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 A Convergent Differential Evolution Algorithm with Hidden Adaptation Selection for Engineering Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zhongbo Hu ◽  
Shengwu Xiong ◽  
Zhixiang Fang ◽  
Qinghua Su
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Population Diversity ◽  
Engineering Optimization ◽  
De Algorithm ◽  
Self Adaptation ◽  
Evolution Algorithm ◽  
Selection For ◽  
Adaptation Scheme

Many improved differential Evolution (DE) algorithms have emerged as a very competitive class of evolutionary computation more than a decade ago. However, few improved DE algorithms guarantee global convergence in theory. This paper developed a convergent DE algorithm in theory, which employs a self-adaptation scheme for the parameters and two operators, that is, uniform mutation and hidden adaptation selection (haS) operators. The parameter self-adaptation and uniform mutation operator enhance the diversity of populations and guarantee ergodicity. The haS can automatically remove some inferior individuals in the process of the enhancing population diversity. The haS controls the proposed algorithm to break the loop of current generation with a small probability. The breaking probability is a hidden adaptation and proportional to the changes of the number of inferior individuals. The proposed algorithm is tested on ten engineering optimization problems taken from IEEE CEC2011.

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.

An Improved Differential Evolution Algorithm for Numerical Optimization Problems

2013 ◽  
Vol 415 ◽  
pp. 349-352
Author(s):  
Hong Wei Zhao ◽  
Hong Gang Xia
Keyword(s):  
Differential Evolution ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Local Optimum ◽  
Local Optima ◽  
De Algorithm ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm

Differential evolution (DE) is a population-based stochastic function minimizer (or maximizer), whose simple yet powerful and straightforward features make it very attractive for numerical optimization. However, DE is easy to trapped into local optima. In this paper, an improved differential evolution algorithm (IDE) proposed to speed the convergence rate of DE and enhance the global search of DE. The IDE employed a new mutation operation and modified crossover operation. The former can rapidly enhance the convergence of the MDE, and the latter can prevent the MDE from being trapped into the local optimum effectively. Besides, we dynamic adjust the scaling factor (F) and the crossover rate (CR), which is aimed at further improving algorithm performance. Based on several benchmark experiment simulations, the IDE has demonstrated stronger convergence and stability than original differential (DE) algorithm and other algorithms (PSO and JADE) that reported in recent literature.

scholarly journals An implementation of differential evolution algorithm for a single product and single period multi-echelon supply chain network model

2018 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
Ayda Emdadian ◽  
S. G. Ponnambalam ◽  
G. Kanagaraj
Keyword(s):  
Supply Chain ◽  
Differential Evolution ◽  
Network Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Value Added ◽  
Raw Material ◽  
Supply Chain Network ◽  
De Algorithm ◽  
Chain Problem

In this paper, five variants of Differential Evolution (DE) algorithms are proposed to solve the multi-echelon supply chain network optimization problem. Supply chain network composed of different stages which involves products, services and information flow between suppliers and customers, is a value-added chain that provides customers products with the quickest delivery and the most competitive price. Hence, there is a need to optimize the supply chain by finding the optimum configuration of the network in order to get a good compromise between several objectives. The supply chain problem utilized in this study is taken from literature which incorporates demand, capacity, raw-material availability, and sequencing constraints in order to maximize total profitability. The performance of DE variants has been investigated by solving three stage multi-echelon supply chain network optimization problems for twenty demand scenarios with each supply chain settings. The objective is to find the optimal alignment of procurement, production, and distribution while aiming towards maximizing profit. The results show that the proposed DE algorithm is able to achieve better performance on a set of supply chain problem with different scenarios those obtained by well-known classical GA and PSO.

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 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 Comparison of a novel dominance-based differential evolution method with the state-of-the-art methods for solving multi-objective real-valued optimization problems

2021 ◽  
pp. 14-25
Author(s):  
Mustafa Tuncay ◽  
Ali Haydar
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
State Of The Art ◽  
Selection Process ◽  
Dominance Rank ◽  
Differential Evolution Algorithm ◽  
Test Problems ◽  
Evolutionary Computations ◽  
De Algorithm ◽  
Art Methods

Differential Evolution algorithm (DE) is a well-known nature-inspired method in evolutionary computations scope. This paper adds some new features to DE algorithm and proposes a novel method focusing on ranking technique. The proposed method is named as Dominance-Based Differential Evolution, called DBDE from this point on, which is the improved version of the standard DE algorithm. The suggested DBDE applies some changes on the selection operator of the Differential Evolution (DE) algorithm and modifies the crossover and initialization phases to improve the performance of DE. The dominance ranks are used in the selection phase of DBDE to be capable of selecting higher quality solutions. A dominance-rank for solution X is the number of solutions dominating X. Moreover, some vectors called target vectors are used through the selection process. Effectiveness and performance of the proposed DBDE method is experimentally evaluated using six well-known benchmarks, provided by CEC2009, plus two additional test problems namely Kursawe and Fonseca & Fleming. The evaluation process emphasizes on specific bi-objective real-valued optimization problems reported in literature. Likewise, the Inverted Generational Distance (IGD) metric is calculated for the obtained results to measure the performance of algorithms. To follow up the evaluation rules obeyed by all state-of-the-art methods, the fitness evaluation function is called 300.000 times and 30 independent runs of DBDE is carried out. Analysis of the obtained results indicates that the performance of the proposed algorithm (DBDE) in terms of convergence and robustness outperforms the majority of state-of-the-art methods reported in the literature

A Cultivated Variant of Differential Evolution Algorithm for Global Optimization

2016 ◽  
pp. 1-19
Author(s):  
Pooja
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Benchmark Problems ◽  
De Algorithm ◽  
Molecular Potential ◽  
Acceleration Rate ◽  
Base Vector ◽  
Molecular Potential Energy

Differential Evolution (DE) algorithm is known as robust, effective and highly efficient for solving the global optimization problems. In this chapter, a modified variant of Differential Evolution (DE) is proposed, named Cultivated Differential Evolution (CuDE) which is different from basic DE in two ways: 1) the selection of the base vector for mutation operation, 2) population generation for the next generation. The performance of the proposed algorithm is validated on a set of eight benchmark problems taken from literature and a real time molecular potential energy problem. The numerical results show that the proposed approach helps in formulating a better trade-off between convergence rate and efficiency. Also, it can be seen that the performance of DE is improved in terms of number of function evaluations, acceleration rate and mean error.

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