First, the reasons of using metaheuristic algorithms are listed for optimum design of reinforced concrete (RC) structures and members. The main reason is the non-linear formulation of RC design problems including various types of design constraints. The basic terms and formulation of optimization methods are presented. A general process of metaheuristic-based optimization methods is presented. This process is summarized as three stages: pre-optimization, analysis, and optimization. Details of several metaheuristic algorithms effectively used in structural engineering problems are summarized by giving all formulations according to the inspiration of algorithms. The flowcharts for the optimization processes are also included.
TopConventional methods can be used to solve optimization problems, but engineering problems generally have high numbers of design constraints. In that case, the solution of optimum design variables cannot be directly calculated since these variables are effective on the analyses of design constraints. This situation makes most of the engineering problem non-linear.
The easiest way to solve a non-linear problem is to use trials with iterative solutions, but this process may last too long. For that reason, the randomization and choosing of candidate design variables must be done in a systematic way by using methodologies employing iterative algorithms. These iterative algorithms are mainly metaheuristic methods. The development of metaheuristic methods includes a process which has the same goal for objective of an optimum design. Every process has objectives to provide or objective functions to minimize or maximize.
Especially, the optimum design of reinforced concrete (RC) structures is more complex than other engineering problems because of following reasons:
Steel has the same strength under tensile and compression. Concrete is a brittle material and has an acceptable compressive strength while the tensile strength is neglected. For the protection of steel from fire and environmental conditions, concrete is an excellent cover with low cost.
If a part of a section of RC member is under tensile, reinforcing bars (rebar) must be added. For civil structures, ductile design must be developed. In other words, when the yielding strength is exceeded, the structure must continue to carry the internal forces resulting from static and dynamic forces. Steel is a ductile material, but this situation cannot be provided with brittle material, concrete. For that reason, several rules are given in design codes. These rules are separately mathematically modelled as design constraints in optimization.
The most basic ductile behavior rule for members under flexural moments is to provide yielding of steel before the fracture of concrete. In that case, the amount of steel is limited. To carry more forces, the parts under compressive stress must also be reinforced with rebar. In that case, candidate solutions may include both reinforcements in tensile and compressive sections, or only reinforcements can be positioned in tensile section. For that reason, the code of optimization methodology must be considering this and similar situations.
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RC structures contain several types of members which are under different types of stresses. For example, beam is dominantly under flexure effects while columns are dominantly under an axial force. Foundations and retaining walls are under the effect of geotechnical constraints in addition to structural constraints.
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Different members of same types are under effects of forces with different intensities. In that case, each member has a separate optimum design. Because of statically undetermined systems, the change of rigidity effects the solution.
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The concrete sections are casted in construction yard. Precise dimensions cannot be provided. This situation leads us to use discrete design variables by uncompromising a precise optimum design.
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In local market, fixed sizes of rebar are found. In that case, the available sizes must be used in random optimization.
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Structures are huge systems and load on structures are not certain. The self-weight of structural and non-structural members are known, but the amount of live load and existing of live load in a span is not known and it is changeable. Additionally, dynamic loads are totally unknown. The earthquake accelerations and wind speed cannot be predicted. Only vibration periods and maximum intensities can be guessed. Additionally, a region may have special forces (earthquake, wind, snow, etc.)
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In addition to specific loads, the requirements of a country may be different because of the usage of different design codes. Also, the constructed structure may have different soil condition and usage purposes.