Home A new neural network–assisted hybrid chaotic hiking optimization algorithm for optimal design of engineering components
Article Open Access

A new neural network–assisted hybrid chaotic hiking optimization algorithm for optimal design of engineering components

  • Ahmet Remzi Özcan

    Dr. Ahmet Remzi Özcan is an Assistant professor in the Department of Mechatronics Engineering at Bursa University, Bursa, Turkey. His research interests are the optimization of mechanical and mechatronic systems, meta-heuristic optimization algorithms.

         , Pranav Mehta

    Mr. Pranav Mehta is an Assistant Professor at the Department of Mechanical Engineering, Dharmsinh Desai University, Nadiad-387001, Gujarat, India. He is currently a Ph.D. research scholar at Dharmsinh Desai University, Nadiad, Gujarat, India. His major research interests are metaheuristics techniques, multiobjective optimization, solar–thermal technologies, and renewable energy.

         , Sadiq M. Sait

    Dr. Sadiq M. Sait received his Bachelor’s degree in Electronics Engineering from Bangalore University, India, in 1981, and his Master’s and Ph.D. degrees in Electrical Engineering from the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, in 1983 and 1987, respectively. He is currently a Professor of Computer Engineering and Director of the Center for Communications and IT Research, KFUPM, Dhahran, Saudi Arabia.

    , Dildar Gürses

    Dr. Dildar Gürses is a lecturer at Bursa Uludağ University, Bursa, Turkey. She completed her BSc, MSc, and Ph.D. degrees at Uludağ University, Bursa, Turkey. Her research interests are thermodynamics, electric vehicles, meta-heuristic optimization algorithms, and applications to industrial problems.

     EMAIL logo     and Ali Riza Yildiz

    Dr. Ali Riza Yildiz is a Professor in the Department of Mechanical Engineering, Bursa Uludağ University, Bursa, Turkey. His research interests are the finite element analysis of structural components, lightweight design, vehicle design, vehicle crashworthiness, shape and topology optimization of vehicle components, metaheuristic optimization techniques, and additive manufacturing.
Published/Copyright: April 14, 2025
Download Article (PDF)
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Materials Testing
From the journal Materials Testing Volume 67 Issue 6

Abstract

In the era of artificial intelligence (AI), optimization and parametric studies of engineering and structural systems have become feasible tasks. AI and ML (machine learning) offer advantages over classical optimization techniques, which often face challenges such as slower convergence, difficulty handling multiobjective functions, and high computational time. Modern AI and ML techniques may not effectively address all critical design engineering problems despite these advancements. Nature-inspired algorithms based on physical phenomena in nature, human behavior, swarm intelligence, and evolutionary principles present a viable alternative for multidisciplinary design optimization challenges. This article explores the optimization of various engineering problems using a newly developed modified hiking optimization algorithm (HOA). The algorithm is inspired by human hiking techniques, such as hill climbing and hiker speed. The advantages of the modified HOA are compared with those of several famous algorithms from the literature, demonstrating superior results in terms of statistical measures.

Keywords: hiking optimization algorithm; artificial neural network; chaotic maps; real-world applications; engineering design

1 Introduction

In the era of artificial intelligence, optimization and parametric study of different systems, including engineering and structural, becomes a feasible task. The domain of artificial intelligence is comparatively more advantageous than classical optimization techniques, which realize several challenges while optimizing the constraint problems. For instance, slower convergence, challenges in handling multiobjective functions, high computational time, and unbalance between exploration–exploitation phase. However, modern trends of AI-ML may not be effective in tackling each critical design engineering problem. Hence, nature-inspired algorithms are one of the most effective options for dealing with multidisciplinary design optimization challenges. The different categories and most recently developed algorithms are indicated in Figure 1. These algorithms are developed by inspiring physical phenomena that exist in nature, human behavior, swarm intelligence, and evolutionary-based [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Some of the recently invented optimizers are the hiking optimization algorithm [11], the Artificial Protozoa algorithm [12], Eel and grouper optimizer [13], Greater can rat algorithm [14], Greylag goose optimizer [15], the Partial reinforcement optimizer [16], Hippopotamus optimizer [17], starfish [18], and Crayfish optimizer [19]. These algorithms are adopted in multidisciplinary fields, including but not limited to manufacturing industries, automobile system optimization, fuzzy circuit optimization, power system optimization, and structural optimization [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37]. Moreover, modifications of several base algorithms have been achieved to improve the results further and realize globally optimized solutions. This being said, effective oppositional-based techniques, chaotic maps, levy flight search, multistrategy enhancement, and hybridization of algorithms are pursued [20], [27], [28], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48]. These modified algorithms are identified to be more effective, and the results obtained are superior compared to other benchmark algorithms vis-à-vis its base version. The article studies the optimization of different engineering problems considering a newly developed hiking optimization algorithm, and modifications have been carried out. The considered algorithm was developed on the basis of the hiking techniques of humans, including hill climbing and the speed of the hiker’s. Moreover, the results of statistics were compared with the results of some of the famous algorithms in the literature .

Figure 1: Chaotic maps and neural networks categories and modified algorithm’s merits.
Figure 1:

Chaotic maps and neural networks categories and modified algorithm’s merits.

2 Hiking optimization algorithm (HOA)

Researchers proposed a unique human-activity–based MH algorithm for the optimization of critical fitness functions. The algorithm is inspired by the hiker’s speed, altitude of mountains, steepness, and their approach to exploring the different regions for hiking. Moreover, Tobler’s hiking function is evaluated to support the identification of the various parametric calculations to attain a better solution. Furthermore, the Tobler’s hiking function can be given by Equation (1) [11].

(1) w i , t = 6 e − 3.5   S i , t + 0.05

with i: hiker at time t and w: hiker’s speed. Also, the slope of the terrain (S i,t) can be given by Equation (2).

(2) S i , t = dh dx = tan θ i , t

with dh: the margin in height and dx: distance traveled by hiker. Accordingly, the present speed of the hiker can be given by Equation (3) [11].

