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Statistical Investigation of the Robustness for the Optimization Algorithms

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Nature-Inspired Metaheuristic Algorithms for Engineering Optimization Applications

Part of the book series: Springer Tracts in Nature-Inspired Computing ((STNIC))

Abstract

Optimization algorithms are widely used in engineering applications to solve complex real-world design problems. The success of an algorithm with a vast scope should be a convergence in a short time with less iteration to keep pace with developing technology. Generally, optimization algorithms are performed without examining the effect of the algorithm parameters and characteristic of the optimization problem, statistically. Therefore, the appropriate algorithm parameter values of the scatter search optimization algorithms in this chapter have been aimed to investigate with the Taguchi method, which is a statistics-based and the robust way. By manipulating fewer trials, it is possible to gain the proper value, which changes according to the minimum or the maximum global solution design among all combinations of the algorithm parameters. Utilizing an orthogonal array proposed by Taguchi is an effective and successful tool. Thus, approaches are intended to achieve the results with less repetition and to increase the accomplishment of the algorithm, taking into account the effect of the algorithm parameters on the result with statistical analysis.

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References

  1. Rao S Engineering optimization: theory and practice—Singiresu—Google Kitaplar. John Wiley Sons

    Google Scholar 

  2. Goldberg DE (1989) Genetic algorithms and Walsh functions: part I, a gentle introduction. Complex Syst 3:129–152

    MATH  Google Scholar 

  3. Geem ZW (2006) Optimal cost design of water distribution networks using harmony search. Eng Optim 38:259–277

    Article  Google Scholar 

  4. Geem ZW, Lee KS, Park Y (2005) Application of harmony search to vehicle routing. Am J Appl Sci 2:1552–1557. https://doi.org/10.3844/ajassp.2005.1552.1557

    Article  Google Scholar 

  5. Carbas S (2016) Design optimization of steel frames using an enhanced firefly algorithm. Eng Optim 48:2007–2025. https://doi.org/10.1080/0305215X.2016.1145217

    Article  Google Scholar 

  6. Uray E, Çarbaş S, Erkan İH, Olgun M (2020) Investigation of optimal designs for concrete cantilever retaining walls in different soils. Chall J Concr Res Lett 11. https://doi.org/10.20528/cjcrl.2020.02.003

  7. Cheng YM, Li L, Fang SS (2011) Improved harmony search methods to replace variational principle in geotechnical problems. J Mech 27:107–119. https://doi.org/10.1017/jmech.2011.12

    Article  Google Scholar 

  8. Niu M, Wan C, Xu Z (2014) A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems. J Mod Power Syst Clean Energy 2:289–297. https://doi.org/10.1007/s40565-014-0089-4

    Article  Google Scholar 

  9. Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci (Ny) 222:175–184. https://doi.org/10.1016/j.ins.2012.08.023

    Article  MathSciNet  Google Scholar 

  10. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(80):671–680. https://doi.org/10.1126/science.220.4598.671

  11. Glover F (1989) Tabu search—part I. ORSA J Comput 1:190–206. https://doi.org/10.1287/ijoc.1.3.190

    Article  MATH  Google Scholar 

  12. Glover F (1990) Tabu search—part II. ORSA J Comput 2:4–32. https://doi.org/10.1287/ijoc.2.1.4

    Article  MATH  Google Scholar 

  13. Dorigo M, Gambardella LM (1997) Ant colonies for the travelling salesman problem. BioSystems 43:73–81. https://doi.org/10.1016/S0303-2647(97)01708-5

    Article  Google Scholar 

  14. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68. https://doi.org/10.1177/003754970107600201

    Article  Google Scholar 

  15. Kennedy J, Eberhart R Particle swarm optimization. In: Proceedings of ICNN’95—international conference on neural networks. IEEE, pp 1942–1948

    Google Scholar 

  16. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization

    Google Scholar 

  17. Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. pp 169–178

    Google Scholar 

  18. Rajabioun R (2011) Cuckoo optimization algorithm. Appl Soft Comput J 11:5508–5518. https://doi.org/10.1016/j.asoc.2011.05.008

    Article  Google Scholar 

  19. Perez RE, Behdinan K (2007) Particle swarm approach for structural design optimization. Comput Struct 85:1579–1588. https://doi.org/10.1016/j.compstruc.2006.10.013

    Article  Google Scholar 

  20. Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci (Ny) 192:120–142. https://doi.org/10.1016/j.ins.2010.07.015

    Article  Google Scholar 

  21. Carbas S, Saka MP (2013) Efficiency of improved harmony search algorithm for solving engineering optimization problems. Iran Univ Sci Technol 3:99–114

    Google Scholar 

  22. Bossek J Smoof: single-and multi-objective optimization test functions

    Google Scholar 

  23. Molga M, Smutnicki C (2005) Test functions for optimization needs

    Google Scholar 

  24. Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes

    Google Scholar 

  25. Uray E, Tan Ö, Çarbaş S, Erkan H (2021) Metaheuristics-based pre-design guide for cantilever retaining walls. Tek Dergi 32. https://doi.org/10.18400/tekderg.561956

  26. Cheng BW, Chang CL (2007) A study on flowshop scheduling problem combining Taguchi experimental design and genetic algorithm. Expert Syst Appl 32:415–421. https://doi.org/10.1016/j.eswa.2005.12.002

    Article  Google Scholar 

  27. Yildirim T, Kalayci CB, Mutlu Ö, İşlem Daire Başkanlığı B, Üniversitesi P, Makalesi A, Article Öz R (2016) Gezgin satıcı problemi için yeni bir meta-sezgisel: kör fare algoritması A novel metaheuristic for traveling salesman problem: blind mole-rat algorithm. dergipark.org.tr 22:64–70. https://doi.org/10.5505/pajes.2015.38981

