An AI-based Lagrange optimization for a design for concrete columns encasing H-shaped steel sections under a biaxial bending

shaped steel sections subjected to biaxial loads. The Lagrange multiplier method is used to optimize cost index (CI_c), and CO₂ emission of the columns. ANNs can be implemented to generalize functions for objective parameters CI_c, and CO₂ emission. Generalized functions can replace complex analytical functions that are difficult to derive when optimizing objective functions. In the AI-based Lagrange multiplier method, dimensions of columns and steel sections are calculated as output parameters corresponding to minimized CI_c, and CO₂ emission. Note that 3D interaction diagrams of SRC columns subjected to biaxial bending and concentric axial loads are also formulated based on optimal results. An accuracy of the ANN-based optimal designs is demonstrated using structural mechanics based on a strain compatibility. A hybrid network based on both ANNs and Lagrange multiplier method identified design parameters which reduced CI_c, and CO₂ emission of a column by 30.7% and 40.4% respectively, when compared with those of a conventionally designed column.