Application of Conjugate Gradient Optimization Method in the Design of Pre-stressed Concrete Beams

The conjugate gradient method is an essential category of approaches for solving unconstrained optimization problems. In this paper, we are considering five variables that are related to the mechanical properties of steel and concrete for a pre-stressed concrete beam. The aim is to optimize two outputs which are maximum principal strain and maximum deflection of the structure.  Two surrogate models are constructed using design sampling method for preparing the involving models. The reliability of the surrogate models is checked by the coefficient of determination ( ). We are using unconstrained nonlinear optimization by applying conjugate gradient method with Polak and Ribiere parameter. Five optimal iterations are executed in the presented algorithm for each model with substitution in each other. Optimized value of each variable in addition to the optimum two surrogate model outputs were determined and verified with the variable range values and exact model outputs. Finally, sensitivity analysis was performed and the main rational percentage effect of each variable on the outputs and their interactions were determined.