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.
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.
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.
The objective of this work is to use machine learning techniques to analyze a big database of papers published since 1990 regarding the conservation of masonry buildings considered as historical heritage. In this study, a database of nearly three thousand papers obtained from Scopus database [1] were investigated. In a first stage, the papers are analyzed using basic statistics in order to describe the evolution of the research during the past thirty years. In the second stage, Genetic Algorithms (GA) were implemented to create bibliometric maps for the visualization of co-word analysis that was performed using the provided database. The obtained diagrams constitute comprehensive maps of relevant characteristics among the investigated literature such as similarities between author keywords or author names. The maps are constructed using a rigorous methodology that involves the mapping of each item (for example, a keyword) to a two-dimensional point. The distances between the items represent their dissimilarity for a specific characteristic. The numerical procedure for the construction of the bibliometric map involves an optimization task solved by means of GA. The obtained result is a powerful tool for data analysis, which provides a deep insight of relevant characteristics of a large database in a very short time.
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