A collection of thirty mathematical functions that can be used for optimization purposes is presented and investigated in detail. The functions are defined in multiple dimensions, for any number of dimensions, and can be used as benchmark functions for unconstrained multidimensional single-objective optimization problems. The functions feature a wide variability in terms of complexity. We investigate the performance of three optimization algorithms on the functions: two metaheuristic algorithms, namely Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), and one mathematical algorithm, Sequential Quadratic Programming (SQP). All implementations are done in MATLAB, with full source code availability. The focus of the study is both on the objective functions, the optimization algorithms used, and their suitability for solving each problem. We use the three optimization methods to investigate the difficulty and complexity of each problem and to determine whether the problem is better suited for a metaheuristic approach or for a mathematical method, which is based on gradients. We also investigate how increasing the dimensionality affects the difficulty of each problem and the performance of the optimizers. There are functions that are extremely difficult to optimize efficiently, especially for higher dimensions. Such examples are the last two new objective functions, F29 and F30, which are very hard to optimize, although the optimum point is clearly visible, at least in the two-dimensional case.

Engineers usually use trial-and-error approaches for dealing with design problems where they need to find the most economical design of a structural element in terms of its material cost while satisfying all the safety requirements imposed by the design codes. In this study, we employ a genetic algorithm (GA) with a dominance-based tournament selection technique for dealing with this design challenge. The methodology is applied in the design of reinforced concrete rectangular-shaped isolated footings in accordance with the American Concrete Institute ACI 318-19. First, the footing is encoded into a set of decision variables and an objective function is defined to compute the total cost based on the different construction materials. Then, the compliance of the design with the ACI 318-19 code is enforced by a constraint function that takes into consideration all the demand–capacity ratios for the different resistance requirements such as the allowable bearing pressure of the supporting soil, and the shear and flexural capacities of the footing, among others. Two numerical examples are presented where the results show a significant advantage in terms of material-cost and design-time reduction in comparison with the commonly used trial and error approach, proving the applicability of optimization algorithms (OAs) into the everyday design routine of the structural engineer.

The modeling and simulation of structural systems is a task that requires high precision and reliable results to ensure the stability and safety of construction projects of all kinds. For many years now, structural engineers have relied on hard computing strategies for solving engineering problems, such as the application of the Finite Element Method (FEM) for structural analysis. However, despite the great success of FEM, as the complexity and difficulty of modern constructions increases, the numerical procedures required for their appropriated design become much harder to process using traditional methods. Therefore, other alternatives such as Computational Intelligence (CI) techniques are gaining substantial popularity among professionals and researchers in the field. In this study, a data-driven bibliometric analysis is presented with the aim to investigate the current research directions and the applications of CI-based methodologies for the simulation and modeling of structures. The presented study is centered on a self-mined database of nearly 8000 publications from 1990 to 2022 with topics related to the aforementioned field. The database is processed to create various two-dimensional bibliometric maps and analyze the relevant research metrics. From the maps, some of the trending topics and research gaps are identified based on an analysis of the keywords. Similarly, the most contributing authors and their collaborations are assessed through an analysis of the corresponding citations. Finally, based on the discovered research directions, various recent publications are selected from the literature and discussed in detail to set examples of innovative CI-based applications for the modeling and simulation of structures. The full methodology that is used to obtain the data and generate the bibliometric maps is presented in detail as a means to provide a clearer interpretation of the bibliometric analysis results.

A new, fast, elegant, and simple stochastic optimization search method is proposed, which exhibits surprisingly good performance and robustness considering its simplicity. We name the algorithm pure random orthogonal search (PROS). The method does not use any assumptions, does not have any parameters to adjust, and uses basic calculations to evolve a single candidate solution. The idea is that a single decision variable is randomly changed at every iteration and the candidate solution is updated only when an improvement is observed; therefore, moving orthogonally towards the optimal solution. Due to its simplicity, PROS can be easily implemented with basic programming skills and any non-expert in optimization can use it to solve problems and start exploring the fascinating optimization world. In the present work, PROS is explained in detail and is used to optimize 12 multi-dimensional test functions with various levels of complexity. The performance is compared with the pure random search strategy and other three well-established algorithms: genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE). The results indicate that, despite its simplicity, the proposed PROS method exhibits very good performance with fast convergence rates and quick execution time. The method can serve as a simple alternative to established and more complex optimizers. Additionally, it could also be used as a benchmark for other metaheuristic optimization algorithms as one of the simplest, yet powerful, optimizers. The algorithm is provided with its full source code in MATLAB for anybody interested to use, test or explore.

This study proposes the DNN-MVLEM, a novel macromodel for the non-linear analysis of RC shear walls based on deep neural networks (DNN); while most RC shear wall macromodeling techniques follow a deterministic approach to find the right configuration and properties of the system, in this study, an alternative data-driven strategy is proposed instead. The proposed DNN-MVLEM is composed of four vertical beam-column elements and one horizontal shear spring. The beam-column elements implement the fiber section formulation with standard non-linear uniaxial material models for concrete and steel, while the horizontal shear spring uses a multi-linear force–displacement relationship. Additionally, three calibration factors are introduced to improve the performance of the macromodel. The data-driven component of the proposed strategy consists of a large DNN that is trained to predict the force–displacement curve of the shear spring and the three calibration factors. The training data is created using a parametric microscopic FEM model based on the multi-layer shell element formulation and a genetic algorithm (GA) that optimizes the response of the macromodel to match the behavior of the microscopic FEM model. The DNN-MVLEM is tested in two types of examples, first as a stand-alone model and then as part of a two-bay multi-story frame structure. The results show that the DNN-MVLEM is capable of reproducing the results obtained with the microscopic FEM model up to 100 times faster and with an estimated error lower than 5%.

Reinforced concrete (RC) shear walls macroscopic models are simplified strategies able to simulate the complex nonlinear behavior of RC shear walls to some extent, but their efficacy and robustness are limited. In contrast, microscopic models are sophisticated finite element method (FEM) models that are far more accurate and reliable. However, their elevated computational cost turns them unfeasible for most practical applications. In this study, a data-driven surrogate model for analyzing RC shear walls is developed using deep neural networks (DNNs). The surrogate model is trained with thousands of FEM simulations to predict the characteristic curve obtained when a static nonlinear pushover analysis is performed. The surrogate model is extensively tested and found to exhibit a high degree of accuracy in its predictions while being extremely faster than the detailed FEM analysis. The complete framework that made this study possible is provided as an open-source project. The project is developed in Python and includes a parametric FEM model of an RC shear wall in OpenSeesPy, the training and validation of the DNN model in TensorFlow, and an application with an interactive graphical user interface to test the methodology and visualize the results.