CO ₂ and cost optimization of reinforced concrete footings using a hybrid big bang-big crunch algorithm

A procedure is developed for the design of reinforced concrete footings subjected to vertical, concentric column loads that satisfies both structural requirements and geotechnical limit states using a hybrid Big Bang-Big Crunch (BB-BC) algorithm. The objectives of the optimization are to minimize cost, CO\(_{2}\) emissions, and the weighted aggregate of cost and CO\(_{2}\). Cost is based on the materials and labor required for the construction of reinforced concrete footings and CO\(_{2}\) emissions are associated with the extraction and transportation of raw materials; processing, manufacturing, and fabrication of products; and the emissions of equipment involved in the construction process. The cost and CO\(_{2}\) objective functions are based on weighted values and are subjected to bending moment, shear force, and reinforcing details specified by the American Concrete Institute (ACI 318-11), as well as soil bearing and displacement limits. Two sets of design examples are presented: low-cost and low-CO\(_{2}\) emission designs based solely on geotechnical considerations; and designs that also satisfy the ACI 318-11 code for structural concrete. A multi-objective optimization is applied to cost and CO\(_{2}\) emissions. Results are presented that demonstrate the effects of applied load, soil properties, allowable settlement, and concrete strength on designs.