206, no. 1 (2008): 56–69. http://dx.doi.org/10.1016/j.amc.2008.08.053.

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36

Qian, Bin, Ling Wang, Rong Hu, Wan-Liang Wang, De-Xian Huang, and Xiong Wang. "A hybrid differential evolution method for permutation flow-shop scheduling." International Journal of Advanced Manufacturing Technology 38, no. 7-8 (2007): 757–77. http://dx.doi.org/10.1007/s00170-007-1115-8.

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37

Kim, Pyungmo, and Jongsoo Lee. "An integrated method of particle swarm optimization and differential evolution." Journal of Mechanical Science and Technology 23, no. 2 (2009): 426–34. http://dx.doi.org/10.1007/s12206-008-0917-4.

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38

Ding, Hui, Guangyao Sun, Lijuan Hao, Bin Wu, and Yican Wu. "A loading pattern optimization method based on discrete differential evolution." Annals of Nuclear Energy 137 (March 2020): 107057. http://dx.doi.org/10.1016/j.anucene.2019.107057.

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39

Leon, Miguel, and Ning Xiong. "Adaptive differential evolution with a new joint parameter adaptation method." Soft Computing 24, no. 17 (2020): 12801–19. http://dx.doi.org/10.1007/s00500-020-05182-2.

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40

Kozlov, Konstantin, and Alexander Samsonov. "DEEP—differential evolution entirely parallel method for gene regulatory networks." Journal of Supercomputing 57, no. 2 (2010): 172–78. http://dx.doi.org/10.1007/s11227-010-0390-6.

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41

Fitriani, Maulida Ayu, Aina Musdholifah, and Sri Hartati. "Adaptive Unified Differential Evolution for Clustering." IJCCS (Indonesian Journal of Computing and Cybernetics Systems) 12, no. 1 (2018): 53. http://dx.doi.org/10.22146/ijccs.27871.

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Various clustering methods to obtain optimal information continues to evolve one of its development is Evolutionary Algorithm (EA). Adaptive Unified Differential Evolution (AuDE), is the development of Differential Evolution (DE) which is one of the EA techniques. AuDE has self adaptive scale factor control parameters (F) and crossover-rate (Cr).. It also has a single mutation strategy that represents the most commonly used standard mutation strategies from previous studies.The AuDE clustering method was tested using 4 datasets. Silhouette Index and CS Measure is a fitness function used as a measure of the quality of clustering results. The quality of the AuDE clustering results is then compared against the quality of clustering results using the DE method.The results show that the AuDE mutation strategy can expand the cluster central search produced by ED so that better clustering quality can be obtained. The comparison of the quality of AuDE and DE using Silhoutte Index is 1:0.816, whereas the use of CS Measure shows a comparison of 0.565:1. The execution time required AuDE shows better but Number significant results, aimed at the comparison of Silhoutte Index usage of 0.99:1 , Whereas on the use of CS Measure obtained the comparison of 0.184:1.

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42

Jin, Long, Yue Ping Chen, Hai Yan Lu, Shu Ping Li, and Yi Chen. "Roundness Error Evaluation Based on Differential Evolution Algorithm." Applied Mechanics and Materials 670-671 (October 2014): 1285–89. http://dx.doi.org/10.4028/www.scientific.net/amm.670-671.1285.

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A new approach for roundness (circularity) error evaluation based on the differential evolution (DE) algorithm is proposed.The mathematical model of the roundness error under the condition of the minimum zone is derived. The background and advantages of DE are introduced, the fundamentals and implementation techniques are also given.The approach is verified by two examples.Compared with other methods, the results show that the proposed method makes the roundness error evaluation more accurate.

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43

Khanum, Rashida Adeeb, Muhammad Asif Jan, Nasser Mansoor Tairan, and Wali Khan Mashwani. "Hybridization of Adaptive Differential Evolution with an Expensive Local Search Method." Journal of Optimization 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/3260940.

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Differential evolution (DE) is an effective and efficient heuristic for global optimization problems. However, it faces difficulty in exploiting the local region around the approximate solution. To handle this issue, local search (LS) techniques could be hybridized with DE to improve its local search capability. In this work, we hybridize an updated version of DE, adaptive differential evolution with optional external archive (JADE) with an expensive LS method, Broydon-Fletcher-Goldfarb-Shano (BFGS) for solving continuous unconstrained global optimization problems. The new hybrid algorithm is denoted by DEELS. To validate the performance of DEELS, we carried out extensive experiments on well known test problems suits, CEC2005 and CEC2010. The experimental results, in terms of function error values, success rate, and some other statistics, are compared with some of the state-of-the-art algorithms, self-adaptive control parameters in differential evolution (jDE), sequential DE enhanced by neighborhood search for large-scale global optimization (SDENS), and differential ant-stigmergy algorithm (DASA). These comparisons reveal that DEELS outperforms jDE and SDENS except DASA on the majority of test instances.

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44

Kaka, Jhansi Rani, and K. Satya Prasad. "Differential Evolution and Multiclass Support Vector Machine for Alzheimer’s Classification." Security and Communication Networks 2022 (January 13, 2022): 1–13. http://dx.doi.org/10.1155/2022/7275433.

