# Abstract

This paper focuses on a comparision of recent algorithms such as the arithmetic optimization algorithm, the slime mold optimization algorithm, the marine predators algorithm, and the salp swarm algorithm. The slime mold algorithm (SMA) is a recent optimization algorithm. In order to strengthen its exploitation and exploration abilities, in this paper, a new hybrid slime mold algorithm-simulated annealing algorithm (HSMA-SA) has been applied to structural engineering design problems. As a result of the rules and practices that have become mandatory for fuel emissions by international organizations and governments, there is increasing interest in the design of vehicles with minimized fuel emissions. Many scientific studies have been conducted on the use of metaheuristic methods for the optimum design of vehicle components, especially for reducing vehicle weight. With the inspiration obtained from the above-mentioned methods, the HSMA-SA has been studied to solve the shape optimization of a design case to prove how the HSMA-SA can be used to solve shape optimization problems. The HSMA-SA provides better results as an arithmetic optimization algorithm than the slime mold optimization algorithm, the marine predators algorithm, and the salp swarm algorithm.

# Acknowledgment

The authors gratefully acknowledge the support of Bursa Uludağ University, Bursa, Dhahran, Kaen University, Khon Kaen, King Fahd University of Petroleum & Minerals and Pandit Deendayal Petroleum University, Gandhinagar.

### References

1 S. Li, H. Chen, M. Wang, A. A. Heidari, S. Mirjalili: Slime mould algorithm: A new method for stochastic optimizatio, Future Generation Computer Systems, Volume 111 (2020), pp. 300-323 DOI:10.1016/j.future.2020.03.05510.1016/j.future.2020.03.055Search in Google Scholar

2 A. R. Yildiz, F. Öztürk: Hybrid Taguchi-Harmony Search Approach for Shape Optimization, Recent Advances in Harmony Search Algorithm Book Series: Studies in Computational Intelligence 270 (2010), pp. 89-98 DOI:10.1007/978-3-642-04317-8_810.1007/978-3-642-04317-8_8Search in Google Scholar

3 B. S. Yildiz: Natural frequency optimization of vehicle components using the interior search algorithm, Materials Testing 59 (2017), No. 5, pp. 456-458 DOI:10.3139/120.11101810.3139/120.111018Search in Google Scholar

4 E. Demirci, A. R. Yildiz: An investigation of the crash performance of magnesium, aluminum and advanced high strength steels and different crosssections for vehicle thin-walled energy absorbers, Materials Testing 60 (2018), No. 7-8, pp. 661-668 DOI:10.3139/120.11120110.3139/120.111201Search in Google Scholar

5 B. S. Yildiz, A. R. Yildiz: Comparison of grey wolf, whale, water cycle optimization algorithm, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod, Materials Testing 60 (2018), No. 3, pp. 311-315 DOI:10.3139/120.11115310.3139/120.111153Search in Google Scholar

6 L. Abualigah, A.Diabat, S. Mirjalili, M. Abd Elaziz, A. H. Gandomi: The Arithmetic Optimization Algorithm, Compututers Methods in Applied Mechanics and Engineering, 376 (2021), No:113609 DOI:10.1016/j.cma.2020.11360910.1016/j.cma.2020.113609Search in Google Scholar

7 Z. Meng, G. Li, X. Wang, S. M. Sait, A. R. Yildiz: A comparative study of metaheuristic algorithms for reliability-based design optimization problems, Archives of Computational Methods in Engineering 28 (2021), pp.1853-1869 DOI:10.1007/s11831-020-09443-z10.1007/s11831-020-09443-zSearch in Google Scholar

8 B. S Yildiz, N. Pholdee, S. Bureerat, A. R. Yildiz, S. M. Sait: Robust design of a robot gripper mechanism using new hybrid grasshopper optimization algorithm, Expert Systems 38 (3) 2021, e12666 DOI:10.1111/exsy.1266610.1111/exsy.12666Search in Google Scholar

