Citation: Uray, E.; Carbas, S.;
Geem, Z.W.; Kim, S. Parameters
Optimization of Taguchi Method
Integrated Hybrid Harmony Search
Algorithm for Engineering Design
Problems. Mathematics 2022, 10, 327.
https://doi.org/10.3390/
math10030327
Academic Editor: Alfredo Milani
Received: 4 December 2021
Accepted: 14 January 2022
Published: 21 January 2022
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Article
Parameters Optimization of Taguchi Method Integrated Hybrid
Harmony Search Algorithm for Engineering Design Problems
Esra Uray
1,
* , Serdar Carbas
1,2
, Zong Woo Geem
3,
* and Sanghun Kim
4
1
Department of Civil Engineering, KTO Karatay University, Konya 42020, Turkey; scarbas@kmu.edu.tr
2
Department of Civil Engineering, Karamanoglu Mehmetbey University, Karaman 70200, Turkey
3
College of IT Convergence, Gachon University, Seongnam 13120, Korea
4
Department of Civil and Environmental Engineering, Temple University, Philadelphia, PA 19122, USA;
sanghun.kim@temple.edu
* Correspondence: esra.uray@karatay.edu.tr (E.U.); geem@gachon.ac.kr (Z.W.G.)
Abstract:
Performance of convergence to the optimum value is not completely a known process due to
characteristics of the considered design problem and floating values of optimization algorithm control
parameters. However, increasing robustness and effectiveness of an optimization algorithm may
be possible statistically by estimating proper algorithm parameters values. Not only the algorithm
which utilizes these estimated-proper algorithm parameter values may enable to find the best fitness
in a shorter time, but also it may supply the optimum searching process with a pragmatical manner.
This study focuses on the statistical investigation of the optimum values for the control parameters of
the harmony search algorithm and their effects on the best solution. For this purpose, the Taguchi
method integrated hybrid harmony search algorithm has been presented as an alternative method for
optimization analyses instead of sensitivity analyses which are generally used for the investigation
of the proper algorithm parameters. The harmony memory size, the harmony memory considering
rate, the pitch adjustment rate, the maximum iteration number, and the independent run number
of entire iterations have been debated as the algorithm control parameters of the harmony search
algorithm. To observe the effects of design problem characteristics on control parameters, the new
hybrid method has been applied to different engineering optimization problems including several
engineering-optimization examples and a real-size engineering optimization design. End of extensive
optimization and statistical analyses to achieve optimum values of control parameters providing rapid
convergence to optimum fitness value and handling constraints have been estimated with reasonable
relative errors. Employing the Taguchi method integrated hybrid harmony search algorithm in
parameter optimization has been demonstrated as it is a reliable and efficient manner to obtain the
optimum results with fewer numbers of run and iteration.
Keywords:
hybrid harmony search algorithm; Taguchi method; algorithm control parameter
optimization; engineering design problems; reinforced cantilever retaining wall design
1. Introduction
The well-functioning optimum designs, which aim to reach stable and economic or
productive mechanisms in engineering regulation, are based on mathematical theorems and
approaches. While optimization methods were applied by Newton, Lagrange, Cauchyeski,
and so on for smaller-sized problems in ancient times, today produce the solutions with
improved or hybrid versions of the optimization algorithms for large-size complex engi-
neering designs. In this conjuncture, metaheuristic optimization algorithms that enable
them to achieve reasonable solutions in a shorter time have been commonly employed in
complicated engineering designs, since environmental and global phenomena due to devel-
oping technology and increasing population have been raised in the last two decades [
1
].
Although each of them adopts a different process and texture within itself, many effective
Mathematics 2022, 10, 327. https://doi.org/10.3390/math10030327 https://www.mdpi.com/journal/mathematics
