Fitness Function of Genetic Algorithm in Structural Constraint Optimization

Abstract

The mathematics models of Reliability-based Structural Optimization (RBSO) were presented in this paper, then how to handle the constraint become sixty-four-dollar question of establishing the fitness function. Based on exterior penalty function method, penalty gene is made adaptively according to population’s evolution, then the fitness function is established, which is mapping formula of objective function and constraints. Subsequently laxity variable is introduced in primary mathematic model, based on Lagrange multiplier method, a new fitness function mapping formula is made, this method can avoid penalty function morbidity by means of adding a Lagrange multiplier, and has a more quick and stable convergence. Then, using GA successfully solved a numerical constrained optimization issue by this two mapping functions. The calculation shows that the two equations are reasonable and efficient, and Lagrange multiplier method has better global optimal capability.