Application of Genetic Algorithm in Multi-objective Optimization

3.2.1.2. Objective Function:
This structural optimization problem was to be formulated by satisfying all implicit and explicit
constraints. The equations of static equilibrium supplied the implicit constraints which were:
∑ 0 and ∑ ∑ 0……………………….(ii)
where, was the force, was the moment with respect to the origin and was the position vector
between the origin and the point where the force was acting. In 3D space, these two vector
equations contributed six scalar constraint equations.
Now, for the three supports, the reaction forces were represented by a vector, where,
=[ , , ] ’ and the total force acting downward was . It was assumed that the only force
acting downward was the self-weight of the structure, F. The length and width of the rectangular
structure were L and W respectively. As the plate was homogeneous, the co-ordinate of the center
of gravity of this plate was (L/2, W/2). In this study, the center of gravity was assumed to be the
origin. Supports as well as the weight of the plate were assumed to be acting in the z-direction.
Thus, equations formulated using static equilibrium were as follows:
∑
………………………………………….(iii)
∑ 0, or ∑
0……………………………..……...(iv)
and ∑ 0, or ∑
0........................................................(v)
The matrix representation of these three equations was used to solve reaction forces acting on three
supports, which is shown below:
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