Reinforced concrete (RC) frames represent the most common structural system in the built environment. Therefore, their efficient design is expected to offer significant economic and environmental benefits. Simultaneously, the optimal design of RC frames remains a complex computational task requiring efficient numerical algorithms. Herein, a variant of the established Flower Pollination Algorithm (FPA) is applied to the optimal design of RC frames. The new variant, called Flower Pollination Algorithm with Pollinator Attraction (FPAPA), accounts additionally for the evolutionary mechanism of pollinator attraction in the natural process of flower pollination. FPAPA is applied to benchmark problems in the structural optimization of concrete frames with known global optimum solutions. It is found that FPAPA offers high quality design solutions within limited computational budgets. Furthermore, comparisons show that FPAPA represents a competitive or superior alternative to the most well-known optimization algorithms.