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A Review of Multi-objective Optimization: Methods and Algorithms in Mechanical Engineering Problems

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Abstract

The optimization problems that must meet more than one objective are called multi-objective optimization problems and may present several optimal solutions. This manuscript brings the most important concepts of multi-objective optimization and a systematic review of the most cited articles in the last years in mechanical engineering, giving details about the main applied multi-objective optimization algorithms and methods in this field. Some of the applications that can be found in this study are: (i) problems in design optimization, (ii) problems in manufacturing: welding, machining and molding and (iii) problems in structural health monitoring. It can be seen that classic optimization methods had their importance in the past, but lost space for new algorithms that emerged with the advancement of computing, better able to deal with a greater number of variables, objectives and nonlinearities. These powerful algorithms, still little used in Mechanical Engineering, showed significant improvement where they were applied. Meta-heuristics with a posteriori decision-making techniques proved to be a modern trend in solving multi-objective problems, although it is not limited due to the constant battle of new algorithms more adapted to specific problems.

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adapted from Zitzler et al. [193]]

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Abbreviations

MOP:

Multi-objective Problems

PF:

Pareto Front

ZDT:

Zitzler-Deb-Thiele test function

DM:

Decision Maker

NBI:

Normal Boundary Intersection

GA:

Genetic Algorithm

MOEA:

Multi-objective Evolutionary Algorithm

VEGA:

Vector Evaluation GA

MOGA:

Multi-objective GA

NSGA (I and II):

Non-dominated Sorting GA

SPEA (I and II):

Strength Pareto Evolutionary Algorithm

MOPSO:

Multi-objective Particle Swarm Optimization

MOGWO:

Multi-objective Grey Wolf Optimizer

MOALO:

Multi-objective Ant Lion Optimizer

OM:

Orthogonal Method

FG:

Functionally Graded

TOPSIS:

Technique to Order of Preference by Similarity to Ideal Solution

ORC:

Organic Rankine Cycles

DMS:

Direct Multi-Search

SAW:

Submerge Arc Welding

FCAW:

Flux Cored Arc Welding

GMAW:

Gas Metal Arc Welding

FEM:

Finite Element Method

DOE:

Design of Experiments

ANOVA:

Analysis of Variance

FSW:

Friction Stir Welding

ANN:

Artificial Neural Network

NSTLBO:

Non-dominated Teaching–Learning Based Algorithm

TLBO:

Teaching–Learning Based Optimization

HMOGWO:

Hybrid grey wolf optimizer

SHM:

Structural Health Monitoring

References

  1. Abidi MH, Al-Ahmari AM, Umer U, Rasheed MS (2018) Multi-objective optimization of micro-electrical discharge machining of nickel-titanium-based shape memory alloy using MOGA-II. Measurement 125:336–349

    Google Scholar 

  2. Afshari H, Hare W, Tesfamariam S (2019) Constrained multi-objective optimization algorithms: review and comparison with application in reinforced concrete structures. Appl Soft Comput 83:105631

    Google Scholar 

  3. Ahire PG, Patil US, Kadam MS (2018) Genetic algorithm based optimization of the process parameters for manual metal arc welding of dissimilar metal joint. Procedia Manuf 20:106–112

    Google Scholar 

  4. Ahmad MA, Sheikh AK, Nazir K (2019) Design of experiment based statistical approaches to optimize submerged arc welding process parameters. ISA Trans. https://doi.org/10.1016/j.isatra.2019.04.003

  5. Ahmadi P, Hajabdollahi H, Dincer I (2011) Cost and entropy generation minimization of a cross flow plate fin heat exchanger using multi-objective genetic algorithm. J Heat Transfer 133(2):021801–021810

    Google Scholar 

  6. Al Dawood ZIA, Saadoon AM (2017) Multi response optimization of submerged arc welding using Taguchi fuzzy logic based on utility theory. Int J Sci Res 6(12):475–481

    Google Scholar 

  7. Alexandrino PDSL, Gomes GF, Cunha SS Jr (2020) A robust optimization for damage detection using multi-objective genetic algorithm, neural network and fuzzy decision making. Inverse Prob Sci Eng 28(1):21–46

    MATH  Google Scholar 

  8. Alkayem NF, Cao M, Zhang Y, Bayat M, Su Z (2017) Structural damage detection using finite element model updating with evolutionary algorithms: a survey. Neural Comput Appl 30(2):389–411

    Google Scholar 

  9. Alkayem NF, Cao M, Ragulskis M (2018) Damage diagnosis in 3D structures using a novel hybrid multiobjective optimization and FE model updating framework. Complexity. https://doi.org/10.1155/2018/3541676 

  10. Almeida FA, Gomes GF, Paula VR, Correa JE, Paiva AP, Gomes JHF, Turrioni JB (2018) A weighted mean square error approach to the robust optimization of the surface roughness in an AISI 12L14 free-machining steel-turning process. J Mech Eng 64(3):147–156

