An Adaptive Correction Function for Structural Optimization with Genetic Algorithms

This paper presents a new self adaptive correction function for the optimisation of size, geometry and topology of space truss structures using the Genetic Algorithm (GA) method, applied to both continuous and discrete design variables. This function guarantees the diversity of the population at the early stages of the optimisation process. In addition, this function moves the final solution to the feasible region. The adaptive correction function proposed is the product of two independent functions. The first is an individual correction function that corresponds to the increase of the objective function that will be necessary to move an unfeasible individual into the feasible region. The second is a penalty function that increases or decreases the imposed correction, achieving this based on the feasibility or infeasibility of the population members during recent generations. The application of this self adaptive correction function to structural optimization was made using a very simple GA algorithm [

1

] with binary codification, standard crossover, mutation and elitism. The adaptive correction function proposed was implemented in the optimal design system DISSENY [

2

]. Numerical experiments were carried out with different structural optimization problems (i.e. crosssectional size, topology and shape optimization of 3-D trusses), with continuous and/or discrete variables, stress, displacement, slenderness and buckling constraints. The obtained results demonstrate that this self adaptive correction function is effective and robust, relieving the user from the burden of having to determinate the penalty parameters for each new problem. The results produced using this self adaptive function are equal or better than those produced using penalty functions.