9 B. S Yildiz, V. Patel, N. Pholdee, S. M. Sait, S. Bureerat, A. R. Yildiz,: Conceptual comparison of the ecogeography-based algorithm, equilibrium algorithm, marine predators algorithm and slime mold algorithm for optimal product design, Materials Testing 63 (2021) 4, pp. 336-340 DOI:10.1515/mt-2020-004910.1515/mt-2020-0049Search in Google Scholar

10 A. R. Yildiz, M. U. Erdaş: A new Hybrid Taguchisalp swarm optimization algorithm for the robust design of real-world engineering problems, Materials Testing 63 (2021), pp. 157-162 DOI:10.1515/mt-2020-002210.1515/mt-2020-0022Search in Google Scholar

11 B. S. Yildiz: The mine blast algorithm for the structural optimization of electrical vehicle components, Materials Testing 62 (2020), No. 5, pp. 497-501 DOI:10.3139/120.11151110.3139/120.111511Search in Google Scholar

12 H. Abderazek, F. Hamza, A. R. Yildiz, S. M. Sait: Comparative investigation of the moth-flame algorithm and whale optimization algorithm for optimal spur gear design, Materials Testing 63 (2021) 3, pp. 266-271 DOI: 10.1515/mt-2020-003910.1515/mt-2020-0039Search in Google Scholar

13 A. R. Yildiz, H. Abderazek, S. Mirjalili: A comparative study of recent nontraditional methods for mechanical design optimization, Archives of Computational Methods in Engineering 27 (2020), pp. 1031-1048 DOI:10.1007/s11831-019-09343-x10.1007/s11831-019-09343-xSearch in Google Scholar

14 A. Faramarzi, M. Heidarinejad, B. Stephens, S. Mirjalili: Equilibrium optimizer:A novel optimization algorithm, Knowledge-Based Systems 191 (2020), No. 105190 DOI:10.1016/j.knosys.2019.10519010.1016/j.knosys.2019.105190Search in Google Scholar

15 E. Kurtuluş, A. R. Yildiz, S. Bureerat, Sadiq M. Sait: A novel hybrid Harris hawks- simulated annealing algorithm and RBF-based metamodel for design optimization of highway guardrails, Materials Testing 62 (2020), No. 3, pp. 251-260 DOI:10.3139/120.11147810.3139/120.111478Search in Google Scholar

16 A. Faramarzi, M. Heidarinejad, S. Mirjalili, A. H. Gandomi: Marine Predators Algorithm: A nature-inspired metaheuristic, Expert Systems with Applications, Volume 152 (2020), No. 113377 DOI:10.1016/j.eswa.2020.11337710.1016/j.eswa.2020.113377Search in Google Scholar

17 B. S Yildiz, N. Pholdee, S. Bureerat, A. R. Yildiz, S. M. Sait: Comparision of the political optimization algorithm, the Archimedes optimization algorithm and the Levy flight algorithm for design optimization in industry, Materials Testing, 63 (2021) 4, pp. 356-359 DOI:10.1515/mt-2020-005310.1515/mt-2020-0053Search in Google Scholar

18 B. S. Yildiz, AR. Yildiz, S. Bureerat, N. Pholdee, Sadiq M. Sait, V. Patel: The Henry gas solubility optimization algorithm for optimum structural design of automobile brake components, Materials Testing 62 (2020), No. 3, pp. 261-264 DOI:10.3139/120.11147910.3139/120.111479Search in Google Scholar

19 A. R. Yildiz, B. S. Yildiz, S. M. Sait, X. Y. Li: The Harris hawks, grasshopper and multi-verse optimization algorithms for the selection of optimal machining parameters in manufacturing operations, Materials Testing 61 (2019), pp. 725-733 DOI:10.3139/120.11137710.3139/120.111377Search in Google Scholar