(3) w i , t = w i , t − 1 + γ i , t   β best − α i , t β i , t

(4) β i , t + 1 = β i , t + w i , t

(5) β i , t = LB + δ   UB − LB

with UB and LB: upper and lower bound ranges

Modifications with chaotic maps and neural network in MH optimizers: By incorporating chaotic maps and neural network techniques, the input options in the form of suggestive populations and solution options increase with the optimizer. This being said, as shown in Figure 1, neural networks improve the capability of the algorithm to examine more possible solutions and identify global solutions out of the available set of solutions. Moreover, augmenting chaotic maps improves the mathematic accuracy of the optimizer vis-à-vis and effectively improves the exploitation phase of the algorithm.

3 HOA for design of optimal engineering components

This section covers applications of a studied algorithm for the optimization of effective economic, weight, manufacturing cost, and system parameters.

3.1 Spring mass optimization using HOA

Figure 2 illustrates a computer-aided diagram of spring subjects to a tensile force, including design parameters such as wire diameter, mean coil diameter, and active coil numbers. For the optimization problem, the mass of the spring is defined as objective function, and three major constraints are considered.

Figure 2: Computer-aided layout of spring with design variables.
Figure 2:

Computer-aided layout of spring with design variables.

Table 1 shows a statistical comparison among 17 algorithms published in a research paper for the present case. Well-known algorithms such as marine predators, salp swarm optimizer, moth flame optimizer, equilibrium optimizer, and multiverse optimizers were compared with a modified hiking optimization algorithm for each case. The MHOA is able to tackle global best values effectively.

Table 1:

Statistical results comparison among MHOA and other modified algorithms.

Compared optimizers Superior values Average values Worst values SD-standard deviations Evaluations numbers
Marine predators algorithm 0.01266835 0.01302 0.019963 1.25369E-04 15,000
Salp swarm algorithm [73] 0.0126684 0.01311 0.019625 1.2691E-03 18,000
Multi-verse optimizer [73] 0.0126934 0.0159 0.018075 1.8089E-03 18,000
Moth flame algorithm [73] 0.0126780 0.01430 0.01777 1.6344E-03 18,000
Equilibrium optimizer [73] 0.0126677 0.01315 0.017773 1.3810E-03 18,000
MHOA 0.0126665 0.012935 0.013021 8.1009E-08 15,000

3.2 Study of the cylindrical pressure vessel for economic optimization using HOA

A cylindrical pressure vessel selected to be optimized in terms of total cost is shown in Figure 3. Accordingly, shell thickness, cylindrical section length, heat thickness, and internal radius of the cylinder are selected as design variables. Table 2 records the statistical results, as well as the mean and deviations for MHOA and other compared algorithms. Moreover, MHOA provides more effective results than the rest of the algorithms.

Figure 3: Cylindrical pressure vessel cross-sectional view with design variables.
Figure 3:

Cylindrical pressure vessel cross-sectional view with design variables.

Table 2:

Results for MHOA and other MHs algorithms.

Compared optimizers Superior values Average values Worst values SD-standard deviations Evaluations numbers
Marine predators algorithm 6,061.587963 6,398.259875 6,870.973 223.8965 5,000
Multiverse optimizer [73] 6,068.511494 6,465.615946 7,335.97353 341.336 25,000
EBO [73] 6,092.567106 6,501.053179 6,830.72863 260.008 25,000
ES [73] 6,059.715421 6,617.432326 7,800.53185 471.316 25,000
MHOA 6,059.714335 6,089.5362 6,108.7 57.356 15,000

3.3 Structural design optimization of three-bar truss by weight optimization

In this study, three elementary truss designs have been optimized for sustaining maximum stress as a condition with minimum system weight as a fitness function. Figure 4 shows the arrangement of each truss element with the cross-sectional area as a design parameter. Table 3 shows results obtained from the MHOA algorithm with a chaotic version and other well-known MH results from the literature. The comparison indicates the dominance of MHOA over other optimizers vis-à-vis algorithm realized minimum functional evaluations with the least deviations.

Figure 4: Computer-aided design model of truss structure.
Figure 4:

Computer-aided design model of truss structure.

Table 3:

Results comparison of MHOA with other optimizers.

Compared optimizers Superior values Average values Worst values SD-standard deviations Evaluations numbers
MPA [73] 263.9863023 263.9986 264.8976 0.135693 5,000
MBA [73] 263.8958522 263.897996 263.915983 3.93E−03 13,280
CS [73] 263.97156 264.0669 – 0.00009 15,000
MHOA 263.8958522 263.897863 263.9123651 2.89E−04 4,500

3.4 Optimization of volume capacity for piston-lever design assembly

Figure 5 represents the computer-aided design of the piston-lever assembly that is used to transfer reciprocating motion to rotational by traversing the crankshaft from 0° to 45°.

Figure 5: Computer-aided layout of piston-lever assembly.
Figure 5:

Computer-aided layout of piston-lever assembly.

Accordingly, height, width, diameter, and stroke are considered decision parameters, with stress and load acting over these systems as constraints. Table 4 records the statistical data of MHOA with other compared optimizers. Again, in this case, MHOA realized effective results with dominance over the other MHs in terms of best values of fitness function and least standard deviations. However, MPA and SSA pursued competitive results with MHOA.

Table 4:

Results comparison of MHOA with other optimizers.

Compared optimizers Superior values Average values Worst values SD-standard deviations Evaluations numbers
MPA [73] 8.4369853 198.8963 224.5369 58.36599 20,000
SSA [73] 8.4220378 276.9405 653.4973 121.4145 25,000
MVO [73] 8.4289960 138.4470 356.2368 138.5046 25,000
MFO [73] 8.4126983 91.12391 167.4727 80.27315 25,000
ASO [73] 213.83459 346.0264 778.6031 115.1357 25,000
HSOGA [73] 8.4127155 128.0854 230.0218 84.22322 25,000
MHOA 8.4126981 8.556963 8.5896321 5.2369854 15,000

3.5 Weight optimization of spur gear design

Spur gears are generally used in mechanical industries and automobile systems to transfer motion at a regular speed ratio. The speed can be reduced or improved by identifying an adequate gear ratio, as shown in Figure 6.

