Logistic Map and Exponential Scaling Factor based Differential Evolution

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Differential Evolution ◽  
Logistic Map ◽  
Differential Evolution Algorithm ◽  
Scaling Factor ◽  
Exploration And Exploitation ◽  
Engineering Problems ◽  
Evolutionary Technique ◽  
Evolution Algorithm ◽  
State Of Art ◽  
Modified Algorithm

Differential evolution (DE), an important evolutionary technique, enhances its parameters such as, initialization of population, mutation, crossover etc. to resolve realistic optimization issues. This work represents a modified differential evolution algorithm by using the idea of exponential scale factor and logistic map in order to address the slow convergence rate, and to keep a very good equilibrium linking exploration and exploitation. Modification is done in two ways: (i) Initialization of population and (ii) Scaling factor.The proposed algorithm is validated with the aid of a 13 different benchmark functions taking from the literature, also the outcomes are compared along with 7 different popular state of art algorithms. Further, performance of the modified algorithm is simulated on 3 realistic engineering problems. Also compared with 8 recent optimizer techniques. Again from number of function evaluations it is clear that the proposed algorithm converses more quickly than the other existing algorithms.

Logistic Map and Exponential Scaling Factor-Based Differential Evolution

2022 ◽  
Vol 13 (1) ◽  
pp. 1-15
Author(s):  
Katyayani Kashyap ◽  
Sunil Pathak ◽  
Narendra Singh Yadav
Keyword(s):  
Differential Evolution ◽  
Logistic Map ◽  
Differential Evolution Algorithm ◽  
Scaling Factor ◽  
Exploration And Exploitation ◽  
Engineering Problems ◽  
Evolutionary Technique ◽  
Evolution Algorithm ◽  
State Of Art ◽  
Modified Algorithm

Differential evolution (DE), an important evolutionary technique, enhances its parameters such as, initialization of population, mutation, crossover etc. to resolve realistic optimization issues. This work represents a modified differential evolution algorithm by using the idea of exponential scale factor and logistic map in order to address the slow convergence rate, and to keep a very good equilibrium linking exploration and exploitation. Modification is done in two ways: (i) Initialization of population and (ii) Scaling factor.The proposed algorithm is validated with the aid of a 13 different benchmark functions taking from the literature, also the outcomes are compared along with 7 different popular state of art algorithms. Further, performance of the modified algorithm is simulated on 3 realistic engineering problems. Also compared with 8 recent optimizer techniques. Again from number of function evaluations it is clear that the proposed algorithm converses more quickly than the other existing algorithms.

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.

Differential Evolution Algorithm for Solving a Nonlinear Single Pendulum Problem

2014 ◽  
Vol 931-932 ◽  
pp. 1129-1133
Author(s):  
Natee Panagant ◽  
Sujin Bureerat
Keyword(s):  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Approximate Solutions ◽  
Scaling Factor ◽  
Fourier Series Expansion ◽  
De Algorithm ◽  
Pendulum Equation ◽  
Expansion Form ◽  
Evolution Algorithm ◽  
Speed And Accuracy

A differential evolution (DE) algorithm has been employed to approximate the solution of a nonlinear single pendulum equation. The solution has been approximated as a Fourier series expansion form. Then, weighted-residual and penalty functions are employed to transform the problem into a constrained optimization problem while optimum solutions will be carried out by DE. This paper also studies an effect of a scaling factor of DE to the results. The results reveal that the scaling factor significantly affects the convergent speed and accuracy of DE. Approximate solutions well agree with the exact solutions for the scaling factor being 0.5.

scholarly journals pSum-SaDE: A Modifiedp-Median Problem and Self-Adaptive Differential Evolution Algorithm for Text Summarization

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Rasim M. Alguliev ◽  
Ramiz M. Aliguliyev ◽  
Chingiz A. Mehdiyev
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Local Optimum ◽  
Exploration And Exploitation ◽  
Median Problem ◽  
Proposed Model ◽  
Adaptive Differential Evolution ◽  
Evolution Algorithm ◽  
Self Adaptive

Extractive multidocument summarization is modeled as a modifiedp-median problem. The problem is formulated with taking into account four basic requirements, namely, relevance, information coverage, diversity, and length limit that should satisfy summaries. To solve the optimization problem a self-adaptive differential evolution algorithm is created. Differential evolution has been proven to be an efficient and robust algorithm for many real optimization problems. However, it still may converge toward local optimum solutions, need to manually adjust the parameters, and finding the best values for the control parameters is a consuming task. In the paper is proposed a self-adaptive scaling factor in original DE to increase the exploration and exploitation ability. This paper has found that self-adaptive differential evolution can efficiently find the best solution in comparison with the canonical differential evolution. We implemented our model on multi-document summarization task. Experiments have shown that the proposed model is competitive on the DUC2006 dataset.

scholarly journals A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2163
Author(s):  
Xingping Sun ◽  
Da Wang ◽  
Hongwei Kang ◽  
Yong Shen ◽  
Qingyi Chen
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Solution Space ◽  
Population Diversity ◽  
Exploration And Exploitation ◽  
Two Stage ◽  
Mutation Strategy ◽  
Strategy Combination ◽  
Evolution Algorithm

For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, DE/current/1, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including DE/current/1 and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal problems.

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