One of the primary aims of radio network planning is to configure the parameters of the base stations such that the deployment achieves the required quality of service. However, the adjustment of radio network parameters in a heterogeneous macro-only cellular network is a complex task, which involves a large number of configuration parameters with interactions among them. Existing commercial planning tools are based on local search methods, e.g., simulated annealing, that require problem-specific and heuristic definitions of the input parameters. The problem with local search methods is that their performance can significantly be degraded if the input parameters are mis-configured. To overcome these difficulties, an iterative optimization procedure based on Taguchi's method is proposed to find near-optimal settings. Taguchi's method was originally applied in manufacturing processes and has recently been used in several engineering fields. Unlike local search methods that heuristically discover the multidimensional parameter space of candidate solutions, Taguchi's method offers a scientifically disciplined methodology to explore the search space and select near-optimal values for the parameters. In this paper, the application of Taguchi's method in radio network optimization is illustrated by setting typical radio network parameters of the Long Term Evolution (LTE) system, i.e., the uplink power control parameters, antenna tilts, and azimuth orientations of trisectored macro base stations. Simulation results reveal that Taguchi's method is a promising approach for radio network optimization with respect to performance and computational complexity. It is shown that Taguchi's method has a comparable performance to simulated annealing in terms of power control and antenna azimuth optimizations; however, it performs better in terms of antenna tilt optimization. Moreover, it is presented that the performance of simulated annealing, as opposed to Taguchi's method, highly depends on the definition of the input parameters.