A Fractal Mutation Factor Modified Differential Evolution Algorithm

2014 ◽  
Vol 598 ◽  
pp. 418-423 ◽  
Author(s):  
Xiao Hong Qiu ◽  
Bo Li ◽  
Zhi Yong Cui ◽  
Jing Li
Keyword(s):  
Brownian Motion ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Hurst Index ◽  
Test Results ◽  
Fractal Brownian Motion ◽  
Mutation Strategy ◽  
Evolution Algorithm ◽  
Better Than

To get better solution by improving the mutation strategy of Differential Evolution algorithm, a fractal mutation strategy is introduced. The fractal mutation factor of the proposed Fractal Mutation factor Differential Evolution (FMDE) algorithm is simulated by fractal Brownian motion with a different Hurst index. The new algorithm is test on 25 benchmark functions presented at 2005 IEEE Congress on Evolutionary Computation (CEC2005). The optimization results of at least 10 benchmark functions are significantly better than the results obtained by JADE and CoDE, and most of the rest of the test results are approximate. This shows that FMDE can significantly improve the accuracy and adaptability to solve optimization problems.

scholarly journals Multiscale Cooperative Differential Evolution Algorithm

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Yongzhao Du ◽  
Yuling Fan ◽  
Xiaofang Liu ◽  
Yanmin Luo ◽  
Jianeng Tang ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Early Stage ◽  
Differential Evolution Algorithm ◽  
Search Range ◽  
Adaptive Parameter ◽  
Mutation Strategy ◽  
Evolution Algorithm ◽  
Evolution Algorithms ◽  
The Individual

A multiscale cooperative differential evolution algorithm is proposed to solve the problems of narrow search range at the early stage and slow convergence at the later stage in the performance of the traditional differential evolution algorithms. Firstly, the population structure of multipopulation mechanism is adopted so that each subpopulation is combined with a corresponding mutation strategy to ensure the individual diversity during evolution. Then, the covariance learning among populations is developed to establish a suitable rotating coordinate system for cross operation. Meanwhile, an adaptive parameter adjustment strategy is introduced to balance the population survey and convergence. Finally, the proposed algorithm is tested on the CEC 2005 benchmark function and compared with other state-of-the-art evolutionary algorithms. The experiment results showed that the proposed algorithm has better performance in solving global optimization problems than other compared algorithms.

scholarly journals An Improved Differential Evolution Algorithm Based on Dual-Strategy

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Xuxu Zhong ◽  
Peng Cheng
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Positive Impact ◽  
Differential Evolution Algorithm ◽  
Population Diversity ◽  
Fitness Value ◽  
Mutation Strategy ◽  
Dual Strategy ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm

In recent years, Differential Evolution (DE) has shown excellent performance in solving optimization problems over continuous space and has been widely used in many fields of science and engineering. How to avoid the local optimal solution and how to improve the convergence performance of DE are hotpot problems for many researchers. In this paper, an improved differential evolution algorithm based on dual-strategy (DSIDE) is proposed. The DSIDE algorithm has two strategies. (1) An enhanced mutation strategy based on “DE/rand/1,” which takes into account the influence of reference individuals on mutation and has strong global exploration and convergence ability. (2) A novel adaptive strategy for scaling factor and crossover probability based on fitness value has a positive impact on population diversity. The DSIDE algorithm is verified with other seven state-of-the-art DE variants under 30 benchmark functions. Furthermore, Wilcoxon sign rank-sum test, Friedman test, and Kruskal–Wallis test are utilized to analyze the results. The experiment results show that the proposed DSIDE algorithm can significantly improve the global optimization performance.

A History-Driven Differential Evolution Algorithm for Optimization in Dynamic Environments

2018 ◽  
Vol 27 (06) ◽  
pp. 1850028
Author(s):  
Zhen Zhu ◽  
Long Chen ◽  
Changgao Xia ◽  
Chaochun Yuan
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Global Optimum ◽  
Trial Vector ◽  
Benchmark Instances ◽  
Evolution Algorithm ◽  
Selection Operator ◽  
New Location ◽  
Better Than

This paper presents a novel differential evolution algorithm to solve dynamic optimization problems. In the proposed algorithm, the entire population is composed of several subpopulations, which are evolved independently and excluded each other by a predefined Euclidian-distance. In each subpopulation, the “DE/best/1” mutation operator is employed to generate a mutant individual in this paper. In order to fully exploit the newly generated individual, the selection operator was extended, in which the newly generated trial vector competed with the worst individual if this trial vector was worse than the target vector in terms of the fitness. Meanwhile, this trial vector was stored as the historical information, if it was better than the worst individual. When the environmental change was detected, some of the stored solutions were retrieved and expected to guide the reinitialized solutions to track the new location of the global optimum as soon as possible. The proposed algorithm was compared with several state-of-the-art dynamic evolutionary algorithms over the representative benchmark instances. The experimental results show that the proposed algorithm outperforms the competitors.

scholarly journals An Enhancing Differential Evolution Algorithm with a Rank-Up Selection: RUSDE

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 569
Author(s):  
Kai Zhang ◽  
Yicheng Yu
Keyword(s):  
Differential Evolution ◽  
Optimization Problem ◽  
Differential Evolution Algorithm ◽  
Iteration Process ◽  
Excellent Performance ◽  
De Algorithm ◽  
Current Population ◽  
Mutation Strategy ◽  
Evolution Algorithm ◽  
Better Than

Recently, the differential evolution (DE) algorithm has been widely used to solve many practical problems. However, DE may suffer from stagnation problems in the iteration process. Thus, we propose an enhancing differential evolution with a rank-up selection, named RUSDE. First, the rank-up individuals in the current population are selected and stored into a new archive; second, a debating mutation strategy is adopted in terms of the updating status of the current population to decide the parent’s selection. Both of the two methods can improve the performance of DE. We conducted numerical experiments based on various functions from CEC 2014, where the results demonstrated excellent performance of this algorithm. Furthermore, this algorithm is applied to the real-world optimization problem of the four-bar linkages, where the results show that the performance of RUSDE is better than other algorithms.

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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