Figure 6: Computer-aided layout of spur gear design.
Figure 6:

Computer-aided layout of spur gear design.

Accordingly, mass minimization of the system is kept as an objective function with five design variables: module, pinion teeth, face width, pinion diameter, and shaft diameter. Moreover, Table 5 shows recorded data from a computational study regarding statistics best, mean, worst, and standard deviation. Hence, MHOA pursued the best value for the fitness function as the minimum weight of the spur gear system with minimum functional evaluations. However, MPA and other optimizers have shown competitive results with MHOA in the present case.

Table 5:

Results comparison of MHOA with other optimizers.

Compared optimizers Superior values Average values Worst values SD-standard deviations Evaluations numbers
MPA 1,538.9986 1,546.1023 1,559.1519 11.02536 20,000
MVO [73] 1,538.9537 1,539.0275 1,539.1666 0.047911 25,000
ASO [73] 1,624.2236 1,713.7505 1,827.0782 49.41359 25,000
MHOA 1,538.94468 1,538.9450 1,538.9462 0.000318 15,000

3.6 Structural optimization of automobile components using MHOA

Structural optimization of vehicle components for obtaining effective efficiency has been carried out using MHOA. In this case study, the objective function is to reduce the weight using structural and volume reduction optimization concepts. However, the element is subjected to several critical constraints as given by Equations (6)–(8).

Objective function: minimum mass of the element

(6) F y = f 1 a

Constraint:

(7) g y ≤ 300   N / mm 2

(8) a i l ≤ a i ≤ a i u , i = 1 , NDV

with, yu and yl,: upper and lower variables limits, respectively.

Moreover, the operating range of the six considered decision parameters are 6.2 < a 1 < 13.9, 35.2 < a 2 < 45, 25.2 < a 3 < 35.6, 18.2 < a 4 < 26.4, 18.2 < a 5 < 26.4, and 6.3 < a 6 < 13.8. Accordingly, the initial computer graphics are shown in Figure 7.

Figure 7: Computer-aided design of automobile component.
Figure 7:

Computer-aided design of automobile component.

The optimum brake pedal design is carried out using the MHOA algorithm, as shown in Figure 6. A minimum mass of 1081.7 g is found with the MHOA, as presented in Table 6.

Table 6:

Optimum results for the brake design.

Compared

optimizers		 Optimized weight in gram Mean values Worst values Standard deviation Stress (MPa)
Initial design 1,583 187
Ship rescue optimizer 1,122.5 1,138.2 1,154.0 4.31 298
Crayfish optimizer 1,096.6 1,125.6 1,136.0 4.23 297
MHOA 1,081.7 1,098.7 1,105.6 1.06 299

Figure 8 shows an optimum design of the brake pedal. Moreover, Table 6 shows the statistical results that were compared to show the dominance of the MHOA over the ship rescue optimizer and the crayfish optimization algorithm.

Figure 8: Optimized design of vehicle brake pedal using MHOA.
Figure 8:

Optimized design of vehicle brake pedal using MHOA.

3.7 Optimization of plate and fin heat exchanger using MHOA

Many industries use different types of heat exchangers to process or heat off fluids in space. The most important examples include but are not restricted to solar-thermal applications, heat recovery devices, power plants, and cryogenics [48]. Using efficient surface areas like fins, ribs, the heat exchanger’s primary job is to move heat from one medium to another. The literature provides a full description of the thermal design [50]. The dense aluminum used to assemble the fin plate heat exchanger has a density of about 2700 kgm−3 [47]. Figure 9 and Table 7, respectively, identify the parametric and the 3-D picture. Furthermore, the study focuses on minimizing the cost of fin plate heat exchanges using the cheetah optimizer.

Figure 9: Optimiation of PFHE.
Figure 9:

Optimiation of PFHE.

Table 7:

Considerations of parameters and constraints.

Parameters to be optimized Min. values Max. values Range
Hot fluid side length (10−3m) 100 1,000 –
Cold fluid side length (10−3m) 100 1,000 –
Fin height (10−3m) 2 10 –
Fin thickness (10−3m) 0.1 0.2 –
Fin pitch (/m) 100 1,000 –
Placing of fin (10−3m) 1 10 –
Critical constraints Difference in pressure at hot fluid side (Pa) – – ≤ 9.5E + 03
Difference in pressure at cold fluid side (Pa) – – ≤ 8E + 03
FPHE overall weight – – <350 kg
Measured effectiveness – – ≥ 88 %

Equation (9) [23] provides the mathematical model for the heat exchanger’s initial cost.

(9) C ini − PFHE = C PFHE * SA N PFHE n 1

(10) C oc − FPHE = P pump + P compressor × t op × COE

(11) C total − FPHE = C in − FPHE i 1 + IR n 1 + IR n − 1 + C oc − FPHE

The objective function can be calculated using Equations (12) and (13), [23].

(12) Minimization of  f y = C total − FPHE + ∑ j = 1 m z j g ‾ j y

(13) z j = C total − FPHE ‾ + g ‾ j y ∑ j = 1 m g ‾ j y 2

Table 8 and 9 can be used to perform statistical analysis by comparing a number of parameters that the MHOA algorithm has achieved, including best, worst, mean, and standard deviation values.

Table 8:

Results in terms of statistics.

Optimizers Best Worst Mean SD SR
MHOA 1,570.64 1,570.01 1,570.46 0.00119 100
ES [22] 1,570.97 1,576.84 1,572.72 2.49 75
SOS [22] 1,570.97 1,571.62 1,571.05 0.172 100
AF [22] 1,570.97 1,571.15 1,571.1 0.0112 100
PVS [22] 1,570.97 1,576.91 1,573.24 1.87 40
SS [22] 1,571.21 1,576.89 1,574.40 2.45 35
GWO [22] 1,570.97 1,571.03 1,570.98 0.0445 100
GOA [22] 1,570.97 1,571.15 1,570.98 0.0428 100
ALO [22] 1,572.08 1,576.82 1,573.29 1.63 55
Table 9:

Optimized results pursued by MHOA.