    Google Scholar 

  11. Almeida FA, Santos ACO, Paiva AP, Gomes GF, Gomes JHF (2020) Multivariate Taguchi loss function optimization based on principal components analysis and normal boundary intersection. Eng Comput, pp 1–17

  12. Arian Nik M, Fayazbakhsh K, Pasini D, Lessard L (2012) Surrogatebased multi-objective optimization of a composite laminate with curvilinear fibers. Compos Struct 94(8):2306–2313

    Google Scholar 

  13. Asanjarani A, Dibajian SH, Mahdian A (2017) Multi-objective crashworthiness optimization of tapered thin-walled square tubes with indentations. Thin-Walled Struct 116:26–36

    Google Scholar 

  14. Ashjari M, Khoshravan MR (2017) Multi-objective optimization of a functionally graded sandwich panel under mechanical loading in the presence of stress constraint. J Mech Behav Mater 26(3–4):79–93

    Google Scholar 

  15. Back T (1996) Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, Oxford

    MATH  Google Scholar 

  16. Bahadormanesh N, Rahat S, Yarali M (2017) Constrained multi-objective optimization of radial expanders in organic Rankine cycles by firefly algorithm. Energy Convers Manage 148:1179–1193

    Google Scholar 

  17. Baril C, Yacout S, Clément B (2011) Design for Six Sigma through collaborative multi-objective optimization. Comput Ind Eng 60:43–55

    Google Scholar 

  18. Belinato G, Almeida FA, Paiva AP, Freitas Gomes JH, Balestrassi PP, Rosa PARC (2018) A multivariate normal boundary intersection PCA-based approach to reduce dimensionality in optimization problems for LBM process. Eng Comput 35(4):1533–1544

    Google Scholar 

  19. Benayoun B, Sussman B (1966) Electre: Une methode pour guider le choix en presence de points de vue multiple. Direction Scientifique, Note de Travail, No. 49

  20. Bilel N, Mohamed N, Zouhaier A, Lotfi R (2016) An improved imperialist competitive algorithm for multi-objective optimization. Eng Optim 48(11):1823–1844. https://doi.org/10.1080/0305215x.2016.1141204

    Article  MathSciNet  Google Scholar 

  21. Brans JP, Vincke P, Mareschal B (1986) How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 24(2):228–238

    MathSciNet  MATH  Google Scholar 

  22. Branke J, Kaußler T, Schmeck H (2001) Guidance in evolutionary multi-objective optimization. Adv Eng Softw 32:499–507

    MATH  Google Scholar 

  23. Brassard G, Bratley P (1988) Algorithmics: theory and practice. Prentice-Hall, Englewood Cliffs, New Jersey

    MATH  Google Scholar 

  24. Brito TG, Paiva AP, Ferreira JR, Gomes JHF (2014) Balestrassi PPA normal boundary intersection approach to multiresponse robust optimization of the surface roughness in end milling process with combined arrays. Precis Eng 38(3):628–638

    Google Scholar 

  25. Brito TG, Paiva AP, Paula TI, Dalosto DN, Ferreira JR, Balestrassi PP (2016) Optimization of AISI 1045 end milling using robust parameter design. Int J Adv Manuf Technol 84(5–8):1185–1199

    Google Scholar 

  26. Cha Y, Buyukozturk O (2015) Structural damage detection using modal strain energy and hybrid multi-objective optimization. Comput Aided Civ Infrastruct Eng 30:347–358

    Google Scholar 

  27. Chen F, Wang Y, Sun S, Ma Z, Huang X (2018) Multi-objective optimization of mechanical quality and stability during micro resistance spot welding. Int J Adv Manuf Technol 101(5):1903–1913

    Google Scholar 

  28. Chiandussi G, Codegone M, Ferrero S, Varesio FE (2012) Comparison of multi-objective optimization methodologies for engineering applications. [S.I.]. pp 912–942, Elsevier, Amsterdam

  29. Choudhary A, Kumar M, Unune DR (2019) Experimental investigation and optimization of weld bead characteristics during submerged arc welding of AISI 1023 steel. Defence Technol 15(1):72–82

    Google Scholar 

  30. Coello Coello CA, Corte´s NC, (2005) Solving multi-objective optimization problems using an artificial immune system. Genet Program Evol Mach 6(2):163–190

    Google Scholar 

  31. Coello C, Lamont B, Van Veldhuizen D (2007) Evolutionary algorithms for solving multi-objective problems. Springer, New York. https://doi.org/10.1007/978-0-387-36797-2.

