Algorithm for Evolutionary Optimization of Reinforced Concrete Frames Subject to Nonlinear Material Deformation

The authors designed an evolutionary procedure for the optimal design of reinforced concrete structures of flat frames manufactured without reinforcement pre stress. The aim of the research is to minimize the planned production cost of the frame with restrictions on strength, hardness and crack resistance. The physically nonlinear behavior of concrete and armature, as well as the possibility of crack formation in cracked concrete is taken into consideration. The search is performed on discrete sets of design parameters: the size of the cross sections of bars, number and diameter of rebars, concrete and reinforcement grades. A genetic algorithm, providing for parallel operation of two populations is formed. Within the main population specimen are exposed to crossing over operations, mutation and selection on the basis of production cost criteria. We also introduce the auxiliary population, used to save the best specimen and provide an iterative process, if necessary, with an elite genetic material. The bulk population is divided into two sub-objects. If any of the objects of the first sub-group is not satisfied with at least one of the active constraints, it is replaced by a supporting population object which is not used in the general population or by a newly formed variant of this carrier system. If the restrictions are not met for the object of the second sub-group, then a fine for the value of its objective function is introduced. Such an approach provides a sufficiently rapid convergence of iterations, which is essential in a fair time-consuming calculation of a structure options in a nonlinear setting. The efficiency of the proposed method is illustrated by the example of a single-span reinforced concrete frame optimization.