20 B. S. Yıldız, A. R. Yildiz, E. I. Albak, H. Abderazek, Sadiq M. Sait, S. Bureerat: Butterfly optimization algorithm for optimum shape design of automobile suspension components, Materials Testing 62 (2020), No. 4, pp. 365-370 DOI:10.3139/120.11149210.3139/120.111492Search in Google Scholar

21 B. S. Yıldız: The spotted hyena optimization algorithm for weight-reduction of automobile brake components, Materials Testing 62 (2020), No. 4, pp. 383-388 DOI:10.3139/120.11149510.3139/120.111495Search in Google Scholar

22 N. Panagant, N. Pholdee, S. Bureerat, A. R. Yildiz, S. M. Sait: Seagull optimization algorithm for solving real-world design optimization problems, Materials Testing 62 (2020), pp. 640-644 DOI:10.3139/120.11152910.3139/120.111529Search in Google Scholar

24 B. S. Yildiz, N. Pholdee, S. Bureerat, S. M. Sait, A. R. Yildiz: Sine-cosine optimization algorithm for the conceptual design of automobile components, Materials Testing 62 (2020), pp. 744-748 DOI:10.3139/120.11154110.3139/120.111541Search in Google Scholar

26 B. Aslan, A. R. Yildiz: Optimum design of automobile components using lattice structures for additive manufacturing, Materials Testing 52 (2020), pp. 633-639 DOI:10.3139/120.11152710.3139/120.111527Search in Google Scholar

27 B. S. Yildiz: A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems, International Journal of Vehicle Design 73 (2017), No. 1-3, pp. 208-218 DOI:10.1504/IJVD.2017.08260310.1504/IJVD.2017.082603Search in Google Scholar

28 A. Karaduman, B. S. Yildiz, A. R. Yildiz: Experimental and numerical fatigue based design optimisation of clutch diaphragm spring in the automotive Industry, International Journal of Vehicle Design 80 (2020), No. 2-4, pp. 330-345 DOI:10.1504/IJVD.2019.10987510.1504/IJVD.2019.109875Search in Google Scholar

29 D. Simon: Biogeography-based optimization, IEEE Transactions On Evolutionary Computation 12 (2008), pp. 702 – 713 DOI:10.1109/TEVC.2008.91900410.1109/TEVC.2008.919004Search in Google Scholar

30 Y. J. Zheng, H. F. Ling, J. Y. Xue, Ecogeography-based optimization: Enhancing biogeography-based optimization with ecogeographic barriers and differentiations, Computers and Operations Research 50 (2014), pp. 115-127 10.1016/j.cor.2014.04.013Search in Google Scholar

31 H. Abderazek, A. R. Yildiz, S. M. Sait: Optimal design of planetary gear train for automotive transmissions using advanced meta-heuristics, International Journal of Vehicle Design 80 (2019), No. 2-4, pp. 121-136 DOI:10.1504/IJVD.2019.10986210.1504/IJVD.2019.109862Search in Google Scholar

32 H. Abderazek, A. R. Yildiz, S. M. Sait: Mechanical engineering design optimisation using novel adaptive differential evolution algorithm, International Journal of Vehicle Design 80 (2019), No. 2-4, pp. 285-329 DOI:10.1504/IJVD.2019.10987310.1504/IJVD.2019.109873Search in Google Scholar

33 N. Panagan, N. Pholdee, K. Wansasueb, S. Bureerat, A. R. Yildiz, S. M. Sait: Comparison of recent algorithms for many-objective optimisation of an automotive floor-frame, International Journal of Vehicle Design 80 (2019), No. 2-4, pp. 176-208 DOI:10.1504/IJVD.2019.10986310.1504/IJVD.2019.109863Search in Google Scholar

34 R. Sarangkum, K. Wansasueb, N. Panagant, N. Pholdee, S. Bureerat, A. R. Yildiz, S. M. Sait: Automated design of aircraft fuselage stiffeners using multiobjective evolutionary optimisation, International Journal of Vehicle Design 80 (2019), No. 2-4, pp. 162-175 DOI:10.1504/IJVD.2019.10986410.1504/IJVD.2019.109864Search in Google Scholar

