genetic algorithm

The steel plate shear wall system is one of the most effective lateral load-resisting systems, offering significant behavioral advantages. However, existing design methods for this system are often overly conservative, leading to economic inefficiencies. This study aims to develop structural designs that ensure both effective safety and cost-efficiency. To achieve this, a genetic optimization algorithm is utilized. Initially, a numerical model is developed and validated using the OpenSees software. This model is then integrated with an optimization code implemented in MATLAB, which iteratively adjusts design parameters to determine optimal cross-sectional areas for 4-, 8-, and 12-story structures. These optimized designs are subsequently compared to conventionally designed models created through a trial-and-error approach. The findings demonstrate that optimization reduces structural weight, enhances performance, and mitigates the conservatism inherent in traditional design methods.

Nowadays, engineering solutions, that guarantee the safety of residents and at the same time pay attention to economic concerns, are proposed in structural engineering.structural Researchers have investigated connections with smaller cross-section in metal structures, demonstrating satisfactory performance in steel bending frames under various cyclic loads. A significant shortcoming of previous research has been the insufficient focus on cost-effectiveness. In addition, many studies have predominantly concentrated on specific types of connections or relied heavily on trial-and-error methods instead of optimizing the dimensions of these connections. This study presents the analysis and optimization of various joint types. Specifically, Reduced Beam Section (RBS) joints were modeled using ABAQUS software through dynamic analysis and numerical methods. The outputs from these analyses were then processed using a genetic algorithm (GA) in MATLAB. The optimal data generated by the GA served as suitable input for neural network modeling, facilitating design refinements. Utilizing two neural networks, the optimal length and cross-section of RBS connections were determined, resulting in more accurate design outcomes, enhanced design efficiency, reduced project execution time, and ultimately, cost savings.

This paper presents a powerful two-step method for damage detection of large-span bridges with variable sections. Bridges are one of the basic infrastructures in the field of urban and suburban transportation, and timely detection of damage during its operation is important. Damage in this category of structures will cause service disruption during natural disasters. The presented method is based on the combination of spectral finite element and modal strain energy damage index, as well as the combination of genetic algorithm and support vector regression to detect and estimate the damage severity. One of the efficient methods in the field of wave propagation is the spectral finite element method, which is capable of modeling with high flexibility and detecting micro damage. Vibration-based methods are widely used to detect structural damage, while the modal strain energy damage index has a higher sensitivity in detecting damage among other vibration-based methods. The case study model is the Crowchild Bridge in Western Canada, which has special characteristics in terms of geometry and the characteristics of structural elements. In this research, the modal strain energy damage index has been modified due to the change of cross-section along the girders. Also, support vector regression has been used as a robust technique in estimation damage severity. In order to increase the accuracy and improve the damage severity estimation method, the genetic algorithm is used to optimize the effective parameters of the support vector regression. The combined method of genetic algorithm and support vector regression has been able to estimate the severity of damages in a favorable way.

The cost of construction is one of the influencing factors in the design of various structures, and the structure can be designed in such a way that with the same construction cost, it has a better performance against the incoming loads. Various methods for optimal design of structures such as genetic algorithm, biological growth and evolutionary algorithms have appeared. The ability of these methods to find the optimal design of structures is much more than mathematical methods.In this research, using the genetic method, the geometric characteristics and height of a two-dimensional Pratt type truss have been improved to make the design more economical. This truss is designed under the concentrated force in the critical position in such a way that with the minimum amount of steel consumption, the maximum stresses in the members do not exceed the limit value. Then this force is considered in a mobile form along the entire length of the truss and its optimal design has been done with the objective function expressed.Finally, the results of two problems are compared. The results show that with the number of about  17000 calls of the objective function during 50 generations, the results lead to a suitable accuracy and the optimal height of the truss in the fixed load mode is equal to 2.53 meters and the moving load mode is 2.56 meters, which for each Two cases are about 50% of the length of each opening. Also, in the case of moving load, the weight of the optimized truss was about 36% more than that of fixed load.

