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## 1 DE/BBO: A Hybrid Differential Evolution with Biogeography-Based Optimization for Global Numerical Optimization

### Citations

817 |
Differential evolution a simple and efficient heuristic for global optimisation over continuous spaces.
- Storn, Price
- 1997
(Show Context)
Citation Context ...or more existing individuals. According to a fitness measure, the selection process favors better individuals to reproduce more often than those that are relatively worse. Differential Evolution (DE) =-=[2]-=- is a simple yet powerful population-based, direct search algorithm with the generationand-test feature for global optimization problems using realThis work was supported by the Fund for Outstanding D... |

443 |
Differential Evolution: A Practical Approach to Global Optimization.
- Price, Storn, et al.
- 2005
(Show Context)
Citation Context ...antages are its simple structure, ease of use, speed and robustness. Price and Storn [2] gave the working principle of DE with single scheme. Later on, they suggested ten different schemes of DE [3], =-=[4]-=-. However, DE has been shown to have certain weaknesses, especially if the global optimum should be located using a limited number of fitness function evaluations (NFFEs). In addition, DE is good at e... |

413 |
An overview of evolutionary algorithms for parameter optimization,
- Bäck, Schwefel
- 1993
(Show Context)
Citation Context ...s (EAs, including genetic algorithms, evolution strategies, evolutionary programming, and genetic programming) have received much attention regarding their potential as global optimization techniques =-=[1]-=-, both in single and in multi-objective optimization. Inspired by the natural evolution and survival of the fittest, EAs utilize a collective learning process of a population of individuals. Descendan... |

343 | Evolutionary programming made faster,”
- Yao, Liu, et al.
- 1999
(Show Context)
Citation Context ...ized as a pair (S, f) , where S ⊆ R D is a bounded set on R D and f : S → R is a D-dimensional realvalued function. The problem is to find a point X ∗ ∈ S such that f(X ∗ ) is the global minimum on S =-=[8]-=-. More specifically, it is required to find an X ∗ ∈ S such that ∀X ∈ S : f(X ∗ ) ≤ f(X) (1) where f does not need to be continuous but it must be bounded. In this work, we only consider the unconstra... |

136 | Biogeography-based optimization,‖
- Simon
- 2008
(Show Context)
Citation Context ...ition, DE is good at exploring the search space and locating the region of global minimum, but it is slow at exploitation of the solution [5]. Biogeography-Based Optimization (BBO), proposed by Simon =-=[6]-=-, is a new global optimization algorithm based on the biogeography theory, which is the study of the geographical distribution of biological organisms. Similar to GAs, BBO is a population-based, stoch... |

125 | Differential evolution algorithm with strategy adaptation for global numerical optimization,”
- Qin, Huang, et al.
- 2009
(Show Context)
Citation Context ...nd the choice of them is often critical for the performance of DE [19], [20]. Second, choosing the best among different mutation schemes available for DE is also not easy for a specific problem [27], =-=[28]-=-. Third, DE is good at exploring the search space and locating the region of global minimum, but it is slow at exploitation of the solution [5]. Due to these drawbacks, many researchers are now workin... |

75 |
Opposition-based differential evolution,”
- Rahnamayan, Tizhoosh, et al.
- 2008
(Show Context)
Citation Context ...ncorporated in DE. Experiments on 28 benchmark problems, including 13 high dimensional functions, showed that the new method is able to find near optimal solutions efficiently [35]. Rahnamayan et al. =-=[36]-=- proposed a novel initialization approach which employs opposition-based learning to generate initial population. Through a comprehensive set of benchmark functions4 they showed that replacing the ra... |

71 |
Suganthan “Self-adaptive Differential Evolution Algorithm for Constrained Real-Parameter Optimization”, In:
- Huang, Qin, et al.
(Show Context)
Citation Context ...dent and the choice of them is often critical for the performance of DE [19], [20]. Second, choosing the best among different mutation schemes available for DE is also not easy for a specific problem =-=[27]-=-, [28]. Third, DE is good at exploring the search space and locating the region of global minimum, but it is slow at exploitation of the solution [5]. Due to these drawbacks, many researchers are now ... |

