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 emissions, and the weighted aggregate of cost and CO. Cost is based on the materials and labor required for the construction of reinforced concrete footings and CO 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 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 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 emissions. Results are presented that demonstrate the effects of applied load, soil properties, allowable settlement, and concrete strength on designs.