Optimized parameters Results
The overall HE weight 350 kg
Loss of hot-side fluid pressure 0.67 kPa
The overall HE cost 1,570.64 ($)

4 Conclusions

This study successfully demonstrates the application and efficacy of the modified hiking optimization algorithm (MHOA) in optimizing various engineering components. The MHOA, inspired by human hiking behavior and enhanced by hiking function, has proven to be effective in solving complex optimization problems. The algorithm was tested on several engineering optimization cases, including spring mass optimization, cylindrical pressure vessel cost optimization, three-bar truss structural optimization, piston-lever design optimization, spur gear weight optimization, heat exchanger, and structural optimization of automobile components. MHOA outperformed other well-known algorithms in each case, achieving superior best values, mean values, and standard deviations. The results indicate that MHOA is a robust and efficient optimization tool capable of addressing multidisciplinary design challenges with improved accuracy and computational efficiency. The success of MHOA in these applications suggests its potential for broader adoption in various engineering optimization problems.

Corresponding author: Dildar Gürses, Hybrid and Electric Vehicle Technology, Vocational School of Gemlik Asım Kocabıyık, Bursa Uludağ University, Bursa, 16600, Türkiye, E-mail:

About the authors

Ahmet Remzi Özcan

Dr. Ahmet Remzi Özcan is an Assistant professor in the Department of Mechatronics Engineering at Bursa University, Bursa, Turkey. His research interests are the optimization of mechanical and mechatronic systems, meta-heuristic optimization algorithms.

Pranav Mehta

Mr. Pranav Mehta is an Assistant Professor at the Department of Mechanical Engineering, Dharmsinh Desai University, Nadiad-387001, Gujarat, India. He is currently a Ph.D. research scholar at Dharmsinh Desai University, Nadiad, Gujarat, India. His major research interests are metaheuristics techniques, multiobjective optimization, solar–thermal technologies, and renewable energy.

Sadiq M. Sait

Dr. Sadiq M. Sait received his Bachelor’s degree in Electronics Engineering from Bangalore University, India, in 1981, and his Master’s and Ph.D. degrees in Electrical Engineering from the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, in 1983 and 1987, respectively. He is currently a Professor of Computer Engineering and Director of the Center for Communications and IT Research, KFUPM, Dhahran, Saudi Arabia.

Dildar Gürses

Dr. Dildar Gürses is a lecturer at Bursa Uludağ University, Bursa, Turkey. She completed her BSc, MSc, and Ph.D. degrees at Uludağ University, Bursa, Turkey. Her research interests are thermodynamics, electric vehicles, meta-heuristic optimization algorithms, and applications to industrial problems.

Ali Riza Yildiz

Dr. Ali Riza Yildiz is a Professor in the Department of Mechanical Engineering, Bursa Uludağ University, Bursa, Turkey. His research interests are the finite element analysis of structural components, lightweight design, vehicle design, vehicle crashworthiness, shape and topology optimization of vehicle components, metaheuristic optimization techniques, and additive manufacturing.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: All authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

References

[1] P. Mehta, S. M. Sait, B. S. Yıldız, M. U. Erdaş, M. Kopar, and A. R. Yıldız, “A new enhanced mountain gazelle optimizer and artificial neural network for global optimization of mechanical design problems,” Mater. Test., vol. 66, no. 4, pp. 544–552, 2024, https://doi.org/10.1515/mt-2023-0332.Search in Google Scholar

[2] S. C. Chu, T. T. Wang, A. R. Yildiz, and J. S. Pan, “Ship rescue optimization: a new metaheuristic algorithm for solving engineering problems,” J. Internet Technol., vol. 25, no. 1, pp. 61–77, 2024, https://doi.org/10.53106/160792642024012501006.Search in Google Scholar

[3] Y. Kanokmedhakul, S. Bureerat, N. Panagant, T. Radpukdee, N. Pholdee, and A. R. Yildiz, “Metaheuristic-assisted complex H-infinity flight control tuning for the Hawkeye unmanned aerial vehicle: a comparative study,” Exp. Syst. Appl., vol. 123428, 2024, https://doi.org/10.1016/j.eswa.2024.123428.Search in Google Scholar

[4] P. Mehta, A. R. Yildiz, S. M. Sait, and B. S. Yildiz, “Enhancing the structural performance of engineering components using the geometric mean optimizer,” Mater. Test., vol. 66, no. 7, pp. 1063–1073, 2024, https://doi.org/10.1515/mt-2024-0005.Search in Google Scholar

[5] H. Jia, X. Zhou, J. Zhang, L. Abualigah, A. R. Yildiz, and A. G. Hussien, “Modified crayfish optimization algorithm for solving multiple engineering application problems,” Artif. Intell. Rev., vol. 57, no. 5, p. 127, 2024, https://doi.org/10.1007/s10462-024-10738-x.Search in Google Scholar

[6] S. M. Sait, P. Mehta, A. R. Yıldız, and B. S. Yıldız, “Optimal design of structural engineering components using artificial neural network-assisted crayfish algorithm,” Mater. Test., vol. 66, no. 9, pp. 1439–1448, 2024, https://doi.org/10.1515/mt-2024-0075.Search in Google Scholar

[7] Z. C. Dou, S. C. Chu, Z. Zhuang, A. R. Yildiz, and J. S. Pan, “GBRUN: a gradient search-based binary Runge Kutta optimizer for feature selection,” J. Internet Technol., vol. 25, no. 3, pp. 341–353, 2024, https://doi.org/10.53106/160792642024052503001.Search in Google Scholar

[8] E. Demirci and A. R. Yildiz, “A new hybrid approach for reliability-based design optimization of structural components,” Mater. Test., vol. 61, no. 2, pp. 111–119, 2019, https://doi.org/10.3139/120.111291.Search in Google Scholar

[9] T. Güler, E. Demirci, A. R. Yıldız, and U. Yavuz, “Lightweight design of an automobile hinge component using glass fiber polyamide composites,” Mater. Test., vol. 60, no. 3, pp. 306–310, 2018, https://doi.org/10.3139/120.111152.Search in Google Scholar