Construction site layout planning is one of the most important and essential early steps in construction management, which significantly influences project’s productivity. Since the tower crane is one of the key facilities on construction sites, optimized planning and managing its operation can improve construction performance. Determining optimal capacity and location of tower crane are complex combinatorial NP-hard optimization problems that are affected by several interrelated factors. This problem cannot be solved using exact mathematical methods on a large-scale site. Therefore, the use of metaheuristic algorithms is necessary in order to solve it. Tower crane’s location has a significant impact on its required capacity and, as a result, on total cost of material transportation, which was not considered in research for a long time. Recently, in a new research, tower crane’s capacity has been considered as a decision variable in the mathematical model. But the problem has been solved on a small-scale and with a precise method. Since the feasible solution space increases on a real-scale site, therefore, using the precise techniques is not practical to achieve the optimal solution. Therefore, it is necessary to utilize meta-heuristic algorithms to solve the problem. Using Genetic Algorithm, this study presents the optimal type and location of tower crane and material supply point as decision variables based on minimizing the total cost of material transportation on the large-scale site. The results indicate that the GA successfully determines the optimal solution, leading to approximately 14% cost reduction compared with when a site layout is decided based on experience.

Ductility of the structure is the ability to withstand trans-elastic deformations of the structure without a significant drop in strength. Examining the results of past earthquakes and the damage to structures makes its ductility and supply in the structure an important issue. In this paper, in order to take advantage of the strengths of the design method based on the performance and computational ease of force design methods, frames with 3, 6, 9, 12, 15 and 20 floors have been considered. Then, a large database consisting of 12960 data was generated and designed with the purpose of 3 types of column stiffness and 3 degrees of bracing thinness and analyzed against 20 earthquakes near pulsed faults for 4 different performance levels. Finally, using the genetic algorithm, the experimental relationships corresponding to the coefficients of behavior, global ductility and link beam ductility are presented. The proposed relationships are influenced by geometric characteristics such as the number of floors, the stiffness ratio of the columns, the slenderness of the braces, the length of link beam, and the ductility levels. The results of seismic design using the proposed relationships on structures outside the range of the defined database, in comparison with the force methods, show the accuracy of this method in estimating the seismic needs of divergent bracing frames. It can be concluded that based on the production relations of the database, and the validation of the production relations, the results of the structural design by the resulting relations have an acceptable validity.

Given the extensive use of cantilever retaining walls in construction and development projects, optimal design and analysis of these walls with due attention to static and seismic loads is a typical engineering problem. As a general rule, a designer seeking to use the Upper Bound Limit Analysis and Limit Equilibrium Method to determine the forces acting on a retaining wall should first search for the mechanism of critical failure. During this procedure, the shape of failure surface can be considered to be planar or circular and failure mechanism can be considered to be translational, rotational, or a combination of multiple scenarios. In the present study, the Upper Bound Limit Analysis Method is used to determine the active pressure on the wall. The failure mechanism consists of two triangular wedges used to determine the active pressure on the wall, and a genetic algorithm is used to optimize the failure wedges. The current results show a good agreement with the results of Coulomb and Rankine Method. The first step for optimal design of cantilever retaining walls is to check their internal and external stability against overturning, sliding, and bearing capacity failure based on a set of assumed dimensions. This initial design should be then completed by checking the wall’s internal stability against shear and bending failures. In case of any change in wall dimensions, the design should be modified such that all factors of safety remain higher than allowable limits and the cost of concrete and steel bars be minimized. All previous works on this subject have only focused on optimizing the structural components of retaining wall, irrespective of the state of its backfill. In the present study, the upper bound limit analysis method was used to determine the shape of critical failure wedges of a retaining wall and its optimal dimensions, and then the formulas provided by ACI 318-05 were used to check its internal stability. The factors of safety against overturning, sliding, and bearing capacity failure were assessed by the limit equilibrium and limit analysis techniques. Given the reciprocal influence of factors of safety and wall dimensions and geometry, the wall’s optimum dimensions the shape of critical failure wedges needed to be determined simultaneously. The results of (upper bound) limit analysis on the stability of retaining wall showed a good agreement with the results of limit equilibrium method and finite element analysis. These results showed that when using limit analysis to determine the most critical instability states of a retaining wall, the critical conditions of failure mechanisms should be checked simultaneously with the optimal structural conditions. This study also used the proposed algorithm to determine the critical direction of earthquake acceleration coefficients. The critical direction of earthquake acceleration coefficient was defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability. The results obtained in this study are in good agreement with the results of similar studies that have been based on limit equilibrium method and finite element analysis. The critical failure mechanism was determined through optimization with genetic algorithm and analysis was validated by comparing the obtained results with the results of other methods. Also, the results show that the geometric dimensions of the wall affect its safety factors and the active pressure on the wall. Consequently, for determination of the most critical state of failure (the lowest safety factors and the highest active pressure), the failure wedges should be optimized while simultaneously determining the optimal wall geometry that can induce the critical state of soil failure. As the results show, in all cases, the values for the safety factors against stability obtained by the Upper Bound Limit Analysis are higher than the allowable values specified by regulations and are in good agreement with the results from the Finite Element Method. Therefore, the use of the limit analysis method (based on the proposed algorithm) with an allowable safety factor higher than values specified by regulations can return results close to those of the conventional methods commonly used for the design of cantilever retaining walls. The results suggest that complementary studies on the subject may produce allowable safety factors for checking the external stability of cantilever retaining walls through the use of the Upper Bound Limit Analysis Method.

