Citation: Sarjamei, S.; Massoudi,
M.S.; Esfandi Sarafraz, M.
Frequency-Constrained Optimization
of a Real-Scale Symmetric Structural
Using Gold Rush Algorithm.
Symmetry 2022, 14, 725. https://
doi.org/10.3390/sym14040725
Academic Editors: Jan Awrejcewicz
and Sergei D. Odintsov
Received: 21 February 2022
Accepted: 31 March 2022
Published: 2 April 2022
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Article
Frequency-Constrained Optimization of a Real-Scale Symmetric
Structural Using Gold Rush Algorithm
Sepehr Sarjamei, Mohammad Sajjad Massoudi * and Mehdi Esfandi Sarafraz
Department of Civil Engineering, West Tehran Branch, Islamic Azad University, Tehran 1468763785, Iran;
sarjamei.sepehr@wtiau.ac.ir (S.S.); sarafraz.m@wtiau.ac.ir (M.E.S.)
* Correspondence: massoudi.ms@wtiau.ac.ir
Abstract:
The optimal design of real-scale structures under frequency constraints is a crucial problem
for engineers. In this paper, linear analysis, as well as optimization by considering natural frequency
constraints, have been used for real-scale symmetric structures. These structures require a lot of
time to minimize weight and displacement. The cyclically symmetric properties have been used
for decreasing time. The structure has been decomposed into smaller repeated portions termed
substructures. Only the substructure elements are needed when analyzing and designing with the
concept of cyclic symmetries. The frequency constrained design of real-scale structures is a complex
optimization problem that has many local optimal answers. In this research, the Gold Rush Optimiza-
tion (GRO) algorithm has been used to optimize weight and displacement performances due to its
effectiveness and robustness against uncertainties. The efficacy of the concept of cyclic symmetry to
minimize the time calculated is assessed by three examples, including Disk, Silo, and Cooling Tower.
Numerical results indicate that the proposed method can effectively reduce time consumption, and
that the GRO algorithm results in a 14–20% weight reduction of the problems.
Keywords:
structural optimization; frequency constraints; cyclic symmetry; Gold Rush Optimization
algorithm
1. Introduction
In vibrational analysis, the optimal design of real-scale symmetric structures under
frequency constraints is a crucial problem. Since the modal properties of a structure
determine its dynamic behavior, the frequency constraints and the capacity to adjust the
values of natural frequencies are sensitive items in the analysis and design. Concerning
the frequency constraints, including non-convex search spaces, sophisticated methods are
needed [
1
]. Since the frequency constrained design of large-scale structures is a complex
optimization problem with many local optima, an appropriate optimization technique is
usually required. Among the research conducted to optimize the design of structures under
frequency constraints, the following studies can be briefly reviewed.
Using laws of momentum and energy between collisions bodies, Kaveh and Mah-
davi [
2
] introduced a new Colliding Bodies Optimization algorithm (CBO). Kaveh and
Mahdavi [
3
] looked into the effectiveness of CBO for the problem and conducted parametric
research on its internal characteristics. Enhanced Colliding Bodies Optimization (ECBO)
introduced by Kaveh and Ilchi Ghazaan [
4
] improved the function of the CBO algorithm.
ECBO uses memory to save some optimal solutions. Enhanced Colliding Bodies Optimiza-
tion (ECBO) was used by Kaveh and Ilchi Ghazaan [
5
] to demonstrate the algorithm’s
efficiency in frequency-constrained structural optimization. Song and Zhang [
6
] assessed
the wind deflection of a railway catenary in a crosswind under frequency constraints, based
on wind tunnel tests and a nonlinear finite element model. Ho-Huu et al. [
7
] proposed
a new version of the Differential Evolution (DE) method called Roulette Wheel Selection-
Elitist-Differential Evolution (ReDE), which employs elitism in the selection phase using the
Symmetry 2022, 14, 725. https://doi.org/10.3390/sym14040725 https://www.mdpi.com/journal/symmetry
