The existing intelligent optimization algorithms face challenges related to premature convergence in the synthesis of array antennas, resulting in low solution accuracy and a tendency to get stuck in local optima. In this paper, a logistic chaos and spiral flight dandelion optimizer (LSDO) algorithm is applied to sparse antenna array synthesis with constraints. To optimize the positions of the array elements and reduce sidelobe levels, the logistic chaotic mapping is employed for population initialization, which generates a diverse and uniformly distributed initial population. Additionally, the dandelion optimizer (DO) algorithms utilize a spiral flight strategy to enhance local exploitation capability and escape from the local optimum of the sidelobe level. For algorithm performance, numerical experimental results show the stability and robustness of the LSDO algorithm. For the optimization of planar sparse arrays, the LSDO algorithm significantly outperforms conventional optimization methods, achieving a peak sidelobe level (PSLL) reduction of 15.5% for DO, 9% for PSO, and 14.56% for IWO. These results confirm the effectiveness and superiority of the proposed algorithm.