35 C. M. Aye, N. Pholdee, A. R. Yildiz, S. Bureerat, S. M. Sait: Multi-surrogate assisted metaheuristics for crashworthiness optimisation, International Journal of Vehicle Design 80 (2019), No. 2-4, pp. 223-240 DOI:10.1504/IJVD.2019.10986610.1504/IJVD.2019.109866Search in Google Scholar

36 A. R. Yildiz: A novel hybrid whale nelder mead algorithm for optimization of design and manufacturing problems, International Journal of Advanced Manufacturing Technology 105 (2019), pp. 5091-5104 DOI:10.1007/s00170-019-04532-110.1007/s00170-019-04532-1Search in Google Scholar

37 A. Baykasoglu, F. B. Ozsoydan, M. E. Senol: Weighted superposition attraction algorithm for binary optimization problems, Operational Research 20 (2020), pp. 2555-2581 DOI:10.1007/s12351-018-0427-910.1007/s12351-018-0427-9Search in Google Scholar

38 İ. Aydoğdu: Cost optimization of reinforced concrete cantilever retaining walls under seismic loading using a biogeography-based optimization algorithm with Levy flights, Engineering Optimization 49 (2017), pp. 381-400 DOI:10.1080/0305215X.2016.119183710.1080/0305215X.2016.1191837Search in Google Scholar

39 S. Carbas: Design optimization of steel frames using an enhanced firefly algorithm, Engineering Optimization 48 (2016), pp. 2007-2025 DOI:10.1080/0305215X.2016.114521710.1080/0305215X.2016.1145217Search in Google Scholar

40 S. Carbas: Optimum structural design of spatial steel frames via biogeography-based optimization, Neural Computing and Applications 28 (2017), pp. 1525-1539 DOI:10.1007/s00521-015-2167-610.1007/s00521-015-2167-6Search in Google Scholar

41 E. Çelik: A powerful variant of symbiotic organisms search algorithm for global optimization, Engineering Applications of Artificial Intelligence 87 (2020), No. 103294 DOI:10.1016/j.engappai.2019.10329410.1016/j.engappai.2019.103294Search in Google Scholar

42 E. Bogar, S. Beyhan: Adolescent Identity Search Algorithm (AISA): A novel metaheuristic approach for solving optimization problems, Applied Soft Computing 95 (2020), No. 106503 DOI:10.1016/j.asoc.2020.10650310.1016/j.asoc.2020.106503Search in Google Scholar

43 B. Hekimoglu: Optimal tuning of fractional order pid controller for dc motor speed control via chaotic atom search optimization algorithm, IEEE ACCESS 7 (2019), pp. 38100-38114 DOI:10.1109/ACCESS.2019.290596110.1109/ACCESS.2019.2905961Search in Google Scholar

44 E. V. Altay, B. Alatas: Bird swarm algorithms with chaotic mapping, Artificial Intelligence Review 53 (2020), pp. 1373-1414 DOI:10.1007/s10462-019-09704-910.1007/s10462-019-09704-9Search in Google Scholar

45 C. D. Chapman, K. Saitou, M. J. Jakiela: Genetic algorithms as an approach to configuration and topology design, Journal of Mechanical Design 116 (1994), pp. 1005-1012 DOI:10.1115/1.291948010.1115/1.2919480Search in Google Scholar

46 A. R. Yildiz, K. Saitou: Topology synthesis of multi-component structural assemblies in continuum domains, Transactions of ASME, Journal of Mechanical Design 133 (2011), No. 1, No. 011008-9 DOI:10.1115/1.400303810.1115/1.4003038Search in Google Scholar

47 H. Zhou, J. Y.Zhang, Y. Q. Junyuan, K. Saitou: Multi-component topology optimization for die casting (MTO-D), Structural and Multidisciplinary Optimization 6 (2019), No. 6, pp. 2265-2279 DOI:10.1007/s00158-019-02317-410.1007/s00158-019-02317-4Search in Google Scholar

