Improved genetic algorithm with two-level multipoint approximation for complex frame structural optimization

In this paper, an improved structural topology and sizing optimization method is developed for the fast and efficient engineering design of complex frame structures where beam elements are mainly used in the structures. Discrete and continuous variables are included that the elimination or existence of beam elements are treated as discrete variables (0,1), and the continuous sizing variables of beam cross sections are considered to be continuous variables. To solve the mixed variable problem, the paper introduces a two-level multipoint approximation strategy (TMA). The first-level approximate problem is established by using the branched multipoint approximate function, which includes both two types of variables. Genetic algorithm (GA) is used to determine the absence or presence of beam members. The second-level approximate problem that only involving retained continuous size variables is made on this basis, which uses Taylor expansion and dual methods to solve the inner layer continuous optimization problem. Meanwhile, a strategy of adding a new complementary design point is adopted to expend the search scopes and improve the precision. Temporal deletion techniques are used to temporarily remove redundant constraints and local vibration modes processing techniques are used for continuum topology optimization under frequency constraints. Several representative examples are investigated to validate the effectiveness of the improved method.