Key detection performance metrics, particularly resolution, are largely determined by the design parameters of ultrasonic arrays. The structural design of the transducer strongly influences critical indicators, including side lobe levels, beam directivity, and focal spot size. To improve parameter selection, this study proposes a multi-objective optimization strategy specifically tailored for cylindrical surface ultrasonic transducers. The geometric parameters of the array and the variables influencing resolution performance are mapped in a nonlinear manner. The NSGA-II algorithm is employed to perform extremum seeking optimization on a trained BPNN, generating a Pareto-optimal solution set by specifying main-lobe width, side-lobe intensity, and sound-pressure uniformity as optimization objectives. For validation, the geometric configurations derived from this solution set are applied in acoustic field simulations. Simulation results demonstrate that the dynamic aperture exhibits clear regularity when the array settings meet millimeter-level resolution requirements. These findings support real-world engineering applications and provide valuable insights for enhancing the geometric design of cylindrical ultrasonic arrays.