scholarly journals A vectorized bimodal distribution based micro differential evolution algorithm (VB-mDE)

2020 ◽  
Vol 16 (3) ◽  
pp. 245-261
Author(s):  
Xu Chen ◽  
Xueliang Miao ◽  
Hugo Tianfield
Keyword(s):  
Differential Evolution ◽  
Performance Enhancement ◽  
Differential Evolution Algorithm ◽  
Main Idea ◽  
Cauchy Distribution ◽  
Bimodal Distribution ◽  
Small Population ◽  
Scale Factor ◽  
Population Diversity ◽  
Solution Accuracy

Micro differential evolution (mDE) refers to algorithms that evolve with a small population to search for good solutions. Although mDEs are very useful for resource-constrained optimization tasks, the research on mDEs is still limited. In this paper, we propose a new mDE, i.e., vectorized bimodal distribution based mDE (called VB-mDE). The main idea is to employ a vectorized bimodal distribution parameter adjustment mechanism in mDE for performance enhancement. Specifically, in the VB-mDE, two important control parameters, i.e., scale factor F and crossover rate C⁢R, are adjusted by bimodal Cauchy distribution. At the same time, to increase the population diversity, the scale factor F is vectorized. The proposed VB-mDE is evaluated on the CEC2014 benchmark functions and compared with the state-of-the-art mDEs and normal DEs. The results show that the proposed VB-mDE has advantages in terms of solution accuracy and convergence speed.

scholarly journals The Cellular Differential Evolution Based on Chaotic Local Search

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Qingfeng Ding ◽  
Guoxin Zheng
Keyword(s):  
Local Search ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Small Region ◽  
Population Diversity ◽  
Evolutionary Stage ◽  
Crossover Operator ◽  
De Algorithm ◽  
Solution Accuracy

To avoid immature convergence and tune the selection pressure in the differential evolution (DE) algorithm, a new differential evolution algorithm based on cellular automata and chaotic local search (CLS) or ccDE is proposed. To balance the exploration and exploitation tradeoff of differential evolution, the interaction among individuals is limited in cellular neighbors instead of controlling parameters in the canonical DE. To improve the optimizing performance of DE, the CLS helps by exploring a large region to avoid immature convergence in the early evolutionary stage and exploiting a small region to refine the final solutions in the later evolutionary stage. What is more, to improve the convergence characteristics and maintain the population diversity, the binomial crossover operator in the canonical DE may be instead by the orthogonal crossover operator without crossover rate. The performance of ccDE is widely evaluated on a set of 14 bound constrained numerical optimization problems compared with the canonical DE and several DE variants. The simulation results show that ccDE has better performances in terms of convergence rate and solution accuracy than other optimizers.

A new differential evolution algorithm with a combined mutation strategy for optimum synthesis of path-generating four-bar mechanisms

2016 ◽  
Vol 231 (14) ◽  
pp. 2690-2705 ◽  
Author(s):  
WY Lin ◽  
KM Hsiao
Keyword(s):  
Differential Evolution ◽  
Synthesis Method ◽  
Differential Evolution Algorithm ◽  
Population Diversity ◽  
Dimensional Synthesis ◽  
Solution Quality ◽  
De Algorithm ◽  
Mutation Operators ◽  
Mutation Strategy ◽  
Solution Accuracy

A one-phase synthesis method using heuristic optimization algorithms can solve the dimensional synthesis problems of path-generating four-bar mechanisms. However, due to the difficulty of the problem itself, there is still room for improvement in solution accuracy and reliability. Therefore, in this study, a new differential evolution (DE) algorithm with a combined mutation strategy, termed the combined-mutation differential evolution (CMDE) algorithm, is proposed to improve the solution quality. In the combined mutation strategy, the DE/best/1 operator and the DE/current-to-best/1 operator are respectively executed on some superior parents and some mediocre parents, and the DE/rand/1 operator is executed on the other inferior parents. Furthermore, the individuals participating in the three mutation operators are randomly selected from the entire set of parents. The proposed CMDE algorithm with the three different search modes possesses better population diversity as well as search ability than the DE algorithm. The effectiveness of the proposed CMDE algorithm is demonstrated using five representative problems. Findings show a marked improvement in solution accuracy and reliability. The most accurate results are obtained with an approximate combination ratio for the three mutation operators.