  28. Russell RA, Chiang WC (2006) Scatter search for the vehicle routing problem with time windows. Eur J Oper Res 169:606–622. https://doi.org/10.1016/j.ejor.2004.08.018

    Article  MathSciNet  MATH  Google Scholar 

  29. Pendharkar PC (2013) Scatter search based interactive multi-criteria optimization of fuzzy objectives for coal production planning. Eng Appl Artif Intell 26:1503–1511. https://doi.org/10.1016/j.engappai.2013.01.001

    Article  Google Scholar 

  30. Naderi B, Ruiz R (2014) A scatter search algorithm for the distributed permutation flowshop scheduling problem. Eur J Oper Res 239:323–334. https://doi.org/10.1016/j.ejor.2014.05.024

    Article  MathSciNet  MATH  Google Scholar 

  31. Hakli H, Ortacay Z (2019) An improved scatter search algorithm for the uncapacitated facility location problem. Comput Ind Eng 135:855–867. https://doi.org/10.1016/j.cie.2019.06.060

    Article  Google Scholar 

  32. Duman E, Ozcelik MH (2011) Detecting credit card fraud by genetic algorithm and scatter search. Expert Syst Appl 38:13057–13063. https://doi.org/10.1016/j.eswa.2011.04.110

    Article  Google Scholar 

  33. Hakli H (2020) A performance evaluation and two new implementations of evolutionary algorithms for land partitioning problem. Arab J Sci Eng 45:2545–2558. https://doi.org/10.1007/s13369-019-04203-z

    Article  Google Scholar 

  34. Khooban Z, Farahani RZ, Miandoabchi E, Szeto WY (2015) Mixed network design using hybrid scatter search. Eur J Oper Res 247:699–710. https://doi.org/10.1016/j.ejor.2015.06.025

    Article  MathSciNet  MATH  Google Scholar 

  35. Keskin BB, Üster H (2007) A scatter search-based heuristic to locate capacitated transshipment points. Comput Oper Res 34:3112–3125. https://doi.org/10.1016/j.cor.2005.11.020

    Article  MATH  Google Scholar 

  36. Pinol H, Beasley JE (2006) Scatter search and bionomic algorithms for the aircraft landing problem. Eur J Oper Res 171:439–462. https://doi.org/10.1016/j.ejor.2004.09.040

    Article  MATH  Google Scholar 

  37. İstinat Duvarlarıyla İlgili Yapılan Hatalar - Serbest Cihangir. http://www.serbestcihangir.com/istinat-duvarlariyla-ilgili-yapilan-hatalar/. Accessed 24 Oct 2020

  38. Chau KW, Albermani F (2003) Knowledge-based system on optimum design of liquid retaining structures with genetic algorithms. J Struct Eng 129:1312

    Article  Google Scholar 

  39. Ceranic B, Fryer C, Baines R (2001) An application of simulated annealing to the optimum design of reinforced concrete retaining structures. Comput Struct

    Google Scholar 

  40. Gandomi AH, Kashani AR, Roke DA, Mousavi M (2015) Optimization of retaining wall design using recent swarm intelligence techniques. Eng Struct 103:72–84. https://doi.org/10.1016/j.engstruct.2015.08.034

    Article  Google Scholar 

  41. Camp C, Akin A (2012) Design of retaining walls using big bang-big crunch optimization. J Struct Eng 138:438–448

    Article  Google Scholar 

  42. Sheikholeslami R, Khalili B, Zahrai S (2014) Optimum cost design of reinforced concrete retaining walls using hybrid firefly algorithm. ijetch.org. https://doi.org/10.7763/IJET.2014.V6.742

  43. Talatahari S, Sheikholeslami R (2014) Optimum design of gravity and reinforced retaining walls using enhanced charged system search algorithm. KSCE J Civ Eng

    Google Scholar 

  44. Temür R, Bekdas G (2016) Teaching learning-based optimization for design of cantilever retaining walls. Struct Eng Mech 57:763–783

    Article  Google Scholar 

  45. Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8:156–166. https://doi.org/10.1111/j.1540-5915.1977.tb01074.x

    Article  Google Scholar 

  46. Martí R, Laguna M, Glover F (2006) Principles of scatter search. Eur J Oper Res 169:359–372. https://doi.org/10.1016/j.ejor.2004.08.004

    Article  MathSciNet  MATH  Google Scholar 

  47. GEO5 Geotechnical software https://www.finesoftware.eu/geotechnical-software/

  48. Das BM (2017) Principles of foundation engineering, 9th edn. Cengage Learning

    Google Scholar 

  49. Das BM (2002) Principles of foundation engineering

    Google Scholar 

  50. Meyerhof GG (1963) Some recent research on the bearing capacity of foundations. Can Geotech J 1:16–26. https://doi.org/10.1139/t63-003

    Article  Google Scholar 

  51. Lin C (2013) A rough penalty genetic algorithm for constrained optimization. Inf Sci (Ny) 241. https://doi.org/10.1016/j.ins.2013.04.001

  52. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186. https://doi.org/10.1016/S0045-7825(99)00389-88

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Uray, E., Hakli, H., Carbas, S. (2021). Statistical Investigation of the Robustness for the Optimization Algorithms. In: Carbas, S., Toktas, A., Ustun, D. (eds) Nature-Inspired Metaheuristic Algorithms for Engineering Optimization Applications. Springer Tracts in Nature-Inspired Computing. Springer, Singapore. https://doi.org/10.1007/978-981-33-6773-9_10

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