This paper presents a many-objective optimization (MaOO) approach to design control and observer gains simultaneously. The many-objective optimization (MaOO) approach finds trade-offs between different nonagreeable design goals. We report the MaOO results of a proportional-integral-derivative (PID) control with a state estimator applied to a second-order oscillator. The overall system is optimized to minimize the peak time, overshoot, tracking error, and control energy, and maximize the rejection of external disturbance and measurement noise, while the relative stability, which is defined by maximum real part of eigenvalues of the closed-loop system, is constrained to be less than or equal to -1. The numerical simulations show promising findings of the proposed method.