AI-based Lagrange optimization for designing reinforced concrete columns

Structural engineers face several code-restricted design decisions. Codes impose many conditions and requirements to the designs of structural frames, such as columns and beams. However, it is difficult to intuitively find optimized solutions, while satisfying all code requirements simultaneously. Engineers commonly make design decisions based on empirical observations. Optimization techniques can be employed to make more rational engineering decisions, which result in designs that can meet various code restrictions simultaneously. Lagrange optimization techniques with constraints, not based on explicit parameterization, are implemented to make rational engineering decisions and find minimized or maximized design values by solving nonlinear optimization problems under strict constraints imposed by design codes. It is difficult to express objective functions analytically directly in terms of design variables to use derivative methods, such as Lagrange multipliers. This study proposes the use of neural network to approximate well-behaved objective functions and other output parameters into one universal function that can also give a generalizable solution for operating Jacobian and Hessian matrices to solve the Lagrangian function. The proposed method was applied successfully in optimizing a cost of a reinforced concrete column under various design requirements. An efficacy of optimal results was also proven by 5 million datasets.