A genetic algorithm encoding for cardinality constraints and automatic variable linking in structural optimization

A genetic algorithm encoding which is able to directly enforce cardinality constraints is proposed to solve the practically important structural optimization problem where the set of distinct values of the design variables (for instance, cross-sectional areas) must be a small subset of a given set of available values. Furthermore, such encoding allows for automatic variable linking, relieving the user from the task of “a priori” choosing which design parameters should be linked in each group. Very good results have been found in the numerical experiments–involving discrete and/or continuous variables–using the proposed encoding within a standard binary coded genetic algorithm equipped with an adaptive penalty scheme.