[10] H. Gökdağ and A. R. Yıldız, “Structural damage detection using modal parameters and particle swarm optimization,” Mater. Test., vol. 64, no. 6, pp. 416–420, 2012, https://doi.org/10.3139/120.110346.Search in Google Scholar

[11] S. O. Oladejo, S. O. Ekwe, and S. Mirjalili, “The Hiking Optimization Algorithm: a novel human-based metaheuristic approach,” Knowl.-Based Syst., vol. 296, p. 111880, 2024, https://doi.org/10.1016/j.knosys.2024.111880.Search in Google Scholar

[12] X. Wang, V. Snášel, S. Mirjalili, J. S. Pan, L. Kong, and H. A. Shehadeh, “Artificial Protozoa Optimizer (APO): a novel bio-inspired metaheuristic algorithm for engineering optimization,” Knowl.-Based Syst., vol. 295, p. 111737, 2024, https://doi.org/10.1016/j.knosys.2024.111737.Search in Google Scholar

[13] A. Mohammadzadeh and S. Mirjalili, “Eel And Grouper Optimizer: A Nature-Inspired Optimization Algorithm,” Cluster Comput., pp. 1–42, 2024.10.1007/s10586-024-04545-wSearch in Google Scholar

[14] J. O. Agushaka, A. E. Ezugwu, A. K. Saha, J. Pal, L. Abualigah, and S. Mirjalili, “Greater cane rat algorithm (GCRA): a nature-inspired metaheuristic for optimization problems,” Heliyon, 2024, https://doi.org/10.1016/j.heliyon.2024.e31629.Search in Google Scholar PubMed PubMed Central

[15] E. S. M. El-Kenawy, N. Khodadadi, S. Mirjalili, A. A. Abdelhamid, M. M. Eid, and A. Ibrahim, “Greylag goose optimization: nature-inspired optimization algorithm,” Exp. Syst. Appl., vol. 238, p. 122147, 2024, https://doi.org/10.1016/j.eswa.2023.122147.Search in Google Scholar

[16] A. Taheri, K. RahimiZadeh, A. Beheshti, “Partial reinforcement optimizer: an evolutionary optimization algorithm,” Exp. Syst. Appl., vol. 238, p. 122070, 2024, https://doi.org/10.1016/j.eswa.2023.122070.Search in Google Scholar

[17] M. H. Amiri, N. Mehrabi Hashjin, M. Montazeri, S. Mirjalili, and N. Khodadadi, “Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm,” Sci. Rep., vol. 14, no. 1, p. 5032, 2024, https://doi.org/10.1038/s41598-024-54910-3.Search in Google Scholar PubMed PubMed Central

[18] C. Zhong, G. Li, Z. Meng, H. Li, A. R. Yildiz, and S. Mirjalili, “Starfish optimization algorithm (SFOA): a bio-inspired metaheuristic algorithm for global optimization compared with 100 optimizers,” Neural Comput. Appl., pp. 1–43, 2025, https://doi.org/10.1007/s00521-024-10694-1.Search in Google Scholar

[19] H. Jia, H. Rao, C. Wen, and S. Mirjalili, “Crayfish optimization algorithm,” Artif. Intell. Rev., vol. 56, no. Suppl 2, pp. 1919–1979, 2023, https://doi.org/10.1007/s10462-023-10567-4.Search in Google Scholar

[20] A. R. Yıldız, “Hybrid immune-simulated annealing algorithm for optimal design and manufacturing,” Int. J. Mater. Prod. Technol., vol. 34, no. 3, pp. 217–226, 2009, https://doi.org/10.1504/IJMPT.2009.024655.Search in Google Scholar

[21] A. R. Yildiz and F. Öztürk, Hybrid Taguchi-Harmony Search Approach for Shape Optimization, Berlin, Germany, Springer, 2010, pp. 89–98.Search in Google Scholar

[22] Z. Meng, B. S. Yıldız, G. Li, C. Zhong, S. Mirjalili, and A. R. Yildiz, “Application of state-of-the-art multiobjective metaheuristic algorithms in reliability-based design optimization: a comparative study,” Struct. Multidiscip. Optim., vol. 66, no. 8, p. 191, 2023, https://doi.org/10.1007/s00158-023-03639-0.Search in Google Scholar

[23] S. Anosri, et al.., “A comparative study of state-of-the-art metaheuristics for solving many-objective optimization problems of fixed wing unmanned aerial vehicle conceptual design,” Arch. Comput. Methods in Eng., vol. 30, no. 6, pp. 3657–3671, 2023, https://doi.org/10.1007/s11831-023-09914-z.Search in Google Scholar

[24] S. M. Sait, P. Mehta, D. Gürses, and A. R. Yildiz, “Cheetah optimization algorithm for optimum design of heat exchangers,” Mater. Test., vol. 65, no. 8, pp. 1230–1236, 2023, https://doi.org/10.1515/mt-2023-0015.Search in Google Scholar

[25] D. Gürses, P. Mehta, S. M. Sait, S. Kumar, and A. R. Yildiz, “A multi-strategy boosted prairie dog optimization algorithm for global optimization of heat exchangers,” Mater. Test., vol. 65, no. 9, pp. 1396–1404, 2023, https://doi.org/10.1515/mt-2023-0082.Search in Google Scholar

[26] A. R. Yildiz, N. Öztürk, N. Kaya, and F. Öztürk, “Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm,” Struct. Multidiscip. Optim., vol. 34, no. 4, pp. 317–332, 2007, https://doi.org/10.1007/s00158-006-0079-x.Search in Google Scholar

[27] P. Mehta, et al.., “A novel generalized normal distribution optimizer with elite oppositional based learning for optimization of mechanical engineering problems,” Mater. Test., vol. 65, no. 2, pp. 210–223, 2023, https://doi.org/10.1515/mt-2022-0259.Search in Google Scholar

