In this study, we propose a new method for generating candidate solutions based on both the Cauchy and the Gaussian probability distributions in order to use the merit of the solutions generated by these distributions. The Cauchy probability distribution has larger probability in the tail region than the Gaussian distribution. Thus, the Cauchy distribution can yield higher probabilities of generating candidate solutions of large-varied variables, which in turn has an advantage of searching wider area of variable space. On the contrary, the Gaussian distribution can yield higher probabilities of generating candidate solutions of small-varied variables, which in turn has an advantage of searching deeply smaller area of variable space. In order to compare and analyze the performance of the proposed method against the conventional method, we carried out experiments using benchmarking problems of real valued functions. From the result of the experiment, we found that the proposed method based on the Cauchy and the Gaussian distributions outperformed the conventional one for most of benchmarking problems, and verified its superiority by the statistical hypothesis test.