The optimal design of reinforced concrete beams (RCBs) and structures with an objective of improving the chosen performances is an important problem in the field of construction works. Recently, the concrete beams, structures, and walls are strengthened externally by bonding fiber-reinforced polymer strips (FRPS). Usually, FRPS are employed in rehabilitation of existing beams, bridges, and other structural elements. This article modifies the problem of designing new RCBs with appropriate selection of FRPS with a goal of exploiting the benefits of FRPS such as higher tensile strength, better corrosion resistance, higher stiffness-to-weight ratio, and longer life. It, firstly, proposes an artificial neural network-based mathematical model for assessing the performances of RCBs bonded with FRPS from the data obtained from 69 FRPS-glued RCBs and then develops an optimal design procedure employing flower pollination-based optimization, which is imitated from the pollination process of plants, for obtaining design parameters of FRPS-glued RCBs with a view of enhancing both the ultimate load and the deflection ductility. It presents optimal design parameters of five FRPS-glued RCBs and experimentally validates the performances.