Theoretical Analysis of Simplex Crossover for Real-Coded Genetic Algorithms

Higuchi, Takahide; Tsutsui, Shigeyoshi; Yamamura, Masatoshi

doi:10.1007/3-540-45356-3_36

Cited by 68 publications

(51 citation statements)

References 6 publications

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“…For example, the binary-coded crossover operator requires the user to specify the number of cross-sites. For real-parameter recombination operators such as SBX [6], BLX [16] and FR [39] require a parameter, controlling the extent of the search, whereas some recombination operators such as PCX [9], UNDX [29], SPX [25], differential evolution (DE) [38], operator in particle swarm optimization (PSO) [28] require more than one parameters to be set by the user.…”

Section: Evolutionary Principlesmentioning

confidence: 99%

Evolutionary Multi-Objective Optimization Without Additional Parameters

Deb

Parameter Setting in Evolutionary Algorithms

233

443

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The present-day evolutionary multi-objective optimization (EMO) algorithms had a demonstrated history of evolution over the years. The initial EMO methodologies involved additional niching parameters which made them somewhat subjective to the user. Fortunately, soon enough parameter-less EMO methodologies have been suggested thereby making the earlier EMO algorithms unpopular and obsolete. In this paper, we present a functional decomposition of a viable EMO methodology and discuss the critical components which require special attention for making the complete algorithm free from any additional parameter. A critical evaluation of existing EMO methodologies suggest that the elitist non-dominated sorting GA (NSGA-II) is one of EMO algorithms which does not require any additional implicit or explicit parameters other than the standard EA parameters, such as population size, operator probabilities, etc. This parameter-less property of NSGA-II is probably the reason for its popularity to most EMO studies thus far.

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Section: Evolutionary Principlesmentioning

confidence: 99%

Evolutionary Multi-Objective Optimization Without Additional Parameters

Deb

Parameter Setting in Evolutionary Algorithms

233

443

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“…Several non-traditional crossover operators for real-coded representation are found in the recent literature. They include SBX (simulated binary crossover) (Ballester & Carter, 2003;2004b;Deb & Agrawal, 1995;Deb & Beyer, 1999;Deb & Kumar, 1995;Deb et al, 2007), UNDX (unimodal normal distribution crossover) (Kita et al, 1998;Ono et al, 1999;Ono & Kobayashi, 1997), SPX (simplex crossover) (Higuchi et al, 2000;Tsutsui & Goldberg, 2002;, PCX (parent-centric crossover) (Ballester & Carter, 2004a;Deb et al, 2002), etc (Herrera et al, 2003;Takahashi & Kita, 2001). Most of them are complex and based on the specific probability distribution of the offspring (SBX, UNDX, and PCX), self-adaptivity (SBX and UNDX), or multiple parents (UNDX and SPX).…”

Section: Previous Operatorsmentioning

confidence: 99%

“…It is reported that, for some problems, real-coded representation and associated techniques outperform conventional binary representation (Eshelman & Schaffer, 1993;Herrera et al, 1998;Janikow & Michalewicz, 1991;Lozano et al, 2004;Ono et al, 1999;Ono & Kobayashi, 1997;Surry & Radcliffe, 1996;Wright, 1991). Several theoretical studies of real-coded GAs have also been performed (Goldberg, 1991;Higuchi et al, 2000;Kita et al, 1998;Qi & Palmieri, 1994a;. However, the role and behavior of genetic operators in real-coded GAs are fundamentally different from those in binary encodings although motivation of the operators and the framework of GAs are similar.…”

Section: Introductionmentioning

confidence: 99%

The Roles of Crossover and Mutation in Real-Coded Genetic Algorithms

Yoon¹,

Kim²

2012

Bio-Inspired Computational Algorithms and Their Applications

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“…This guideline means that the distribution of offspring generated by crossovers should preserve the statistics such as the mean vector and the covariance matrix of the parental population. Several real-coded crossovers have been proposed following this guideline and the validity thereof has been verified [6] [5]. This guideline regards that a real-coded crossover is an operator which maps the probability distribution of parents to that of offspring.…”

Section: Introductionmentioning

confidence: 99%

“…Then we show that KDE can be actually designed from crossover Unimodal Normal Distribution Crossover (UNDXm) [6] and Simplex Crossover (SPX) [5].…”

Section: Introductionmentioning

confidence: 99%

Real-coded crossover as a role of kernel density estimation

Sakuma

Kobayashi

2005

Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation

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This paper presents a kernel density estimation method by means of real-coded crossovers. Estimation of density algorithms (EDAs) are evolutionary optimization techniques, which determine the sampling strategy by means of a parametric probabilistic density function estimated from the population. Real-coded Genetic Algorithm (RCGA) does not explicitly estimate any probabilistic distribution, however, the probabilistic model of the population is implicitly estimated by crossovers and the sampling strategy is determined by this implicit probabilistic model. Based on this understanding, we propose a novel density estimation algorithm by using crossovers as nonparametric kernels and apply this kernel density estimation to the Gaussian Mixture modeling. We show that the proposed method is superior in the robustness of the computation and in the accuracy of the estimation by the comparison of conventional EM estimation.

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Theoretical Analysis of Simplex Crossover for Real-Coded Genetic Algorithms

Cited by 68 publications

References 6 publications

Evolutionary Multi-Objective Optimization Without Additional Parameters

Evolutionary Multi-Objective Optimization Without Additional Parameters

The Roles of Crossover and Mutation in Real-Coded Genetic Algorithms

Real-coded crossover as a role of kernel density estimation

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