[en] The computational cost of multigrid solvers for steady state flows may be improved by using careful tuned explicit multistage relaxation methods. Optimal performance requires a balance of error propagation and high-frequency Fourier error mode damping. Solution accuracy requires minimal artificial dissipation which, in turn, can adversely affect the damping properties of the relaxation method. This research focuses on optimizing modified Runge-Kutta methods to provide fast multigrid performance, using a goal attainment method to minimize multiple objectives. Multigrid performance is improved by minimizing the amplification factor, arising from the application of the relaxation method, over the high-frequency domain. Error propagation is improved by maximizing the relaxation timestep. Optimal coefficients for quasi-one-dimensional flow and two-dimensional flow are presented, for both fine-grid and coarse-grid relaxation schemes. A substantial improvement in computational cost is demonstrated relative to existing relaxation schemes. (author)