The mechanical behavior of the fasting system on the clamping forces has not been fully studied because of structural complexity. The goal of this research is studying the effect of nonlinear of the rail fastening system on the clamping forces in the railway bridges. A numerical model is proposed to analyze the problem of fasteners. The model is conducted by using a code in FORTRAN. In this study, fasteners are modelled as springs. The calculated results show a good agreement with values referred from manufacturer. As a result, the numerical simulation is believed to indicate an approximate value of clamping force considering the nonlinear behavior of fastening system.

To find economic mixing proportions of 60MPa high strength self compacting concrete optimizing a multi-objective problem was performed, which was implemented numerically on MathCAD15 to calculate the economic and optimal mix proportion considering multi-objective characterizing the five performances like compressive strength, passing ability, segregation resistance, manufacturing cost and bulk density depending on the factors like water-binder ratio, cement content, fine aggregate percentage, fly ash content and superplasticizer content.

NSGAⅡ algorithm was employed to optimize the multi-objective problem to find mixing proportions of 60MPa high strength self compacting concrete, which was implemented numerically on MATLAB to calculate the optimal mix proportion considering multi-objective characterizing the four performances like compressive strength, passing ability, segregation resistance and manufacturing cost depending on the factors like water-binder ratio, cement content, fine aggregate percentage, fly ash content and superplasticizer content.

Multi-objective optimization using response surface methodology-based surrogate model was employed to find optimal design parameter of TMD installed on structure under the El Centro earthquake. It is found that the RSM based weighted multi-objective optimized damper improves frequency responses and root mean square displacements of the structure without TMD by 31.6% and 82.3% under El Centro earthquake, respectively, and has an equal or higher performance than the conventionally designed dampers with respect to frequency responses and root mean square displacements and when applied to earthquakes.

Multi-objective optimization coupled with GA-ANN Metamodeling Method and NSGAⅡ was implemented to optimize TMD installed on 10 story structure under El Centro earthquake. Layer number and nodes of ANN were optimized by use of genetic algorithm and NSGA-Ⅱalgorithm was applied to solve multi-objective optimization problem prepared by GA-ANN metamodel. It is found that the GA-ANN multi-objective optimized damper improved frequency responses and root mean square displacements of the structure without TMD by 34.7% and 76.4% under El Centro earthquake, respectively.