[28] B. S. Yildiz, et al.., “A novel hybrid flow direction optimizer-dynamic oppositional based learning algorithm for solving complex constrained mechanical design problems,” Mater. Test., vol. 65, no. 1, pp. 134–143, 2023, https://doi.org/10.1515/mt-2022-0183.Search in Google Scholar

[29] P. Champasak, N. Panagant, N. Pholdee, S. Bureerat, P. Rajendran, and A. R. Yildiz, “Grid-based many-objective optimiser for aircraft conceptual design with multiple aircraft configurations,” Eng. Appl. Artif. Intell., vol. 126, p. 106951, 2023, https://doi.org/10.1016/j.engappai.2023.106951.Search in Google Scholar

[30] N. Sabangban, et al.., “Simultaneous aerodynamic and structural optimisation of a low-speed horizontal-axis wind turbine blade using metaheuristic algorithms,” Mater. Test., vol. 65, no. 5, pp. 699–714, 2023, https://doi.org/10.1515/mt-2022-0308.Search in Google Scholar

[31] P. Mehta, B. S. Yildiz, S. M. Sait, and A. R. Yildiz, “A novel hybrid Fick’s law algorithm-quasi oppositional-based learning algorithm for solving constrained mechanical design problems,” Mater. Test., vol. 65, no. 12, pp. 1817–1825, 2023, https://doi.org/10.1515/mt-2023-0235.Search in Google Scholar

[32] C. M. Aye, et al.., “Airfoil shape optimisation using a multi-fidelity surrogate-assisted metaheuristic with a new multi-objective infill sampling technique,” CMES-Comput. Model. Eng. Sci., vol. 137, no. 3, 2023, https://doi.org/10.32604/cmes.2023.028632.Search in Google Scholar

[33] S. Gupta, H. Abderazek, B. S. Yıldız, A. R. Yildiz, S. Mirjalili, and S. M. Sait, “Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems,” Exp. Syst. Appl., p. 115351, 2021, https://doi.org/10.1016/j.eswa.2021.115351.Search in Google Scholar

[34] A. Garg and K. Tai, “Review of genetic programming in modeling of machining processes,” in 2012 Proceedings of International Conference on Modelling, Identification and Control, 2012, pp. 653–658.Search in Google Scholar

[35] A. R. Yildiz, “A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations,” Appl. Soft Comput., vol. 13, no. 3, pp. 1561–1566, 2013, https://doi.org/10.1016/j.asoc.2011.12.016.Search in Google Scholar

[36] Z. G. Wang, M. Rahman, Y. S. Wong, and J. Sun, “Optimization of multi-pass milling using parallel genetic algorithm and parallel genetic simulated annealing,” Int. J. Mach. Tools and Manuf., vol. 45, no. 15, pp. 1726–1734, 2005, https://doi.org/10.1016/j.ijmachtools.2005.03.009.Search in Google Scholar

[37] G. C. Onwubolu, “Performance-based optimization of multi-pass face milling operations using tribes,” Int. J. Mach. Tools and Manuf., vol. 46, nos. 7–8, pp. 717–727, 2006, https://doi.org/10.1016/j.ijmachtools.2005.07.041.Search in Google Scholar

[38] R. V. Rao and P. J. Pawar, “Parameter optimization of a multi-pass milling process using non-traditional optimization algorithms,” Appl. Soft Comput., vol. 10, no. 2, pp. 445–456, 2010, https://doi.org/10.1016/j.asoc.2009.08.007.Search in Google Scholar

[39] P. J. Pawar and R. V. Rao, “Parameter optimization of machining processes using teaching-learning-based optimization algorithm,” Int. J. Adv. Des. Manuf. Technol., vol. 67, nos. 5–8, pp. 995–1006, 2013, https://doi.org/10.1007/s00170-012-4524-2.Search in Google Scholar

[40] A. R. Yildiz, “Cuckoo search algorithm for the selection of optimal machining parameters in milling operations,” Int. J. Adv. Des. Manuf. Technol., vol. 64, no. 1, pp. 55–61, 2013, https://doi.org/10.1007/s00170-012-4013-7.Search in Google Scholar

[41] J. Huang, L. Gao, and X. Li, “An effective teaching-learning-based cuckoo search algorithm for parameter optimization problems in structure designing and machining processes,” Appl. Soft Comput., vol. 36, pp. 349–356, 2015, https://doi.org/10.1016/j.asoc.2015.07.031.Search in Google Scholar

[42] A. R. Yıldız, B. S. Yıldız, S. M. Sait, S. Bureerat, and N. Pholdee, “A new hybrid Harris hawks-Nelder-Mead optimization algorithm for solving design and manufacturing problems,” Mater. Test., vol. 61, no. 8, pp. 735–743, 2019, https://doi.org/10.3139/120.111378.Search in Google Scholar

[43] B. S. Yıldız, P. Mehta, N. Panagant, S. Mirjalili, and A. R. Yildiz, “A novel chaotic Runge Kutta optimization algorithm for solving constrained engineering problems,” J. Comput. Des. Eng., vol. 9, no. 6, pp. 2452–2465, 2022, https://doi.org/10.1093/jcde/qwac113.Search in Google Scholar

[44] H. Abderazek, F. Hamza, A. R. Yildiz, and S. M. Sait, “Comparative investigation of the moth-flame algorithm and whale optimization algorithm for optimal spur gear design,” Mater. Test., vol. 63, no. 3, pp. 266–271, 2021, https://doi.org/10.1515/mt-2020-0039.Search in Google Scholar

[45] D. Gures, S. Bureerat, S. M. Sait, and A. R. Yildiz, “Comparison of the arithmetic optimization algorithm, the slime mold optimization algorithm, the marine predators algorithm, the salp swarm algorithm for real-world engineering applications,” Mater. Test., vol. 63, no. 5, pp. 448–452, 2021, https://doi.org/10.1515/mt-2020-0076.Search in Google Scholar

[46] A. R. Yildiz and F. Ozturk, “Hybrid enhanced genetic algorithm to select optimal machining parameters in turning operation,”Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf., vol. 220, no. 12, pp. 2041–2053, 2006, https://doi.org/10.1243/09544054JEM570.Search in Google Scholar

