scholarly journals Differential Evolution with Population and Strategy Parameter Adaptation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
V. Gonuguntla ◽  
R. Mallipeddi ◽  
Kalyana C. Veluvolu
Keyword(s):  
Differential Evolution ◽  
Population Size ◽  
Optimization Problems ◽  
Search Space ◽  
Benchmark Problems ◽  
Parameter Adaptation ◽  
De Algorithm ◽  
Probabilistic Technique ◽  
Number Of Individuals ◽  
Strategy Parameters

Differential evolution (DE) is simple and effective in solving numerous real-world global optimization problems. However, its effectiveness critically depends on the appropriate setting of population size and strategy parameters. Therefore, to obtain optimal performance the time-consuming preliminary tuning of parameters is needed. Recently, different strategy parameter adaptation techniques, which can automatically update the parameters to appropriate values to suit the characteristics of optimization problems, have been proposed. However, most of the works do not control the adaptation of the population size. In addition, they try to adapt each strategy parameters individually but do not take into account the interaction between the parameters that are being adapted. In this paper, we introduce a DE algorithm where both strategy parameters are self-adapted taking into account the parameter dependencies by means of a multivariate probabilistic technique based on Gaussian Adaptation working on the parameter space. In addition, the proposed DE algorithm starts by sampling a huge number of sample solutions in the search space and in each generation a constant number of individuals from huge sample set are adaptively selected to form the population that evolves. The proposed algorithm is evaluated on 14 benchmark problems of CEC 2005 with different dimensionality.

scholarly journals SWARM DIRECTIONS EMBEDDED DIFFERENTIAL EVOLUTION FOR FASTER CONVERGENCE OF GLOBAL OPTIMIZATION PROBLEMS

2012 ◽  
Vol 21 (03) ◽  
pp. 1240013 ◽  
Author(s):  
MUSRRAT ALI ◽  
MILLIE PANT ◽  
AJITH ABRAHAM ◽  
CHANG WOOK AHN
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Empirical Studies ◽  
Real Life ◽  
Search Space ◽  
Benchmark Problems ◽  
De Algorithm ◽  
Information Sharing Mechanism

In the present study we propose a new hybrid version of Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms called Hybrid DE or HDE for solving continuous global optimization problems. In the proposed HDE algorithm, information sharing mechanism of PSO is embedded in the contracted search space obtained by the basic DE algorithm. This is done to maintain a balance between the two antagonist factors; exploration and exploitation thereby obtaining a faster convergence. The embedding of swarm directions to the basic DE algorithm is done with the help of a "switchover constant" called α which keeps a record of the contraction of search space. The proposed HDE algorithm is tested on a set of 10 unconstrained benchmark problems and four constrained real life, mechanical design problems. Empirical studies show that the proposed scheme helps in improving the convergence rate of the basic DE algorithm without compromising with the quality of solution.

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.

scholarly journals Evaluation and application of Fuzzy Differential Evolution approach for benchmark optimization and reservoir operation problems

2013 ◽  
Vol 15 (4) ◽  
pp. 1456-1473 ◽  
Author(s):  
Dejan Vucetic ◽  
Slobodan P. Simonovic
Keyword(s):  
Differential Evolution ◽  
Reservoir Operation ◽  
Optimization Problems ◽  
Search Space ◽  
Search Technique ◽  
Continuous Space ◽  
De Algorithm ◽  
Alternative Approach ◽  
Fuzzy Interval

The differential evolution (DE) algorithm is a powerful search technique for solving global optimization problems over continuous space. The search initialization for this algorithm is handled stochastically and therefore does not adequately capture vague preliminary knowledge. This paper proposes a novel Fuzzy Differential Evolution (FDE) algorithm, as an alternative approach, where the vague information on the search space can be represented and used to deliver a more focused search. The proposed FDE algorithm utilizes (a) fuzzy numbers to represent vague knowledge and (b) random alpha-cut levels for the search initialization. The alpha-cut intervals created during the initialization are used for fuzzy interval based mutation in successive search iterations. Four benchmark functions are used to demonstrate performance of the new FDE and its practical value. Additionally, the application of the FDE algorithm is illustrated through a reservoir operation case study problem. The new algorithm shows faster convergence in most of these functions.

scholarly journals An enhanced differential evolution algorithm with adaptation of switching crossover strategy for continuous optimization

2020 ◽  
Vol 45 (2) ◽  
pp. 97-124
Author(s):  
Pikul Puphasuk ◽  
Jeerayut Wetweerapong
Keyword(s):  
Differential Evolution ◽  
Population Size ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Continuous Optimization ◽  
Optimization Method ◽  
Benchmark Problems ◽  
Systems Of Nonlinear Equations ◽  
Wide Range ◽  
Evolution Algorithm

AbstractDesigning an efficient optimization method which also has a simple structure is generally required by users for its applications to a wide range of practical problems. In this research, an enhanced differential evolution algorithm with adaptation of switching crossover strategy (DEASC) is proposed as a general-purpose population-based optimization method for continuous optimization problems. DEASC extends the solving ability of a basic differential evolution algorithm (DE) whose performance significantly depends on user selection of the control parameters: scaling factor, crossover rate and population size. Like the original DE, the proposed method is aimed at e ciency, simplicity and robustness. The appropriate population size is selected to work in accordance with good choices of the scaling factors. Then, the switching crossover strategy of using low or high crossover rates are incorporated and adapted to suit the problem being solved. In this manner, the adaptation strategy is just a convenient add-on mechanism. To verify the performance of DEASC, it is tested on several benchmark problems of various types and di culties, and compared with some well-known methods in the literature. It is also applied to solve some practical systems of nonlinear equations. Despite its much simpler algorithmic structure, the experimental results show that DEASC greatly enhances the basic DE. It is able to solve all the test problems with fast convergence speed and overall outperforms the compared methods which have more complicated structures. In addition, DEASC also shows promising results on high dimensional test functions.

