Solving some ordinary differential equations numerically using differential evolution algorithm with a simple adaptive mutation scheme

2021 ◽  
Author(s):  
Werry Febrianti ◽  
Kuntjoro Adji Sidarto ◽  
Novriana Sumarti
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Ordinary Differential Equations ◽  
Differential Evolution Algorithm ◽  
Adaptive Mutation ◽  
Evolution Algorithm ◽  
Mutation Scheme

Enhanced Directed Differential Evolution Algorithm for Solving Constrained Engineering Optimization Problems

2019 ◽  
Vol 10 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Ali Wagdy Mohamed ◽  
Ali Khater Mohamed ◽  
Ehab Z. Elfeky ◽  
Mohamed Saleh
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Test Problems ◽  
New Mutation ◽  
De Algorithm ◽  
Engineering Problems ◽  
Evolution Algorithm ◽  
Mutation Scheme ◽  
Exploration Exploitation

The performance of Differential Evolution is significantly affected by the mutation scheme, which attracts many researchers to develop and enhance the mutation scheme in DE. In this article, the authors introduce an enhanced DE algorithm (EDDE) that utilizes the information given by good individuals and bad individuals in the population. The new mutation scheme maintains effectively the exploration/exploitation balance. Numerical experiments are conducted on 24 test problems presented in CEC'2006, and five constrained engineering problems from the literature for verifying and analyzing the performance of EDDE. The presented algorithm showed competitiveness in some cases and superiority in other cases in terms of robustness, efficiency and quality the of the results.

scholarly journals Application of Improved Differential Evolution Algorithm in Solving Equations

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Guiying Ning ◽  
Yongquan Zhou
Keyword(s):  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Convergence Speed ◽  
Evolutionary Strategy ◽  
Adaptive Mutation ◽  
Local Optimum ◽  
Algebraic Equations ◽  
Evolution Algorithm ◽  
Roots Of Equations ◽  
Improved Differential Evolution Algorithm

AbstractThe problem of finding roots of equations has always been an important research problem in the fields of scientific and engineering calculations. For the standard differential evolution algorithm cannot balance the convergence speed and the accuracy of the solution, an improved differential evolution algorithm is proposed. First, the one-half rule is introduced in the mutation process, that is, half of the individuals perform differential evolutionary mutation, and the other half perform evolutionary strategy reorganization, which increases the diversity of the population and avoids premature convergence of the algorithm; Second, set up an adaptive mutation operator and a crossover operator to prevent the algorithm from falling into the local optimum and improve the accuracy of the solution. Finally, classical high-order algebraic equations and nonlinear equations are selected for testing, and compared with other algorithms. The results show that the improved algorithm has higher solution accuracy and robustness, and has a faster convergence speed. It has outstanding effects in finding roots of equations, and provides an effective method for engineering and scientific calculations.

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