Multi-objective optimization of ground structures with constraints of over- lapping bars and maximum stresses

Resumo

Structural multi-objective optimization problems are common in real-world problems of the Engineering
field where one or more objective functions may be considered and desired to be optimized. In general, these
functions are conflicting, leading to complex optimization problems. This paper analyses the multi-objective
structural optimization of truss ground structures considering the weight minimization (or volume) as the first
objective function and compliance as the second one. The constraints refer to the allowable axial stresses in the
bars and also the bars overlapping. Thus, the structural optimization problems consider sizing and topology design
variables simultaneously, and they can be continuous, discrete, or mixed. After obtaining the Pareto Front, one of
the most important steps is defining which solution or solutions will be considered after obtaining the Pareto curve.
Unfortunately, this task is not trivial, and a Multi-Tournament Decision method is applied to extract the solutions
from the Pareto based on Decision-Maker preferences. The search algorithm adopted here is a modified version of
the Differential Evolution called Third Evolution Step Differential Evolution (GDE3).