60 |
A fuzzy adaptive differential evolution algorithm,”
- Liu, Lampinen
- 2005
(Show Context)
Citation Context ...ointed out that there are three main drawbacks of the original DE algorithm. First, the parameters of DE are problem dependent and the choice of them is often critical for the performance of DE [19], =-=[20]-=-. Second, choosing the best among different mutation schemes available for DE is also not easy for a specific problem [27], [28]. Third, DE is good at exploring the search space and locating the regio... |

55 |
Accelerating differential evolution using an adaptive local search,”
- Noman, Iba
- 2008
(Show Context)
Citation Context ...e of SADE. H. Comparison with other DE hybrids In this section, we make a comparison with other DE hybrids. Since there are many variants of DE, we only compare our approach with DEahcSPX proposed in =-=[5]-=-, ODE proposed in [36], and DE/EDA proposed in [30]. 1) Comparison with DEahcSPX and ODE: Firstly, we compare our approach with DEahcSPX and ODE. In DEahcSPX, a crossover-based adaptive local search o... |

51 | Fast Evolution Strategies,
- Yao, Liu
- 1997
(Show Context)
Citation Context ...mputation (EC) [1] to solve the global optimization has been very active, producing different kinds of EC for optimization in the continuous domain, such as genetic algorithms [9], evolution strategy =-=[10]-=-, evolutionary programming [8], particle swarm optimization [11], immune clonal algorithm [12], differential evolution [2], etc. B. Differential evolution The DE algorithm [2] is a simple EA that crea... |

48 |
Methods of Statistical Analysis.
- Goulden
- 1960
(Show Context)
Citation Context ...The paired t-test determines whether two paired sets differ from each other in a significant way under the assumptions that the paired differences are independent and identically normally distributed =-=[38]-=-. with many local minima (f08 - f13), DE/BBO can obtain the V TR = 10 −8 over all 50 runs within the Max NFFEs. However, DE may trap into the local minima for five out of six functions. This indicates... |

47 |
A Trigonometric Mutation Operation to Differential Evolution.
- Fan, Lampinen
- 2003
(Show Context)
Citation Context ...rformed the original DE and some other compared adaptive/self-adaptive DE variants [28]. Hybridization with other different algorithms is another direction for the improvement of DE. Fan and Lampinen =-=[29]-=- proposed a new version of DE that uses an additional mutation operation called trigonometric mutation operation. They showed that the modified DE algorithm can outperform the classic DE algorithm for... |

39 | Two improved differential evolution schemes for faster global search,”
- Das, Konar, et al.
- 2005
(Show Context)
Citation Context ...obakhti and Wang [23] proposed a Randomized Adaptive Differential Evolution (RADE) method, where a simple randomized self-adaptive scheme was proposed for the mutation weighting factor F . Das et al. =-=[24]-=- proposed 1 Since the mutation operator of BBO is not used in our approach, we do not describe it here. Interested readers can refer to [6] and [18]. two variants of DE, DERSF and DETVSF, that use var... |

31 | A multiagent genetic algorithm for global numerical optimization. - Zhong, Liu, et al. - 2004 |

28 | Automatic Clustering Using an Improved Differential Evolution Algorithm”,
- Das, Abraham, et al.
- 2008
(Show Context)
Citation Context ...outperforms traditional EAs. Among DE’s advantages are its simple structure, ease of use, speed and robustness. Due to these advantages, it has many real-world applications, such as data mining [13], =-=[14]-=-, pattern recognition, digital filter design, neural network training, etc. [4], [15], [16]. Most recently, DE has also been used for the global permutation-based combinatorial optimization problems [... |

28 |
Exploring dynamic self-adaptive populations in differential evolution,”
- Teo
- 2006
(Show Context)
Citation Context ...escribe it here. Interested readers can refer to [6] and [18]. two variants of DE, DERSF and DETVSF, that use varying scale factors. They concluded that those variants outperform the original DE. Teo =-=[25]-=- presented a dynamic self-adaptive populations DE, where the population size is self-adapting. Through five De Jong’s test functions, they showed that DE with self-adaptive populations produced highly... |

25 | DE/EDA: a new evolutionary algorithm for global optimization,”
- Sun, Zhang, et al.
- 2005
(Show Context)
Citation Context ... mutation operation called trigonometric mutation operation. They showed that the modified DE algorithm can outperform the classic DE algorithm for some benchmarks and real-world problems. Sun et al. =-=[30]-=- proposed a new hybrid algorithm based on a combination of DE with Estimation of Distribution Algorithm (EDA). This technique uses a probability model to determine promising regions in order to focus ... |