Genetic algorithm (GA) is one of the meta-heuristic optimization algorithms. In this paper, the effects of spectral dynamic and equivalent static analysis methods on the calculated optimum weight of the frame are investigated by the means of GA. In the equivalent static analysis, the applied lateral load and design constraints are considered according to ASCE and LRFD-AISC specifications. The internal forces of the frame members are calculated using finite element method. Analysis and optimization of the frame are performed using a program written in MATLAB programming language. Three types of selection including stochastic selection, tournament selection, and ranking selection as well as three different types of crossover, single point, two-point, and continuous crossover are utilized in this study. Moreover, a comparison between equivalent static analysis and spectral dynamic analysis is presented. The results indicate that the difference between the optimum weight of the structure analyzed by spectral dynamic and equivalent static methods increases as the applied load is increased

Diagrid structure is diagonal elements that simultaneously carry the load of horizontal and vertical loads. In diagrid structures, unlike most common systems of high-rise buildings in which incoming loads are transmitted through shear and flexural mechanisms, the diagrid structures, due to their triangular configuration and removal of vertical columns, have a central load transfer mechanism, in other words, they have truss performance. Diagrid structures are developed for effectiveness and beauty of architecture and structure.Diagrid structures as a structural system in high-rise buildings in terms of performance, is an improved system of frame and pipe structure, which reduces the structural weight by decreasing the shear lag. The goal of this research is to optimize the diameter structure of buildings to minimize the weight of the structure, to determine the number of horizontal and vertical segments. Grasshopper graphical programming plugin for Rhino software, with parameterization of the written program, provides algorithm optimization. Optimization in the program written by the genetic algorithm is done through the Galapagos plugin based on the outcomes of the structure analysis engine of the Karamba plugin. The simulation results indicate that for a 40-store diameter structure of 900 square meters in each floor, the optimal mode with the horizontal and vertical divisions of 8, and 26, and the angle of 64 with the horizontal axis will be 21508 tons of the total structure.

Hyperbolic structures are grid-based space structures. The shape of the structures is similar to a square with fillet edges. If the mid-point of the square sides is connected in orthogonal x and y directions, the “+” shaped configuration remains at its position if the edges become even more curved and their elevation (z coordinates) do not change. Nonetheless, the elevation of the remaining points changes and form the hyperbolic structure. The application of hyperbolic structures is in covering long-span. In this study, a particular hyperbolic structure is optimized both in terms of shape and size. The Charged System Search (CSS) algorithm is used to carry out the optimization. Subsequently, optimization results are compared with corresponding results from the genetic algorithm method.

