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.