DNA computing has efficient computational power, but requires high requirements on the DNA sequences used for coding, and reliable DNA sequences can effectively improve the quality of DNA encoding. And designing reliable DNA sequences is an NP problem, because it requires finding DNA sequences that satisfy multiple sets of conflicting constraints from a large solution space. To better solve the DNA sequence design problem, we propose an improved bare bones particle swarm optimization algorithm (IBPSO). The algorithm uses dynamic lensing opposition-based learning to initialize the population to improve population diversity and enhance the ability of the algorithm to jump out of local optima; An evolutionary strategy based on signal-to-noise ratio(SNR) distance is designed to balance the exploration and exploitation of the algorithm; Then an invasive weed optimization algorithm with niche crowding(NCIWO) is used to eliminate low-quality solutions and improve the search efficiency of the algorithm. In addition, we introduce the triplet-bases unpaired constraint to further improve the quality of DNA sequences. Finally, the effectiveness of the improved strategy is demonstrated by ablation experiments; and the DNA sequences designed by our algorithm are of higher quality compared with those generated by the six advanced algorithms.