A New Differential Evolution Based Metaheuristic for Discrete Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 15-32 ◽  
Author(s):  
Ricardo Sérgio Prado ◽  
Rodrigo César Pedrosa Silva ◽  
Frederico Gadelha Guimarães ◽  
Oriane Magela Neto
Keyword(s):  
Combinatorial Optimization ◽  
Differential Evolution ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Search Space ◽  
Combinatorial Problems ◽  
Combinatorial Optimization Problems ◽  
De Algorithm ◽  
The Difference

The Differential Evolution (DE) algorithm is an important and powerful evolutionary optimizer in the context of continuous numerical optimization. Recently, some authors have proposed adaptations of its differential mutation mechanism to deal with combinatorial optimization, in particular permutation-based integer combinatorial problems. In this paper, the authors propose a novel and general DE-based metaheuristic that preserves its interesting search mechanism for discrete domains by defining the difference between two candidate solutions as a list of movements in the search space. In this way, the authors produce a more meaningful and general differential mutation for the context of combinatorial optimization problems. The movements in the list can then be applied to other candidate solutions in the population as required by the differential mutation operator. This paper presents results on instances of the Travelling Salesman Problem (TSP) and the N-Queen Problem (NQP) that suggest the adequacy of the proposed approach for adapting the differential mutation to discrete optimization.

scholarly journals Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

2021 ◽  
Author(s):  
Prachi Agrawal ◽  
Talari Ganesh ◽  
Ali Wagdy Mohamed
Keyword(s):  
Life Span ◽  
Population Size ◽  
Linear Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Knapsack Problems ◽  
Local Optima ◽  
Knowledge Based ◽  
Two Stages

AbstractThis article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

Optimization of Antenna Design Problems Using Binary Differential Evolution

2018 ◽  
pp. 614-636
Author(s):  
Sotirios K. Goudos
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Phase Shifters ◽  
Antenna Design ◽  
Design Problems ◽  
Array Design ◽  
Search Spaces ◽  
De Algorithm ◽  
Discrete Phase ◽  
Binary Differential Evolution

Differential Evolution (DE) is a popular evolutionary algorithm that has been applied to several antenna design problems. However, DE is best suited for continuous search spaces. Therefore, in order to apply it to combinatorial optimization problems for antenna design a binary version of the DE algorithm has to be used. In this chapter, the author presents a design technique based on Novel Binary DE (NBDE). The main benefit of NBDE is reserving the DE updating strategy to binary space. This chapter presents results from design cases that include array thinning, phased array design with discrete phase shifters, and conformal array design with discrete excitations based on NBDE.

scholarly journals Differential Evolution with Linear Bias Reduction in Parameter Adaptation

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 283
Author(s):  
Vladimir Stanovov ◽  
Shakhnaz Akhmedova ◽  
Eugene Semenkin
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Bias Reduction ◽  
Benchmark Problems ◽  
Basic Algorithm ◽  
Optimization Stage ◽  
Speed Up ◽  
Comparison Of The Results ◽  
Lehmer Mean

In this study, a new parameter control scheme is proposed for the differential evolution algorithm. The developed linear bias reduction scheme controls the Lehmer mean parameter value depending on the optimization stage, allowing the algorithm to improve the exploration properties at the beginning of the search and speed up the exploitation at the end of the search. As a basic algorithm, the L-SHADE approach is considered, as well as its modifications, namely the jSO and DISH algorithms. The experiments are performed on the CEC 2017 and 2020 bound-constrained benchmark problems, and the performed statistical comparison of the results demonstrates that the linear bias reduction allows significant improvement of the differential evolution performance for various types of optimization problems.

Centroid Opposition-Based Differential Evolution

2014 ◽  
Vol 5 (4) ◽  
pp. 1-25 ◽  
Author(s):  
Shahryar Rahnamayan ◽  
Jude Jesuthasan ◽  
Farid Bourennani ◽  
Greg F. Naterer ◽  
Hojjat Salehinejad
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Extreme Points ◽  
Search Space ◽  
Population Based ◽  
Effective Population ◽  
Centroid Point ◽  
Opposite Point ◽  
Novel Concept ◽  
Multiple Variants

The capabilities of evolutionary algorithms (EAs) in solving nonlinear and non-convex optimization problems are significant. Differential evolution (DE) is an effective population-based EA, which has emerged as very competitive. Since its inception in 1995, multiple variants of DE have been proposed with higher performance. Among these DE variants, opposition-based differential evolution (ODE) established a novel concept in which individuals must compete with theirs opposites in order to make an entry in the next generation. The generation of opposite points is based on the current extreme points (i.e., maximum and minimum) in the search space. This paper develops a new scheme that utilizes the centroid point of a population to calculate opposite individuals. The classical scheme of an opposite point is modified. Incorporating this new scheme into DE leads to an enhanced ODE that is identified as centroid opposition-based differential evolution (CODE). The accuracy of the CODE algorithm is comprehensively evaluated on well-known complex benchmark functions and compared with the performance of conventional DE, ODE, and other state-of-the-art algorithms. The results for CODE are found to be promising.

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.

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