The Algebraic Riccati Matrix Equation for Eigendecomposition of Canonical Forms

The algebraic Riccati matrix equation is used for eigendecomposition of special structured matrices. This is achieved by similarity transformation and then using the algebraic Riccati matrix equation to the triangulation of matrices. The process is the decomposition of matrices into small and specially structured submatrices with low dimensions for easy finding of eigenpairs. Here, we show that previous canonical forms I, II, III, and so on are special cases of the presented method. Numerical and structural examples are included to show the efficiency of the present method

Material Generation Algorithm: A Novel Metaheuristic Algorithm for Optimization of Engineering Problems

A new algorithm, Material Generation Algorithm (MGA), was developed and applied for the optimum design of engineering problems. Some advanced and basic aspects of material chemistry, specifically the configuration of chemical compounds and chemical reactions in producing new materials, are determined as inspirational concepts of the MGA. For numerical investigations purposes, 10 constrained optimization problems in different dimensions of 10, 30, 50, and 100, which have been benchmarked by the Competitions on Evolutionary Computation (CEC), are selected as test examples while 15 of the well-known engineering design problems are also determined to evaluate the overall performance of the proposed method. The best results of different classical and new metaheuristic optimization algorithms in dealing with the selected problems were taken from the recent literature for comparison with MGA. Additionally, the statistical values of the MGA algorithm, consisting of the mean, worst, and standard deviation, were calculated and compared to the results of other metaheuristic algorithms. Overall, this work demonstrates that the proposed MGA is able provide very competitive, and even outstanding, results and mostly outperforms other metaheuristics

Optimization of Engineering Design Problems Using Atomic Orbital Search Algorithm

In this paper, optimum design of engineering problems is considered by means of the Atomic Orbital Search (AOS), a recently proposed metaheuristic optimization algorithm. The mathematical development of the algorithm is based on principles of quantum mechanics focusing on the act of electrons around the nucleus of an atom. For numerical investigation, 20 of well-known constrained design problems in different engineering fields are considered; some of which have been benchmarked by the 2020 Competitions on Evolutionary Computation (CEC 2020) for real-world optimization purposes. Statistical results including the best, mean, worst and standard deviation of multiple optimization runs are reported for the AOS algorithm. These results are compared to similar data from previous metaheuristic algorithms found in the literature to establish the efficiency and usefulness of the AOS. It is concluded that the AOS has acceptable behavior in dealing with all the considered constrained optimization problems while the maximum difference of about 40% between the best optimum values of the AOS and other approaches is noted for the robot gripper benchmark problem

Evaluation of the Mechanical Properties of Normal Concrete Containing Nano-MgO under Freeze–Thaw Conditions by Evolutionary Intelligence

In this research, different amounts of nano-MgO were added to normal concrete samples, and the effect of these particles on the durability of the samples under freeze and thaw conditions was investigated. The compressive and tensile strength as well as the permeability of concrete containing nanoparticles were measured and compared to those of plain samples (without nanoparticles). The age of concrete samples, percentage of nanoparticles, and water-to-binder ratio are the variables of the current research. Based on the results, the addition of 1% nano-MgO to the normal concrete with a water-to-binder ratio of 0.44 can reduce the permeability up to 63% and improve the compressive and tensile strengths by 9.12% and 10.6%, respectively. Gene Expression Programming (GEP) is applied, and three formulations are derived for the prediction of mechanical properties of concrete containing nano-MgO. In this method, 80% of the dataset is used randomly for the training process and 20% is utilized for testing the formulation. The results obtained by GEP showed acceptable accuracy

Attraction and diffusion in nature-inspired optimization algorithms

Nature-inspired algorithms usually use some form of attraction and diffusion as a mechanism for exploitation and exploration. In this paper, we investigate the role of attraction and diffusion in algorithms and their ways in controlling the behaviour and performance of nature-inspired algorithms. We highlight different ways of the implementations of attraction in algorithms such as the firefly algorithm, charged system search, and the gravitational search algorithm. We also analyze diffusion mechanisms such as random walks for exploration in algorithms. It is clear that attraction can be an effective way for enhancing exploitation, while diffusion is a common way for exploration. Furthermore, we also discuss the role of parameter tuning and parameter control in modern metaheuristic algorithms, and then point out some key topics for further research

Advances of swarm intelligent systems in gene expression data classification

The step forward in the development of microarray technology of gene expression has created new opportunities in further exploration of living systems, source of disease and drug development and cancer biology. In the analysis of gene expression profiles, the number of tissue samples with genes expression levels available is usually small compared with the number of genes. This can lead either to possible overfitting and dimensionality curse or even to a complete failure in analysis of microarray data. So, the dramatic increase in genomic data volumes make it a challenging task to select genes that are really indicative of the tissue classification a key step to accurately pick out the information from such microarrays. On the other hand, in the last decades, swarm intelligent systems have gained much attention and wide applications in different fields such as solving the gene expression data classification problem. These algorithms are efficient in dealing with optimization issues, and they are also relatively simple to implement with the ability to fast converge to a reasonably good solution. They engage probabilistic rules instead of deterministic ones and require neither derivatives of cost function. In this paper, a hybrid algorithm based on swarm intelligence systems is utilized to classify gene expression dat

Determining the Optimum Section of Tunnels Using Ant Colony Optimization

Ant colony optimization is developed to determine optimum cross sections of tunnel structures. Tunnel structures are expensive infrastructures in terms of material, construction, and maintenance and the application of optimization methods has a great role in minimizing their costs. This paper presents the formulation of objective function and constraints of the problem for the first time, and the ant colony optimization, as a developed metaheuristic approach, has been used to solve the problem. The results and comparisons based on numerical examples show the efficiency of the algorithm

The Algebraic Riccati Matrix Equation for Eigendecomposition of Canonical Forms

The algebraic Riccati matrix equation is used for eigendecomposition of special structured matrices. This is achieved by similarity transformation and then using the algebraic Riccati matrix equation to the triangulation of matrices. The process is the decomposition of matrices into small and specially structured submatrices with low dimensions for easy finding of eigenpairs. Here, we show that previous canonical forms I, II, III, and so on are special cases of the presented method. Numerical and structural examples are included to show the efficiency of the present method