# Member grouping optimization in a multi-objective structural problem of a steel spatial frame

## Palavras-chave:

Multi-objective Optimization, Steel spatial frame, Member Grouping## Resumo

Structural optimization problems arise from a demand for a low-cost and high-performance structure.

Thus, the structures are optimized to minimize the weight, volume, or cost concerning their mechanical aspects of

strength and displacements. In theory, these optimization problems are searching to find structures with various

elements such as columns and beams. On the order hand, in practice, the wide variety of distinct elements can be

an inconvenience in the case of real constructions. This paper analyzes the optimum design of steel spatial frames

in which these frames are submitted to a multi-objective optimization considering the weight as the first objective

function and the number of distinct members in the frame as the second objective function, both to be minimized.

Thus, the paper aims to evaluate the behavior of these two conflicting objective functions to provide to the designer

the benefits and disadvantages of increasing the number of distinct profiles in a frame. As a result, a Pareto front

that summarizes the conflict between the number of distinct members and the structure’s weight will be placed. In

addition, the paper compares this curve of conflicting objective functions with other existing alternatives, such as

those obtained by using cardinality constraints.