[47] B. S. Yildiz, N. Pholdee, S. Bureerat, A. R. Yildiz, and S. M. Sait, “Robust design of a robot gripper mechanism using new hybrid grasshopper optimization algorithm,” Exp. Syst., vol. 38, no. 3, 2021, https://doi.org/10.1111/exsy.12666.Search in Google Scholar

[48] B. S. Yildiz, S. Kumar, N. Pholdee, S. Bureerat, S. M. Sait, and A. R. Yildiz, “A new chaotic Levy flight distribution optimization algorithm for solving constrained engineering problems,” Exp. Syst., https://doi.org/10.1111/exsy.12992.Search in Google Scholar

[49] C. M. Aye, N. Pholdee, A. R. Yildiz, S. Bureerat, and S. M. Sait, “Multi-surrogate-assisted metaheuristics for crashworthiness optimisation,” Int. J. Veh. Des., vol. 80, nos. 2/3/4, p. 223, 2019, https://doi.org/10.1504/IJVD.2019.109866.Search in Google Scholar

[50] B. S. Yildiz, N. Pholdee, N. Panagant, S. Bureerat, A. R. Yildiz, and S. M. Sait, “A novel chaotic Henry gas solubility optimization algorithm for solving real-world engineering problems,” Eng. Comput., https://doi.org/10.1007/s00366-020-01268-5.Search in Google Scholar

[51] A. R. Yildiz and F. Öztürk, Hybrid taguchi-harmony search approach for shape optimization, pp. 89–98, 2010, https://doi.org/10.1007/978-3-642-04317-8_8.Search in Google Scholar

[52] T. Güler, E. Demirci, A. R. Yıldız, and U. Yavuz, “Lightweight design of an automobile hinge component using glass fiber polyamide composites,” Mater. Test., vol. 60, no. 3, pp. 306–310, 2018, https://doi.org/10.3139/120.111152.Search in Google Scholar

[53] A. R. Yildiz, N. Kaya, F. Öztürk, and O. Alankuş, “Optimal design of vehicle components using topology design and optimisation,” Int. J. Veh. Des., vol. 34, no. 4, pp. 387–398, 2004, https://doi.org/10.1504/IJVD.2004.004064.Search in Google Scholar

[54] B. S. Yıldız, “Marine predators algorithm and multi-verse optimisation algorithm for optimal battery case design of electric vehicles,” Int. J. Veh. Des., vol. 88, no. 1, p. 1, 2022, https://doi.org/10.1504/IJVD.2022.124866.Search in Google Scholar

[55] A. Karaduman, B. S. Yıldız, and A. R. Yıldız, “Experimental and numerical fatigue-based design optimisation of clutch diaphragm spring in the automotive industry,” Int. J. Veh. Des., vol. 80, nos. 2/3/4, p. 330, 2019, https://doi.org/10.1504/IJVD.2019.109875.Search in Google Scholar

[56] A. R. Yıldız, “Optimization of multi-pass turning operations using hybrid teaching learning-based approach,” Int. J. Adv. Manuf. Technol., vol. 66, pp. 1319–1326, 2013, https://doi.org/10.1007/s00170-012-4410-y.Search in Google Scholar

[57] P. Mehta, B. S. Yildiz, S. M. Sait, and A. R. Yildiz, “Hunger games search algorithm for global optimization of engineering design problems,” Mater. Test., vol. 64, no. 4, pp. 524–532, 2022, https://doi.org/10.1515/mt-2022-0013.Search in Google Scholar

[58] B. S. Yildiz, S. Bureerat, N. Panagant, P. Mehta, and A. R. Yildiz, “Reptile search algorithm and kriging surrogate model for structural design optimization with natural frequency constraints,” Mater. Test., vol. 64, no. 10, pp. 1504–1511, 2022, https://doi.org/10.1515/mt-2022-0048.Search in Google Scholar

[59] D. Gürses, P. Mehta, V. Patel, S. M. Sait, and A. R. Yildiz, “Artificial gorilla troops algorithm for the optimization of a fine plate heat exchanger,” Mater. Test., vol. 64, no. 9, pp. 1325–1331, 2022, https://doi.org/10.1515/mt-2022-0049.Search in Google Scholar

[60] B. S. Yildiz, V. Patel, N. Pholdee, S. M. Sait, S. Bureerat, and A. R. Yildiz, “Conceptual comparison of the ecogeography-based algorithm, equilibrium algorithm, marine predators algorithm and slime mold algorithm for optimal product design,” Mater. Test., vol. 63, no. 4, pp. 336–340, 2021, https://doi.org/10.1515/mt-2020-0049.Search in Google Scholar

[61] D. Gürses, P. Mehta, S. M. Sait, and A. R. Yildiz, “African vultures optimization algorithm for optimization of shell and tube heat exchangers,” Mater. Test., vol. 64, no. 8, pp. 1234–1241, 2022, https://doi.org/10.1515/mt-2022-0050.Search in Google Scholar

[62] J. Luo, H. Chen, A. A. Heidari, Y. Xu, Q. Zhang, and C. Li, “Multi-strategy boosted mutative whale-inspired optimization approaches,” Appl. Math. Modell., vol. 73, pp. 109–123, 2019, https://doi.org/10.1016/j.apm.2019.03.046.Search in Google Scholar

[63] T. Kunakote, et al.., “Comparative performance of twelve metaheuristics for wind farm layout optimisation,” Arch. Comput. Methods Eng., vol. 29, no. 1, pp. 717–730, 2022, https://doi.org/10.1007/s11831-021-09586-7.Search in Google Scholar

[64] A. R. Yildiz, “Optimal structure design of vehicle components using topology design and optimization,” Mater. Test., vol. 50, no. 4, pp. 224–228, 2008, https://doi.org/10.3139/120.100880.Search in Google Scholar

[65] H. Abderazek, S. M. Sait, and A. R. Yildiz, “Optimal design of planetary gear train for automotive transmissions using advanced meta-heuristics,” Int. J. Veh. Des., vol. 80, nos. 2/3/4, p. 121, 2019, https://doi.org/10.1504/IJVD.2019.109862.Search in Google Scholar