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Early diagnosis of Alzheimer’s helps a doctor to decide the treatment for the patient based on the stages. The existing methods involve applying the deep learning methods for Alzheimer’s classification and have the limitations of overfitting problems. Some researchers were involved in applying the feature selection based on the optimization method, having limitations of easily trapping into local optima and poor convergence. In this research, Differential Evolution-Multiclass Support Vector Machine (DE-MSVM) is proposed to increase the performance of Alzheimer’s classification. The image normalization method is applied to enhance the quality of the image and represent the features effectively. The AlexNet model is applied to the normalized images to extract the features and also applied for feature selection. The Differential Evolution method applies Pareto Optimal Front for nondominated feature selection. This helps to select the feature that represents the characteristics of the input images. The selected features are applied in the MSVM method to represent in high dimension and classify Alzheimer’s. The DE-MSVM method has accuracy of 98.13% in the axial slice, and the existing whale optimization with MSVM has 95.23% accuracy.

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45

Khaparde, Amit Ramesh. "Analysis of New Distributed Differential Evolution Algorithm with Best Determination Method and Species Evolution." Procedia Computer Science 167 (2020): 263–72. http://dx.doi.org/10.1016/j.procs.2020.03.220.

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46

Ali, Musrrat, Millie Pant, and Ajith Abraham. "Unconventional initialization methods for differential evolution." Applied Mathematics and Computation 219, no. 9 (2013): 4474–94. http://dx.doi.org/10.1016/j.amc.2012.10.053.

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47

Magagula, V. M., S. S. Motsa, and P. Sibanda. "A Multi-Domain Bivariate Pseudospectral Method for Evolution Equations." International Journal of Computational Methods 14, no. 04 (2017): 1750041. http://dx.doi.org/10.1142/s0219876217500414.

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In this paper, we present a new general approach for solving nonlinear evolution partial differential equations. The novelty of the approach is in the combination of spectral collocation and Lagrange interpolation polynomials with Legendre–Gauss–Lobatto grid points to descritize and solve equations in piece-wise defined intervals. The method is used to solve several nonlinear evolution partial differential equations, namely, the modified KdV–Burgers equation, modified KdV equation, Fisher’s equation, Burgers–Fisher equation, Burgers–Huxley equation and the Fitzhugh–Nagumo equation. The results are compared with known analytic solutions to confirm accuracy, convergence and to get a general understanding of the performance of the method. In all the numerical experiments, we report a high degree of accuracy of the numerical solutions. Strategies for implementing various boundary conditions are discussed.

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48

Panagant, Natee, and Sujin Bureerat. "Solving Partial Differential Equations Using a New Differential Evolution Algorithm." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/747490.

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This paper proposes an alternative meshless approach to solve partial differential equations (PDEs). With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA) is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE) is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.

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Chang, Songtao, Yongji Wang, Lei Liu, and Xing Wei. "Attainability Analysis for Entry Vehicles Based on Differential Evolution." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/306947.

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Attainable region provides crucial information on mission planning of entry vehicles. In order to obtain it, a series of nonlinear optimal control problems which have similar formulations are needed to be solved. However, it is difficult to compute due to severe nonlinearity of the dynamics and various constraints. In this paper, a novel method is established to generate the attainable region at the end of the entry phase. It utilizes the parallel feature of differential evolution (DE) and the high accuracy of Chebyshev polynomial interpolation. By using the Chebyshev polynomial interpolation, the original problem is transformed to several nonlinear programming problems to facilitate employing DE. Each individual in DE’s population represents a candidate point on the boundary of the attainable region. In order to lead the population to the boundary simultaneously, a scheme is devised by exploiting the parallel feature of DE. Different from conventional methods which generate one point of the boundary in each run, our proposed method generates one side of the boundary of the attainable region. A scenario is presented to evaluate the designed method and some analyses are conducted to evaluate the influence of the vehicle’s design parameters on the attainable region.

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Sun, Peng, Ming Wu Luo, and Chao Xia Sun. "Enchanted Multi-Objective Differential Evolutional Algorithm for Economic/Environmental Dispatch." Advanced Materials Research 960-961 (June 2014): 1494–500. http://dx.doi.org/10.4028/www.scientific.net/amr.960-961.1494.

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An enchanted multi-objective differential evolutional algorithm was proposed, and was applied to solve the environmental economic dispatch problem. Duo to the weakness of random initial population, the orthogonal method was used in the initialization. Based on survival of the fittest, improved differential operation was proposed, combined with the corresponding parameters control method proposed. With the combination of B-coefficient method and restrain dominance, the process of solving equation and selection operation were used to make the individuals meet the equality constrain. Then the algorithm was tested on the IEEE-30 test system, the results are compared with the results of non-dominated genetic algorithm-II、multi-objective differential evolution and the known results in the papers, and the validity is verified. Keywords: Security constrained economic/environmental dispatch,Constrained multi-objective differential evolution,Feasible region and infeasible region

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