It is crucial to accurately categorize cancers using microarray data. Researchers have employed a variety of computational intelligence approaches to analyze gene expression data. It is believed that the most difficult part of the problem of cancer diagnosis is determining which genes are informative. Therefore, selecting genes to study as a starting point for cancer classification is common practice. We offer a novel approach that combines the Runge Kutta optimizer (RUN) with a support vector machine (SVM) as the classifier to select the significant genes in the detection of cancer tissues. As a means of dealing with the high dimensionality that characterizes microarray datasets, the preprocessing stage of the ReliefF method is implemented. The proposed RUN–SVM approach is tested on binary-class microarray datasets (Breast2 and Prostate) and multi-class microarray datasets in order to assess its efficacy (i.e., Brain Tumor1, Brain Tumor2, Breast3, and Lung Cancer). Based on the experimental results obtained from analyzing six different cancer gene expression datasets, the proposed RUN–SVM approach was found to statistically beat the other competing algorithms due to its innovative search technique.