[66] H. Abderazek, A. R. Yildiz, and S. M. Sait, “Mechanical engineering design optimisation using novel adaptive differential evolution algorithm,” Int. J. Veh. Des., vol. 80, nos. 2/3/4, p. 285, 2019, https://doi.org/10.1504/IJVD.2019.109873.Search in Google Scholar

[67] M. Mehta, B. S. Yildiz, S. M. Sadiq, and A. R. Yildiz, “Gradient-based optimizer for economic optimization of engineering problems,” Mater. Test., vol. 64, no. 5, pp. 690–696, 2020, https://doi.org/10.1515/mt-2022-0055.Search in Google Scholar

[68] N. Öztürk, A. R. Yildiz, N. Kaya, and F. Öztürk, “Neuro-Genetic design optimization framework to support the integrated robust design optimization process in CE,” Concurr. Eng., vol. 14, no. 1, pp. 5–16, 2006, https://doi.org/10.1177/1063293X06063314.Search in Google Scholar

[69] B. S. Yildiz, “The mine blast algorithm for the structural optimization of electrical vehicle components,” Mater. Test., vol. 62, no. 5, pp. 497–502, 2020, https://doi.org/10.3139/120.111511.Search in Google Scholar

[70] A. R. Yildiz, et al.., “The equilibrium optimization algorithm and the response surface based metamodel for optimal structural design of vehicle components,” Mater. Test., vol. 62, no. 5, pp. 492–496, 2020, https://doi.org/10.3139/120.111509.Search in Google Scholar

[71] B. S. Yildiz, et al.., “A new hybrid artificial hummingbird-simulated annealing algorithm to solve constrained mechanical engineering problems,” Mater. Test., vol. 64, no. 7, pp. 1043–1050, 2022, https://doi.org/10.1515/mt-2022-0123.Search in Google Scholar

[72] P. Champasak, N. Panagant, N. Pholdee, S. Bureerat, P. Rajendran, and A. R. Yildiz, “Grid-based many-objective optimiser for aircraft conceptual design with multiple aircraft configurations,” Eng. Appl. Artif. Intell., vol. 126, 2023, https://doi.org/10.1016/j.engappai.2023.106951.Search in Google Scholar

[73] S. Kumar, B. S. Yildiz, P. Mehta, “Chaotic marine predators algorithm for global optimization of real-world engineering problems,” Knowl.-Based Syst., vol. 261, p. 110192, 2023, https://doi.org/10.1016/j.knosys.2022.110192.Search in Google Scholar
Published Online: 2025-04-14
Published in Print: 2025-06-26

© 2025 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Frontmatter
  2. Effect of flush grinding on corrosion fatigue behavior of step-aged 7020 aluminum alloys
  3. Bending behavior of corrugated sandwich panels with various core shapes
  4. Comparison of crash performance of auxetic structures for CF15, PA6/GF30, and GF30PP materials
  5. Combined effect of ball milling and high-pressure torsion on mechanical properties of Al2O3/Al composite
  6. Liquid metal embrittlement susceptibility of galvanized advanced high strength steel with high manganese content
  7. Kinetic study on nickel aluminides formed on Monel 400 alloy
  8. Finite element simulation of natural gas pipelines in service welding repair
  9. Biomechanical effects of material selection and micro-groove design for dental implants
  10. Design, FEA and experimental validation of 3D-printed PLA/PCL intervertebral cages for lumbar spinal fusion
  11. Effect of tool tilt angles on the formation of YSZ/Al2O3 hybrid surface composites on friction stir processed magnesium alloy AZ31
  12. Coating of AISI 304 stainless steel surface with addition of Cr3C2 to NiCrCo medium entropy alloy powder
  13. Numerical and analytical stress analysis for a FGM beam
  14. Mechanical and wear behaviour of hybrid AA8011 metal matrix composite reinforced with aluminum silicate and titanium dioxide
  15. A new neural network–assisted hybrid chaotic hiking optimization algorithm for optimal design of engineering components
  16. Cup drawing predictions for a 6016-T4 aluminum alloy
https://doi.org/10.1515/mt-2024-0519
Keywords for this article
hiking optimization algorithm; artificial neural network; chaotic maps; real-world applications; engineering design
Creative Commons
BY 4.0

Articles in the same Issue

  1. Frontmatter
  2. Effect of flush grinding on corrosion fatigue behavior of step-aged 7020 aluminum alloys
  3. Bending behavior of corrugated sandwich panels with various core shapes
  4. Comparison of crash performance of auxetic structures for CF15, PA6/GF30, and GF30PP materials
  5. Combined effect of ball milling and high-pressure torsion on mechanical properties of Al2O3/Al composite
  6. Liquid metal embrittlement susceptibility of galvanized advanced high strength steel with high manganese content
  7. Kinetic study on nickel aluminides formed on Monel 400 alloy
  8. Finite element simulation of natural gas pipelines in service welding repair
  9. Biomechanical effects of material selection and micro-groove design for dental implants
  10. Design, FEA and experimental validation of 3D-printed PLA/PCL intervertebral cages for lumbar spinal fusion
  11. Effect of tool tilt angles on the formation of YSZ/Al2O3 hybrid surface composites on friction stir processed magnesium alloy AZ31
  12. Coating of AISI 304 stainless steel surface with addition of Cr3C2 to NiCrCo medium entropy alloy powder
  13. Numerical and analytical stress analysis for a FGM beam
  14. Mechanical and wear behaviour of hybrid AA8011 metal matrix composite reinforced with aluminum silicate and titanium dioxide
  15. A new neural network–assisted hybrid chaotic hiking optimization algorithm for optimal design of engineering components
  16. Cup drawing predictions for a 6016-T4 aluminum alloy
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 23.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/mt-2024-0519/html?srsltid=AfmBOoq4scuxVB5NUZXQ9C_UpwkRCCO7ergdA_30yUKJ8ab7LkAlFRUT
Scroll to top button