48 A. R. Yildiz: Designing of optimum vehicle components using new generation optimization methods, Journal of Polytechnic 20 (2017), No. 2, pp. 319-323 DOI:10.2339/2017.20.2 325-33210.2339/2017.20.2325-332Search in Google Scholar

49 Y. Zhou, K. Saitou: Gradient-based multicomponent topology optimization for stamped sheet metal assemblies (MTO-S), Structural and Multidisciplinary Optimization 58 (2018), pp. 83-94 DOI:10.1007/s00158-017-1878-y10.1007/s00158-017-1878-ySearch in Google Scholar

50 D. Guirguis, K. Hamza, M. Aly, H. Hegazi, K. Saitou: Multiobjective topology optimization of multi-component continuum structures via a Kriging interpolated level-set approach, Structural and Multidisciplinary Optimization 51 (2015), No. 3, pp. 733-748 DOI:10.1007/s00158-014-1154-310.1007/s00158-014-1154-3Search in Google Scholar

51 S. Arora, S. Singh: Butterfly optimization algorithm: A novel approach for global optimization, Soft Computing 23 (2019), pp. 715-734 DOI:10.1007/s00500-018-3102-4A10.1007/s00500-018-3102-4ASearch in Google Scholar

52 H. Özkaya, M. Yildiz, A. R. Yildiz, S. Bureerat, B. S. Yildiz, Sadiq M. Sait: The equilibrium optimizationalgorithm and the response surface based metamodel for optimal structural design of vehicle components, Materials Testing 62 (2020), pp. 492-496 DOI:10.3139/120.11150910.3139/120.111509Search in Google Scholar

53 W. Zhao, L. Wang, Z. Zhang: A novel atom search optimization for dispersion coefficient estimation in groundwater, Future Generation Computer Systems 91 (2019), pp. 601-610 DOI:10.1016/j.future.2018.05.03710.1016/j.future.2018.05.037Search in Google Scholar

54 S. Gupta, K. Deep: Improved sine cosine algorithm with crossover scheme for global optimization, Knowledge-Based Systems 165 (2019), pp. 374-406 DOI:DOI:10.1016/j.knosys.2018.12.00810.1016/j.knosys.2018.12.008Search in Google Scholar

55 E. Demirci, A. R. Yildiz: An experimental and numerical investigation of the effects of geometry and spot welds on the crashworthiness of vehicle thinwalled structures, Materials Testing 60 (2018), No. 6, pp. 553-561 DOI:10.3139/120.11118710.3139/120.111187Search in Google Scholar

56 H. Abderazek, A. R. Yildiz, S. Mirjalili: Comparison of recent optimization algorithms for design optimization of a cam-follower mechanism, Knowledge-Based Systems 105 (2020), No: 105237 DOI:10.1016/j.knosys.2019.10523710.1016/j.knosys.2019.105237Search in Google Scholar

57 A. Kaveh, S. Talatahari: Charged system search for optimal design of frame structures, Applied Soft Computing 12 (2012), pp. 382-393 DOI:10.1016/j.asoc.2011.08.03410.1016/j.asoc.2011.08.034Search in Google Scholar

58 H. J. Soh, J. H. Yoo: Optimal shape design of a brake calliper for squeal noise reduction considering system instability, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 224 (2010), No. 7, pp. 909-925 DOI:10.1243/09544070JAUTO138510.1243/09544070JAUTO1385Search in Google Scholar

59 M.-Y. Cheng, D. Prayogo: Symbiotic organisms search: a new metaheuristic optimization algorithm, Computers & Structures 139 (2014), pp. 98-112 10.1016/j.compstruc.2014.03.007Search in Google Scholar

60 S. Mirjalili: SCA: a sine cosine algorithm for solving optimization problems, Knowledge Based System 96 (2016), pp. 120-133 DOI:10.1016/j.knosys.2015.12.02210.1016/j.knosys.2015.12.022Search in Google Scholar