23 | Enhancing differential evolution performance with local search for high dimensional function optimization,
- Noman, Iba
- 2005
(Show Context)
Citation Context ...over to improve the performance of DE. They showed that the proposed approach performs better than the classical DE in terms of the quality, speed, and stability of the final solutions. Noman and Iba =-=[32]-=- proposed fittest individual refinement, a crossover-based local search (LS) method DE to solve the high dimensional problems. Based on their previous work [32], they incorporated LS into the classica... |

21 |
Differential Evolution
- Feoktistov
- 2006
(Show Context)
Citation Context ...use, speed and robustness. Due to these advantages, it has many real-world applications, such as data mining [13], [14], pattern recognition, digital filter design, neural network training, etc. [4], =-=[15]-=-, [16]. Most recently, DE has also been used for the global permutation-based combinatorial optimization problems [17]. The pseudo-code of the original DE algorithm is shown in Algorithm 1. Where D is... |

20 |
MODENAR: multi-objective differential evolution algorithm formining numeric association rules,”Applied
- Alatas, Akin, et al.
- 2008
(Show Context)
Citation Context ...often outperforms traditional EAs. Among DE’s advantages are its simple structure, ease of use, speed and robustness. Due to these advantages, it has many real-world applications, such as data mining =-=[13]-=-, [14], pattern recognition, digital filter design, neural network training, etc. [4], [15], [16]. Most recently, DE has also been used for the global permutation-based combinatorial optimization prob... |

19 |
Making a difference to differential evolution,”
- Yang, He, et al.
- 2008
(Show Context)
Citation Context ...east comparably, to classic DE algorithm. Kaelo and Ali [33] adopted the attraction-repulsion concept of electromagnetismlike algorithm to boost the mutation operation of the original DE. Yang et al. =-=[34]-=- proposed a neighborhood search based DE algorithm. Experimental results showed that DE with neighborhood search has significant advantages over other existing algorithms on a broad range of different... |

16 |
Population size reduction for the differential evolution algorithm
- Brest, Maučec
- 2008
(Show Context)
Citation Context ...ulations DE, where the population size is self-adapting. Through five De Jong’s test functions, they showed that DE with self-adaptive populations produced highly competitive results. Brest and Mauěc =-=[26]-=- proposed an improved DE method, where the population size is gradually reduced. They concluded that their approach improved efficiency and robustness of DE. Qin and Suganthan [27] proposed a self-ada... |

13 | Hybrid Evolutionary Algorithms, - Grosan, Abraham, et al. - 2007 |

10 |
A simple self-adaptive Differential Evolution algorithm with application on
- Nobakhti, Wang
- 2008
(Show Context)
Citation Context ...t eliminates the need for manual tuning of control parameters. In SDE, the mutation weighting factor F is self-adapted by a mutation strategy similar to the mutation operator of DE. Nobakhti and Wang =-=[23]-=- proposed a Randomized Adaptive Differential Evolution (RADE) method, where a simple randomized self-adaptive scheme was proposed for the mutation weighting factor F . Das et al. [24] proposed 1 Since... |

10 |
Generalization of the strategies in differential evolution.
- Feoktistov, Janaqi
- 2004
(Show Context)
Citation Context ... population size will increase the diversity of possible movements, promoting the exploration of the search space. However, the probability to find the correct search direction decreases considerably =-=[39]-=-. The influence of population size is investigated in this section. For both DE/BBO and DE, all the parameter settings are the same as mentioned in Section VA, only except for NP = 50, NP = 150, and N... |

9 |
Differential evolution algorithms using hybrid mutation
- Kaelo, Ali
- 2007
(Show Context)
Citation Context ...of the search, using a hillclimbing heuristic. Through the experiments, they showed that the proposed new version of DE performs better, or at least comparably, to classic DE algorithm. Kaelo and Ali =-=[33]-=- adopted the attraction-repulsion concept of electromagnetismlike algorithm to boost the mutation operation of the original DE. Yang et al. [34] proposed a neighborhood search based DE algorithm. Expe... |

