  Toxicity evaluation of chemical compounds has traditionally relied on animal
experiments;however, the demand for non-animal-based prediction methods for
toxicology of compounds is increasing worldwide. Our aim was to provide a
classification method for compounds based on \textit{in vitro} gene expression
profiles. The \textit{in vitro} gene expression data analyzed in the present
study was obtained from our previous study. The data concerned nine compounds
typically employed in chemical management.We used agglomerative hierarchical
clustering to classify the compounds;however, there was a statistical
difficulty to be overcome.We needed to properly extract RNAs for clustering
from more than 30,000 RNAs. In order to overcome this difficulty, we introduced
a combinatorial optimization problem with respect to both gene expression
levels and the correlation between gene expression profiles. Then, the
simulated annealing algorithm was used to obtain a good solution for the
problem. As a result, the nine compounds were divided into two groups using
1,000 extracted RNAs. Our proposed methodology enables read-across, one of the
frameworks for predicting toxicology, based on \textit{in vitro} gene
expression profiles.