The landslides occurred due to an earthquake have ever caused great losses of life and property. Earth slope stability is influenced by many factors that should be taken into account for a comprehensive assessment of it. However, slope seismic analyses are complicated due to the necessity of concerning the dynamic stresses caused by an earthquake and the soil resistance changes in seismic conditions. Seismic slope instability can arise from two significant factors including the increase of inertia forces and the decrease of soil shear strength. Moreover, the earthquake motions can produce considerable dynamic shear and vertical stresses in earth slopes. If these stresses are added to the static stresses existing in the soil mass, they may lead to slope instability [1]. The methods of analyzing the earth slopes stability can be pseudo-static and stress-strain analyses or simplified integration method (Newmark rigid-block method). In the pseudo-static analysis, slope seismic safety factor is determined in a very similar way as what is done in static equilibrium analysis. In the stress-strain analysis, first of all, soil mass is divided into the finite elements. Afterwards, by using numerical methods, the stresses and strains caused by external and internal forces in soil mass is calculated. Although this method is accurate and gives a realistic model of the earth slopes, it requires the special expertise and precise input information. The rigid-block model assumes that permanent deformation initiates when the earthquake-induced accelerations acting on a slide mass exceed the yield resistance on the slip surface. The resistance is quantified by the seismic yield coefficient (ky). At this point, the slide mass breaks away from the rest of the underlying slope and sliding occurs at a constant rate of acceleration equal to ky. During this time, the velocity of the ground is greater than the velocity of the slide mass. Sliding continues until the following conditions are met: (1) accelerations fall below ky, and (2) velocity of the slide mass and the underlying ground coincide [2]. In deterministic computation methods, input data such as viscosity, inner friction angle, inclination of slope, etc. is considered as fixed values; therefore, by using these methods, the probabilistic variation of a parameter cannot be considered. In other words, deterministic methods do not include the uncertainty related to the effective design parameters. In the probabilistic method, instead of using a fixed value for a parameter, the probability distribution function (Probability Density Function) of it is used. Due to the possibility of performing fast extensive numerical calculations by computer, the numerical simulation methods such as Monte Carlo simulation have been employed in slope stability analysis. Assuming homogeneity of materials, along with, absence of underground water on one hand, and considering that the slope seismic yield coefficient is a function of the angle of slope β, height of slope h, soil bulk density γ, the coefficient of soil cohesion c and internal friction angle φ, on the other hand, a closed-form relationship between the above-mentioned parameters can be achieved using the extensive results of limit equilibrium analysis and artificial intelligence methods such as genetic algorithm [4]. Any change in each of the stated parameters can lead to a change in slope seismic yield coefficient. The uncertainty in calculation of slope seismic yield coefficient can be taken into account by utilizing genetic algorithm and probability distribution functions of input parameters.
Due to the fact that coseismic slope deformation is a function of seismic yield coefficient (ky) and other effective parameters, using the statistical analysis, the statistical distribution and the standard deviation of ky can be assessed. In the present study, the following steps were taken for studying the variation of ky: Implementing a pseudo-static analysis of earth slopes having various physical and mechanical parameters, determining the relationship between slope seismic yield coefficient and other given parameters using curve fitting and genetic algorithm method (evolutionary strategy method), simulating the effective parameters on ky by means of Monte Carlo method based on a specified statistical distribution [9]. The Monte Carlo simulation procedure is as follows: - Providing a deterministic model for solving the problem. - Selecting the random variables including soil characteristics, slope geometry and proper probability density functions. - Generating the input parameters by taking into account the density functions and random variables dependency (parameters’ dependency) to each other. - Using simulated numbers related to all independent parameters, along with defined deterministic model, the value of slope seismic yield coefficient and probability density function of it are obtained. Consequently, the following results were concluded: 1. If normal distribution is selected for the parameters affecting ky, slope seismic yield coefficient will be normally distributed. 2. The coefficient of variation of ky has a direct relationship with coefficient of variation of parameters affecting it. If slope seismic yield coefficient is increased, the acceleration coefficient will be decreased. 3. With selecting the minimum amount of coefficient of variation for effective factors, the range of coefficient of variation of slope seismic yield coefficient is between 5 and 11 percent. 4. With considering the maximum amount of coefficient of variation for effective factors, the range of coefficient of variation of slope seismic yield coefficient is between 25 and 59 percent. 5. With taking into consideration the minimum amounts of the coefficient of variation for effective parameters, and increasing mean value of slope yield acceleration from 0.1 to 0.35, its variation coefficient (COV%) decreases from 11 percent to 5 percent. 6. With taking into account the maximum values of the coefficient of variation for the effective parameters, and increasing mean value of slope yield acceleration from 0.1 to 0.35, its variation coefficient (COV%) decreases from 59 percent to 25 percent. In this study, coefficient of variation of ky is calculated assuming that the properties of a soil layer changes similarly in all points of it. If these properties vary from point to point, there is a need to employ random field method (stochastic finite element) in order to simulate the spatial variation of soil properties.

Optimization of structures for minimum weight has become important in the recent designs. In this study, a genetic optimization algorithm for weight minimization of steel frames has been used. The genetic algorithm is an optimization and search technique based on the principles of genetics and natural selection. Constraints regarding material strength and serviceability are taken from “AISC code (1989)” and implemented in the algorithm. The design process obtains a frame and bracing pattern with the least weight by selecting appropriate sections for beams, columns and bracing members from the standard set of steel sections. The results of this study indicates that the optimization based on weight minimization is also able to improve structural performance.

Most civil projects applied to heavy vertical and horizontal loads or in lands do not have enough strength against applied load. Despite heavy expenses, it is necessary to use pile. Pile foundations are much more expensive than spread and mat foundations; hence, determining number, dimensions and distances should be done with special care so that these parameters are not determined excessively. For optimized design of pile groups, cost analyses based on settlement equations and bearing capacities to determine number, dimensions and piles distances are necessary. In this research, a computer program has been written in MATLAB language, and by using genetic algorithm which can optimize pile groups design. Outputs of this computer program consist of diameter and length of piles, thickness of pile cap, number of piles and their distances in each direction; therefore, this computer program can design an optimized pile group which tackles technical problems while it is the most economical.