In this paper, an optimization approach was presented for the flexural strength and stiffness design of reinforced concrete beams. Surrogate modeling based on machine learning was applied to predict the responses of the structural system in three-point flexure tests. Three design input variables, the area of steel bars in the compression zone, the area of steel bars in the tension zone, and the area of steel bars in the shear zone, were adopted for the dataset and arranged by the Box-Behnken design method. The dataset was composed of thirteen specimens of reinforced concrete beams. The specimens were tested under three-point flexure loading at the age of 28 days and both the failure load and the maximum deflection values were recorded. Compression and tension tests were conducted to obtain the concrete data for the analysis and numerical modeling. Afterward, finite element modeling was performed for all the specimens using the ATENA program to verify the experimental tests. Subsequently, the surrogate models for the flexural strength and the stiffness were constructed. Finally, optimization was conducted supporting on the factorial method for the predicted responses. The adopted approach proved to be an excellent tool to optimize the design of reinforced concrete beams for flexure and stiffness. In addition, experimental and numerical results were in very good agreement in terms of both the failure type and the cracking pattern.

In this work, meta models considering the non-linearity of the problem are dedicated to determining the displacements of the crest and the foundation of the Koyna dam model. ABAQUS 6.14 program is used to create the numerical simulations by employing extended finite element method XFEM with the presence of Koyna earthquake time history data for 10 seconds. Five factors related to the foundation's material properties and reservoir depth are involved in an optimization study. The Pareto optimization method is adopted with the support of MATLAB codes to calculate the optimized values of the participating factors. A multi-objective function authorized by two meta models is being optimized to predict the optimized minimum displacements of the Koyna dam during seismic action in addition to crack damage propagation. The results declared that the meta models are 100% efficient in estimating the response of the structural system of the dam. The optimized values of the five factors were determined. The optimized minimum crest displacement was 1.372 m and the optimized minimum foundation displacement was 0.319 m, which approved the minimum optimality compared to the minimum model of the related outputs generated for the meta models. Consequently, the dam's stability and crack damage control were accomplished with high reliability by verifying the results with the adopted benchmark.

We use multi-objective optimization and numerical simulations to optimize the shear strength of a reinforced concrete T-beam. The optimization process involves four factors that are related to the Young's modulus of elasticity and density of both the steel reinforcement and the concrete. The factors, which have a limited range, are utilized in the construction of the regression equation that forecasts the reinforced concrete T-beam's ductility and elastic shear strain. Using ABAQUS finite element programs, 27 models were prepared for numerical analysis and simulation using the well-known sampling technique Box-Behnken design. To find the coefficients that correspond to the regression equations, MATLAB codes are utilized to solve complex matrices using the least squares method. Checking the regression equation's reliability to compare the outcomes of the numerical simulations and the regression equations, a reliability check for the regression equation has been implemented. Due to the simultaneous R² values of 1 and 1 for ductility and elastic shear strain, the reliability check was 100%. The optimization of the reinforced concrete T-beam's shear strength capacity can be easily determined, according to multi-objective optimization results, and the design of this structural system is highly controllable.

In this paper, we consider a fuzzy linear fractional programming (FLFP) problem under the condition that the objective function is represented by triangular and trapezoidal fuzzy numbers, while the values of the right-hand side and left-hand side constraints are represented by real numbers. And defined a new ranking function for convert fuzzy linear fractional programming problem into crisp linear fractional programming problem. This proposed approach is based on a crisp linear programming and has a simple structure. Comparing the proposed method to the exiting methods for solving FLFP problems we see it is simple to apply and acceptable. Finally, numerical illustrations are used to demonstrate the suggested methods.

The entire research study is about the optimization of design variables for an earth-fill dam utilizing multi-objective optimization approach. We have considered three variables that are related to the soil material properties which are core density, foundation Young's modulus of elasticity, and shell coefficient of permeability. A limited range of each variable is applied depending on the literature and numerical simulations are dedicated for the response of the global structure using ABAQUS program. Box-Behnken design method along with MATLAB codes with least-square method are being used to construct two surrogate models for the displacements of the earth-fill dam. Fifteen numerical models are involved in the process with the presence of non-linear equations for the objective function for the optimization process. The objective functions were for the pore water pressure and the maximum principal stress were they would be first checked for reliability by the coefficient of determination check R2. The reliability of the objective function was 100% which enhanced them to be ready for the multi-objective optimization step. The results of the optimized variables for both objective functions were determined and compared with the minimal responses of the considered models of the numerical simulations of the global structure. The optimum results of both objective functions of the earth-fill dam were determined and approved which is an indication of excellent result for the optimization of the design variables.