Keywords: structural optimization, reinforced concrete plane frames, particle swarm, ant colony optimization, harmony search scheme, cost optimization.

In comparison to steel structures, the optimization of reinforced concrete (RC) structures is more complicated, since RC structures can be framed with a semi-infinite set of member sizes and various patterns of reinforcement. In the optimization of steel structures, just one material is considered and the cost is directly proportional to the weight of the structure. While in the case of RC structures, because of having multi-material, three different cost items consisting of concrete, steel and formwork have to be considered, and each of these parameters influence the total cost of the structure. Hence the optimization problem converts into the selection of an appropriate combination of sections dimensions and the quantity of reinforcement while ensuring that the overall cost of structure is kept to a minimum. Constructing two databases of beam and column sections in a practical range, can reduce the complexity of reinforced concrete frame optimization.

This paper presents the application of a heuristic particle swarm-ant colony optimization (HPSACO) to the optimum design of reinforced concrete planar frames subjected to combinations of gravity and lateral loads, based on ACI 318-08 code specifications. Columns are assumed to resist axial loads and bending moments, and beams resist only bending moments. Second-order effects are also considered for the compression members, and columns are checked for their slenderness and their end moments are magnified when it has become necessary. The objective function is the total cost of the frame which includes the cost of concrete, formwork and reinforcing steel for all members of the frame.

HPSACO is based on particle swarm optimization with passive congregation (PSOPC), ant colony optimization (ACO) and harmony search (HS). In this algorithm, ACO helps PSO procedure in the global exploration phase and HS is employed for the variable boundary handling. Here, by using the capacity of the big bang-big crunch algorithm with regard to generation of new solutions, the performance of the HPSACO is improved.

Two RC frame examples are optimized using HPSACO, and the results are compared to those obtained previously using a genetic algorithm.

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