We propose a new Real-coded GA(RCGA) using the combination of two crossovers, UNDX-m and EDX. The search region of UNDX-m is biased to the inside area that the population of the RCGA covers. Because of this search bias, the GA using UNDX-m causes stagnation of its search if the cost function has a kind of structure, so called, a ridge structure or a multiple-peak structure. In order to overcome this stagnation, we propose a new crossover EDX, whose search is biased (...) toward extrapolative one. Experimental results show that RCGA with EDX can deal with both ridge-structure function whose dimension reaches more than hundreds and multiple-peak function whose optimum resides at the corner of the search area. (shrink)

This paper presents the Real-coded Genetic Algorithms(RCGA) which can treat with high-dimensional ill-scaled structures, what is called, k -tablet structure. The k -tablet structure is the landscape that the scale of the fitness function is different between the k -dimensional subspace and the orthogonal (n-k) -dimensional subspace. The search speed of traditional RCGAs degrades when high-dimensional k -tablet structures are included in the landscape of fitness function. In this structure, offspring generated by crossovers is likely to spread wider region than (...) the region where the parental population covers. This phenomenon causes the stagnation of the search. To resolve this problem, we propose a new crossover LUNDX- m, which uses only m -dimensional latent variables. The effectiveness of the proposal method is tested with several benchmark functions including k -tablet structures and we show that our proposal method performs better than traditional crossovers especially when the dimensionality n is higher than 100. (shrink)

This paper presents a kernel density estimation method by means of real-coded crossovers. Functions of real-coded crossover operators are composed of probabilistic density estimation from parental populations and sampling from estimated models. Real-coded Genetic Algorithm (RCGA) does not explicitly estimate probabilistic distributions, however, probabilistic model estimation is implicitly included in algorithms of real-coded crossovers. Based on this understanding, we exploit the implicit estimation of probabilistic distribution of crossovers as a kernel density estimator. We also propose an application of crossover kernels (...) to Expectation-Maximization estimation (EM) of Gaussian mixtures. (shrink)