Application of Genetic Algorithm in Multi-objective Optimization

3. Methodology:
3.1. Developing an Indeterminate Structure with an Unconstrained
Solution Space:
The objective of the work was to formulate Genetic Algorithms based multi-objective optimization
methodology for solving a support location problem of an indeterminate structure. To reach that
goal, the first step was to develop a generic and simplified indeterminate structure. The support
locations of that structure were determined by satisfying multiple objectives. These multiple
objectives were not apparent to solve and posed competing nature. Having contending multiple
objectives means the optimal value of one objective might negatively impact the optimality of other
objectives. The balancing of all objectives in a proper way was a prerequisite to lead towards the
acceptable optimal results. The structure required to be designed in such a way that the heuristic
calculation could provide a benchmark to evaluate the optimal objective solution.
3.1.1. Test Case:
An 8x6 meter rectangular shaped solid indeterminate plate was considered as a simple and generic
test case in this work. A myriad of similar examples would be found in real life including decorative
overhung lights. The target was to overhang this structure, made out of aluminum, with three cables
in a way that the load is evenly distributed among the cables while ensuring maximum stability. So,
the objectives included the minimization of the tension difference in the supports and the
maximization of the area enclosed by the support locations to increase stability. It was assumed that
the support locations in the geometric coordinate system were , , , and , , and
the reactive forces acting upon the supports were , and , respectively. These reactive forces
and the force due to the self-weight of the plate (F) were assumed to be acting in the z- direction
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