外文翻譯--差分演化的最新進(jìn)展一項(xiàng)調(diào)查和實(shí)驗(yàn)分析（英文）

1、Artif Intell Rev (2010) 33:61–106 DOI 10.1007/s10462-009-9137-2Recent advances in differential evolution: a survey and experimental analysisFerrante Neri · Ville TirronenPublished online: 27 October 2009 © Spri

2、nger Science+Business Media B.V. 2009Abstract Differential Evolution (DE) is a simple and efficient optimizer, especially for continuous optimization. For these reasons DE has often been employed for solving vari- ous en

3、gineering problems. On the other hand, the DE structure has some limitations in the search logic, since it contains too narrow a set of exploration moves. This fact has inspired many computer scientists to improve upon D

4、E by proposing modifications to the original algorithm. This paper presents a survey on DE and its recent advances. A classification, into two macro-groups, of the DE modifications is proposed here: (1) algorithms which

5、integrate additional components within the DE structure, (2) algorithms which employ a modified DE structure. For each macro-group, four algorithms representative of the state-of-the-art in DE, have been selected for an

6、in depth description of their working principles. In order to compare their performance, these eight algorithm have been tested on a set of benchmark problems. Experiments have been repeated for a (relatively) low dimens

7、ional case and a (relatively) high dimensional case. The working principles, differences and similarities of these recently proposed DE-based algorithms have also been highlighted throughout the paper. Although within bo

8、th macro-groups, it is unclear whether there is a superiority of one algorithm with respect to the others, some conclusions can be drawn. At first, in order to improve upon the DE performance a modification which include

9、s some additional and alternative search moves integrating those contained in a standard DE is necessary. These extra moves should assist the DE framework in detecting new promising search directions to be used by DE. Th

10、us, a limited employment of these alternative moves appears to be the best option in suc- cessfully assisting DE. The successful extra moves are obtained in two ways: an increase in the exploitative pressure and the intr

11、oduction of some randomization. This randomization should not be excessive though, since it would jeopardize the search. A proper increase in the randomization is crucial for obtaining significant improvements in the DE

12、functioning.F. Neri (B ) · V. Tirronen Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, Agora, 40014 Jyväskylä, Finland e-mail: ferrante.neri@jyu.fiV. Tirr

13、onen e-mail: ville.tirronen@jyu.fi123Recent advances in differential evolution 63– DE with Trigonometric Mutation, see Fan and Lampinen (2002, 2003b), Hu et al. (2005) Angira and Santosha (2007), and Angira and Santosh (

14、2008) – DE with Simplex Crossover Local Search, see Noman and Iba (2005, 2008) – DE with Population Size Reduction, see Brest and Mauˇ cec (2008) and Brest et al. (2008) – DE with Scale Factor Local Search, see Neri and

15、Tirronen (2009), Tirronen et al. (2009), and Neri et al. (2009)Section 5 describes the following algorithmic families:– Self Adaptive Control Parameters, see Brest et al. (2006a,b, 2007), Zamuda et al. (2007), and Brest

16、et al. (2008) – Opposition Based DE, see Rahnamayan et al. 2006a,b, 2007, 2008a, Rahnamayan and Wang (2008), and Rahnamayan et al. (2008b) – Global-Local Search DE, see Chakraborty et al. (2006) and Das et al. (2009) – S

17、elf Adaptive Coordination of Multiple Mutation Rules, see Qin and Suganthan (2005), Yang et al. (2008b), Qin et al. (2009)In order to analyze the benefits and drawbacks of each algorithmic family listed above, a rapresen

18、tative algorithm from each group has been implemented and tested on a broad set of various test problems. Numerical results are reported in Sect. 6. Finally, Sect. 7 gives the conclusion of this work.2 Standard different

19、ial evolutionIn order to clarify the notation used throughout this chapter we refer to the minimization problem of an objective function f (x), where x is a vector of n design variables in a decision space D. According t

20、o its original definition given in Storn and Price (1995), DE consists of the following steps. An initial sampling of Spop individuals is performed pseudo-randomly with a uniform distribution function within the decision

21、 space D. At each generation, for each individual xi of the Spop, three mutually distinct individuals xr, xs and xt are pseudo-ran- domly extracted from the population. According to DE logic, a provisional offspring x? o

22、ff is generated by mutation as:x? off = xt + F(xr ? xs) (1)where F ∈ [0, 1+[ is a scale factor which controls the length of the exploration vector (xr ? xs) and thus determines how far from point xi the offspring should

23、be generated. With F ∈ [0, 1+[, it is meant here that the scale factor should be a positive value which cannot be much greater than 1, see Price et al. (2005). While there is no theoretical upper limit for F, effective v

24、alues are rarely greater than 1.0. The mutation scheme shown in Eq. (1) is also known as DE/rand/1. Other variants of the mutation rule have been subsequently proposed in literature, see Qin and Suganthan (2005):– DE/bes

25、t/1: x? off = xbest + F (xs ? xt) – DE/cur-to-best/1: x? off = xi + F (xbest ? xi) + F (xs ? xt) – DE/best/2: x? off = xbest + F (xs ? xt) + F (xu ? xv) – DE/rand/2: x? off = xr + F (xs ? xt) + F (xu ? xv) – DE/rand-to-b

26、est/2: x? off = xt + F (xbest ? xi) + F (xr ? xs) + F (xu ? xv)where xbest is the solution with the best performance among individuals of the population, xu and xv are two additional pseudo-randomly selected individuals.