Real-coded GA for High-dimensional k-tablet Structures

Proposal and Evaluation of Latent Variable Crossover LUNDX-m

Abstract

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.