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The problem of the linear optimal control (LOC) has been strongly involved with selecting the weighting matrices in the cost function. The cost function is parameterized by two matrices, Q and R that weight the state and control vectors, respectively. In fact, the challenge lies in how these weights are chosen. This paper introduces a method to design the elements of Q and R by using genetic algorithm (GA). This method is employed for a single machine against infinite bus model of the power system. Since such controller has potential to excite the torsional modes of the shaft system and in order to avoid negative interactions, these modes are taken into account fully in the controller design. Based on the proposed GA-LOC, a controller has been designed and its performance on the power system is evaluated in both frequency and time domains. Moreover, the effectiveness of the controller is compared with the one when Q and R are to be identity matrices.