III. OBJECTIVE FUNCTIONS AND CONSTRAINT CONDITIONS Optimal solutions for the multi-objective functions can be calculated by taking the constraint conditions. Two objective functions are considered in this study. The first objective function is minimization of the total amounts of FRP bracings. To reduce the number of variables, the thickness of FRP is only used as variable in this function. The second objective function is the minimization of coefficient of variation (COV) for inter-story drift ratio. This function is to prevent the story collapse and a need of this is proposed from various study [12]. Three constraint conditions are applied to calculate the optimal solutions. First condition is the ratio of the maximum inter story drift to allowable inter story drift. If this ratio is high, it means dangerous state and the penalty is granted. This study refer to FEMA 356 [13]. IO level, LS level and CP level are considered. Second is prevention of building collapse. To reduce the damage on human life, precondition that performance point cannot exceed the collapse point is granted. Third condition is the constraint for the rotational deformation capacity of column and beam. Lateral force and axial force lead to the rotational deformation at structural frame. Since plastic hinge or failure of elements can be occurred, damage of structural elements should be minimized. Thus, to induce the elastic behavior of structural elements, third condition is necessary.