Many-objective truss structural optimization considering stability and vibrational aspects

Resumo

Many-objective structural optimization problems are well-known and have been discussed in the literature. Concerning framed structures, most formulations consider two objective functions: minimizing weight and minimizing the maximum nodal displacement. This paper aims to expand on and discuss many-objective truss structural optimization problems (MaOSOPs) with seven objectives. The objective functions are the weight, the number of different cross-section types, the maximum nodal displacement, the first natural frequency of vibration, the first load factor concerning the structure’s global stability, the sum of the absolute values of the first vibration mode, and the sum of the absolute values of the first stability mode. The sizing design variables are the cross-sectional areas of the bars, and the constraints are the nodal displacements and axial stress at the bars. The experiments are traditional benchmark problems in the literature. The algorithms used are the multi-objective meta-heuristic with iterative parameter distribution estimation (MM-IPDE), the success history–based adaptive multi-objective differential evolution (SHAMODE), the success history–based adaptive multi-objective differential evolution with whale optimization (SHAMODE-WO), and the third non-dominated sorting genetic algorithm (NSGA-III). Pareto fronts are obtained by providing the decision-maker with a set of non-dominated solutions that can be chosen according to their preferences.