scholarly journals Synthesis of Sparse Concentric Ring Arrays Based on Fitness-Associated Differential Evolution Algorithm

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Xujian Wang ◽  
Minli Yao ◽  
Fenggan Zhang ◽  
Dingcheng Dai
Keyword(s):  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Population Diversity ◽  
Concentric Ring ◽  
Exploration Process ◽  
De Algorithm ◽  
Crossover Probability ◽  
Negative Effect ◽  
Evolution Algorithm ◽  
Enrich Population

In this paper, fitness-associated differential evolution (FITDE) algorithm is proposed and applied to the synthesis of sparse concentric ring arrays under constraint conditions, whose goal is to reduce peak sidelobe level. In unmodified differential evolution (DE) algorithm, crossover probability is constant and remains unchanged during the whole optimization process, resulting in the negative effect on the population diversity and convergence speed. Therefore, FITDE is proposed where crossover probability can change according to certain information. Firstly, the population fitness variance is introduced to the traditional differential evolution algorithm to adjust the constant crossover probability dynamically. The fitness variance in the earlier iterations is relatively large. Under this circumstance, the corresponding crossover probability shall be small to speed up the exploration process. As the iteration progresses, the fitness variance becomes small on the whole and the crossover probability should be set large to enrich population diversity. Thereby, we construct three variation strategies of crossover probability according to the above changing trend. Secondly, FITDE is tested on benchmark functions, and the best one of the three strategies is determined according to the test results. Finally, sparse concentric ring arrays are optimized using FITDE, of which the results are compared with reference algorithms. The optimization results manifest the advantageous effectiveness of FITDE.

scholarly journals Differential Evolution With Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

2021 ◽  
Author(s):  
Patricia Ochoa ◽  
Oscar Castillo ◽  
Patricia Melin ◽  
José Soria
Keyword(s):  
Differential Evolution ◽  
Fuzzy Systems ◽  
General Type ◽  
Differential Evolution Algorithm ◽  
Main Idea ◽  
Dynamic Parameter ◽  
Performance Comparison ◽  
Parameter Adaptation ◽  
Fuzzy Controllers

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

scholarly journals Structural Design and Optimization of a Resonant Micro-Accelerometer Based on Electrostatic Stiffness by an Improved Differential Evolution Algorithm

Micromachines ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 38
Author(s):  
Libin Huang ◽  
Qike Li ◽  
Yan Qin ◽  
Xukai Ding ◽  
Meimei Zhang ◽  
...  
Keyword(s):  
Resonant Frequency ◽  
Differential Evolution ◽  
Structural Design ◽  
Proof Mass ◽  
Differential Evolution Algorithm ◽  
Scale Factor ◽  
Global Optimality ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm ◽  
Micro Accelerometer

This study designed an in-plane resonant micro-accelerometer based on electrostatic stiffness. The accelerometer adopts a one-piece proof mass structure; two double-folded beam resonators are symmetrically distributed inside the proof mass, and only one displacement is introduced under the action of acceleration, which reduces the influence of processing errors on the performance of the accelerometer. The two resonators form a differential structure that can diminish the impact of common-mode errors. This accelerometer realizes the separation of the introduction of electrostatic stiffness and the detection of resonant frequency, which is conducive to the decoupling of accelerometer signals. An improved differential evolution algorithm was developed to optimize the scale factor of the accelerometer. Through the final elimination principle, excellent individuals are preserved, and the most suitable parameters are allocated to the surviving individuals to stimulate the offspring to find the globally optimal ability. The algorithm not only maintains the global optimality but also reduces the computational complexity of the algorithm and deterministically realizes the optimization of the accelerometer scale factor. The electrostatic stiffness resonant micro-accelerometer was fabricated by deep dry silicon-on-glass (DDSOG) technology. The unloaded resonant frequency of the accelerometer resonant beam was between 24 and 26 kHz, and the scale factor of the packaged accelerometer was between 54 and 59 Hz/g. The average error between the optimization result and the actual scale factor was 7.03%. The experimental results verified the rationality of the structural design.

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