Multi-objective truss structural optimization considering natural frequencies of vibration and global stability

Abstract Conflicting objectives such as minimizing weight and minimizing the maximum nodal displacement, with constraints on normal stresses in the bars, is a common multi-objective structural optimization problem widely found in the literature. This paper proposes multi-objective structural optimization problems with the combination of new conflicting objectives functions and constraints, such as the natural frequencies of vibration and the load factors concerning the global stability of the structure. The solution for these problems may be of great interest in the field of structural engineering, not yet discussed in the literature. The problems analyzed in this paper deal with both discrete and continuous sizing, shape, and layout design variables. The search algorithm adopted here is a modified version of the Differential Evolution called the Third Evolution Step Differential Evolution (GDE3). Several experiments are analyzed with their Pareto-fronts showing the non-dominated solutions. The solutions are defined after obtaining the Pareto curve, which is one of the most important steps and a task that may not be trivial for the Decision Maker. This paper involves a strategy that establishes criteria defining weights (importance) for each objective function and, through these values, enables comparison scenarios. The numerical experiments include plane and spatial benchmark trusses.