Reconfigurable intelligent surface (RIS) is a promising technology for controlling wireless signals. In particular, it has the potential to provide remarkable performance improvements for wireless links, which is especially appealing for millimeter-wave (mmWave) communications. With this purpose, a proper design of the RIS's reflection beam patterns is highly required. In this paper, a direct method is firstly introduced for multi-beam generations based on RIS. Then, equipped with the artificial bee colony (ABC) algorithm, an efficient multi-beam generation method is proposed to configure RIS for high-performance multi-beam patterns on top of the direct method as the initial design. Finally, by employing a fabricated mmWave RIS, we conduct numerical simulations and experimental measurements, and the measured results validate that the proposed method can obtain higher-quality RIS-based multi-beam patterns with an average 7.96 dB side-lobe level reduction, which may provide an efficient way to enhance the capacity of mmWave communications.