Tri-objective truss structural optimization considering sizing design variables

Resumo

Structural multi-objective optimization problems are common in the Engineering field’s real-world
problems where one or more objective functions, in general conflicting, may be considered to be optimized, leading
to complex optimization problems. Two objective functions problems represent the great majority of formulations
in this context where Pareto fronts can be easily represented and provided to the Decision Maker (DM). For
instance, in the trusses’ structural optimization, these conflicting objective functions may be the weight and the
maximum nodal displacements to be minimized. This paper presents the formulation of multi-objective truss
structural optimization problems considering three objective functions, such as the weight, the maximum nodal
displacement, and the first natural frequency of vibration. The constraints refer to the allowable axial stresses
in the bars. Several experiments inspired in the benchmark mono-objective optimization are analyzed in this
paper, presenting their Pareto surfaces showing the non-dominated solutions. The structural optimization problems
consider sizing and shape design variables simultaneously, and they can be continuous, discrete, or mixed. The
search algorithm adopted to solve these problems is a modified version of the Differential Evolution called Third
Evolution Step Differential Evolution (GDE3). One of the most important steps, after obtaining the Pareto surfaces,
is the definition of which solution or solutions will be chosen by the decision-maker (DM), a non-trivial task. A
Multi-Tournament Decision method, commonly used in bi-objective optimization, is adapted in this paper to extract
the solutions from the Pareto surfaces based on DM preferences.