61 A. R. Yildiz, U. A. Kılıçarpa, E. Demirci: Topography and topology optimization of diesel engine components for lightweight design in the automotive industry, Materials Testing 61 (2019), No. 1, pp. 27-34 DOI:10.3139/120.11127710.3139/120.111277Search in Google Scholar

62 E. Demirci, A. R. Yildiz: A new hybrid approach for reliability-based design optimization of structural components, Materials Testing 61 (2019), pp. 111-119 DOI:10.3139/120.11129110.3139/120.111291Search in Google Scholar

63 S. Bureerat, N. Pholdee: Optimal truss sizing using an adaptive differential evolution algorithm, Journal of Computing in Civil Engineering 30 (2015), No. 2, No. 04015019 DOI:10.1061/(ASCE)CP.1943-5487.000048710.1061/(ASCE)CP.1943-5487.0000487Search in Google Scholar

64 A. Kaveh, M. Khayatazad: A new meta-heuristic method: ray optimization, Computers and Structures 112 (2012), pp. 283-294 10.1016/j.compstruc.2012.09.00365Search in Google Scholar

65 H. J. Soh, J. H. Yoo: Optimal shape design of a brake calliper for squeal noise reduction considering system instability, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 224 (2010), No. 7, pp. 909-925 DOI:10.1243/09544070JAUTO138510.1243/09544070JAUTO1385Search in Google Scholar

66 F. A. Hashim, E. H. Houssein, M. S. Mabrouk, W. Al-Atabany, S. Mirjalili: Henry gas solubility optimization: A novel physics-based algorithm, Future Generation Computer Systems 101 (2019), pp. 646-667 DOI:10.1016/j.future.2019.07.01510.1016/j.future.2019.07.015Search in Google Scholar

67 P. Champasak, N.Panagant, N. Pholdee, S. Bureerat, A. R. Yildiz: Selfadaptive many-objective meta-heuristic based on decomposition for manyobjective conceptual design of a fixed wing unmanned aerial vehicle, Aerospace Science and Technology 100 (2020), pp. 1-11 DOI:10.1016/j.ast.2020.10578310.1016/j.ast.2020.105783Search in Google Scholar

68 B. S. Yildiz: Optimal design of automobile structures using moth-flame optimization algorithm and response surface methodology, Materials Testing 62 (2020), No. 4, pp.372-377 DOI:10.3139/120.11149410.3139/120.111494Search in Google Scholar

69 A. Heidari, S. Mirjalili, H. Farris, I. Aljarah, M. Mafarja, H. Chen: Harris hawks optimization: Algorithm and applications, Future Generation Computer Systems 97 (2019), pp. 849-872 DOI:10.1016/j.future.2019.02.02810.1016/j.future.2019.02.028Search in Google Scholar

70 T. Güler, A. Demirci, A. R. Yildiz, U. Yavuz: Lightweight design of an automobile hinge component using glass fiber polyamide composites, Materials Testing 60 (2018), No. 3, pp. 306-310 DOI: DOI:10.3139/120.11115210.3139/120.111152Search in Google Scholar

71 F. Hamza, H. Abderazek, S. Lakhdar, D. Ferhat, A. R. Yildiz: Optimum design of cam-roller follower mechanism using a new evolutionary algorithm, The International Journal of Advanced Manufacturing Technology 99 (2018), No. 5-8, pp. 1261-1282 DOI:10.1007/s00170-018-2543-310.1007/s00170-018-2543-3Search in Google Scholar

72 A. R. Yildiz, N. Kaya, N. Öztürk, F. Öztürk: Hybrid approach for genetic algorithm and Taguchi’s method based design optimization in the automotive industry, International Journal of Production Research 44 (2006), pp. 4897-4914 DOI:10.1080/0020754060061993210.1080/00207540600619932Search in Google Scholar

**Published Online:**2021-05-23

**Published in Print:**2021-05-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston, Germany