Improved genetic algorithm with two-level approximation using shape sensitivities for truss layout optimization

Truss layout optimization is a procedure for optimizing truss structures under the combined influence of size, shape and topology variables. This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA) that uses continuous shape variables and shape sensitivities to minimize the weight of trusses under static or dynamic constraints. A uniform optimization model including continuous size/shape variables and discrete topology variables is established. With the introduction of shape sensitivities, the first-level approximations of constraint functions are constructed with respect to shape/topology/size variables. This explicit problem is solved by implementation of a real-coded GA for continuous shape variables and binary-coded GA for 0/1 topology variables. Acceleration techniques are used to overcome the convergence difficulty of the mixed-coded GA. When calculating the fitness value of each member in the current generation, a second-level approximation method is embedded to optimize the continuous size variables effectively. The results of numerical examples show that the usage of continuous shape variables and shape sensitivities improves the algorithm performance significantly.