9 |
A dynamic clustering based differential evolution algorithm for global optimization,”
- Wang, Zhang, et al.
- 2007
(Show Context)
Citation Context ...E algorithm. Experimental results showed that DE with neighborhood search has significant advantages over other existing algorithms on a broad range of different benchmark functions [34]. Wang et al. =-=[35]-=- proposed a dynamic clustering-based DE for global optimization, where a hierarchical clustering method is dynamically incorporated in DE. Experiments on 28 benchmark problems, including 13 high dimen... |

8 |
et al., “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions
- Liang
- 2006
(Show Context)
Citation Context ...y active, producing different kinds of EC for optimization in the continuous domain, such as genetic algorithms [9], evolution strategy [10], evolutionary programming [8], particle swarm optimization =-=[11]-=-, immune clonal algorithm [12], differential evolution [2], etc. B. Differential evolution The DE algorithm [2] is a simple EA that creates new candidate solutions by combining the parent individual a... |

8 | Liang et al., “Problem definitions and evaluation criteria for theCEC 2005 special session on real-parameter optimization - Suganthan, Hansen, et al. - 2005 |

7 |
The Matlab code of biogeography-based optimization,”
- Simon
- 2008
(Show Context)
Citation Context ...useful information from good solutions. This makes BBO be good at exploiting the information of the current population. More details about the two operators can be found in [6] and in the Matlab code =-=[18]-=-. III. RELATED WORK TO DE Some previous researches pointed out that there are three main drawbacks of the original DE algorithm. First, the parameters of DE are problem dependent and the choice of the... |

7 |
Boskovie B, et al. Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems
- Brest, Greiner
(Show Context)
Citation Context ...ters is one possible improvement. Liu and Lampinen [20] proposed a Fuzzy Adaptive DE (FADE), which employs fuzzy logic controllers to adapt the mutation and crossover control parameters. Brest et al. =-=[21]-=- proposed self-adapting control parameter settings. Their proposed approach encodes the F and CR parameters into the chromosome and uses a self-adaptive control mechanism to change them. Salman et al.... |

4 |
Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization,
- Onwubolu, Davendra
- 2009
(Show Context)
Citation Context ...], pattern recognition, digital filter design, neural network training, etc. [4], [15], [16]. Most recently, DE has also been used for the global permutation-based combinatorial optimization problems =-=[17]-=-. The pseudo-code of the original DE algorithm is shown in Algorithm 1. Where D is the number of decision variables. NP is the size of the parent population P . F is the mutation scaling factor. CR is... |

4 |
A fast and robust differential evolution based on
- Gong, Cai, et al.
- 2006
(Show Context)
Citation Context ...bination of DE with Estimation of Distribution Algorithm (EDA). This technique uses a probability model to determine promising regions in order to focus the search process on those areas. Gong et al. =-=[31]-=- employed the two level orthogonal crossover to improve the performance of DE. They showed that the proposed approach performs better than the classical DE in terms of the quality, speed, and stabilit... |

3 |
Quantum-inspired immune clonal algorithm for global numerical optimization
- Jiao, Li, et al.
- 2008
(Show Context)
Citation Context ...kinds of EC for optimization in the continuous domain, such as genetic algorithms [9], evolution strategy [10], evolutionary programming [8], particle swarm optimization [11], immune clonal algorithm =-=[12]-=-, differential evolution [2], etc. B. Differential evolution The DE algorithm [2] is a simple EA that creates new candidate solutions by combining the parent individual and several other individuals o... |

1 |
Home page of differential evolution. Available online at http://www.ICSI.Berkeley.edu/˜storn/code.html
- Storn, Price
- 2008
(Show Context)
Citation Context ...irection information from the current population to guide the further search. It won the third place at the first International Contest on Evolutionary Computation on a real-valued function testsuite =-=[3]-=-. Among DE’s advantages are its simple structure, ease of use, speed and robustness. Price and Storn [2] gave the working principle of DE with single scheme. Later on, they suggested ten different sch... |

1 |
A parameter study for differential evolution
- Gäperle, Müler, et al.
(Show Context)
Citation Context ...ches pointed out that there are three main drawbacks of the original DE algorithm. First, the parameters of DE are problem dependent and the choice of them is often critical for the performance of DE =-=[19]-=-, [20]. Second, choosing the best among different mutation schemes available for DE is also not easy for a specific problem [27], [28]. Third, DE is good at exploring the search space and locating the... |