  32. Cohon JL, Marks DH (1975) A review and evaluation of multi-objective programming techniques. Water Resour Res 11(2):208–220

    Google Scholar 

  33. Cohon JL (1978) Multi-objective programming and planning. Academic Press, Cambridge

    MATH  Google Scholar 

  34. Cui Y, Geng Z, Zhu Q, Han Y (2017) Review: multi-objective optimization methods and application in energy saving. Energy 125:681–704

    Google Scholar 

  35. Custódio AL, Madeira JFA, Vaz AIF, Vicente LN (2011) Direct multisearch for multi-objective optimization. SIAM J Optim 21(3):1109–1140

    MathSciNet  MATH  Google Scholar 

  36. Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631–657

    MathSciNet  MATH  Google Scholar 

  37. Deb K (2008) Introduction to evolutionary multi-objective optimization. multi-objective optimization. Springer, Berlin, pp 59–96

    Google Scholar 

  38. Deb K,Agrawal S, Pratab A,Meyarivan T (2000) A fast elitist non dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In:Schoenauer M, Deb K,Rudolph G, Yao X, Lutton E, Merelo JJ, Schwefel H-P (eds) Proceedings of the parallel problem solving from nature VI conference, pp 849–858, Paris, France. Lecture Notes in Computer Science No. 1917, Springer, Berlin

  39. Dhiman G, Singh KK, Soni M, Nagar A, Dehghani M, Slowik A, Cengiz K (2020) MOSOA: a new multi-objective seagull optimization algorithm. Expert systems with applications, p 114150

  40. Dhiman G, Singh KK, Slowik A, Chang V, Yildiz AR, Kaur A, Garg M (2020) EMOSOA: a new evolutionary multi-objective seagull optimization algorithm for global optimization. Int J Mach Learn Cybern 12(2):571–596

    Google Scholar 

  41. Diniz CA, Mendez YAD, Almeida FA, Cunha Jr SS (2021) Optimum design of composite structures with ply dropp-offs using responde surface methodology. Eng Comput

  42. Duckstein L (1984) Multi-objective optimization in structural design: the model choice problem. In: Atrek E, Gallagher RH, Ragsdell KM, Zienkiewicz OC (eds) New directions in optimum structural design. John Wiley and Sons, New Jersey, pp 459–481

    Google Scholar 

  43. Dumbhare AP, Dubey S, Deshpande V, Y., Andhare, A. B., & Barve, P. S. (2018) Modelling and multi-objective optimization of surface roughness and kerf taper angle in abrasive water jet machining of steel. J Braz Soc Mech Sci Eng 40(5):259

    Google Scholar 

  44. Ebrahimi-Nejad S, Kheybari M, Borujerd SVN (2020) Multi-objective optimization of a sports car suspension system using simplified quarter-car models. Mech Ind 21(4):412

    Google Scholar 

  45. Emmerich MTM, Deutz AH (2018) A tutorial on multi-objective optimization: fundamentals and evolutionary methods. Nat Comput 17(3):585–609. https://doi.org/10.1007/s11047-018-9685-y

    Article  MathSciNet  Google Scholar 

  46. Fadaee M, Radzi MAM (2012) Multi-objective optimization of a stand-alone hybrid renewable energy system by using evolutionary algorithms: a review. Renew Sustain Energy Rev 16(5):3364–3369

    Google Scholar 

  47. Fan H, Zhang J, Zhang W, Liu B (2020) Multiparameter and multiobjective optimization design based on orthogonal method for mixed flow fan. Energies 13(11):2819

    Google Scholar 

  48. Ferentinos KP, Tsiligiridis TA (2007) Adaptive design optimization of wireless sensor networks using genetic algorithms. Comput Netw 51(4):1031–1051

    MATH  Google Scholar 

  49. Fonseca CM, Fleming PJ (1994) An overview of evolutionary algorithms in multi-objective optimization. Technical report, department of automatic control and systems engineering, University of Sheffield, Sheffield, UK

  50. Fonseca CM, Fleming PJ (1993) Genetic algorithms for multi-objective optimization: Formulation discussion and generalization. In: Proceedings of the international conference on genetic algorithms, vol 93. Citeseer, pp 416–423

  51. Fossati GG, Miguel LFF, Casas WJP (2019) Multi-objective optimization of the suspension system parameters of a full vehicle model. Optim Eng 20:151–177

    MATH  Google Scholar 

  52. Fourman MP (1985) Compaction of symbolic layout using genetic algorithms. In: Grefenstette JJ (ed) Genetic algorithms and their applications: proceedings of the first international conference on genetic algorithms, pp 141–153. Lawrence Erlbaum, Hillsdale, New Jersey

  53. Francisco MB, Pereira JLJ, Oliver GA, Silva FHS, Cunha SS, Gomes GF (2021) Multi-objective design optimization of crp isogrid tubes using sunflower multi-objective optimization based on metamodel. Comput Struct 249:106508

    Google Scholar 

  54. Franco Correia VM, Aguilar Madeira JF, Araújo AL, Mota Soares CM (2018) Multi-objective optimization of ceramic-metal functionally graded plates using a higher order model. Compos Struct 183:146–160

    Google Scholar 

  55. Franco Correia VM, Aguilar Madeira JF, Araújo AL, Mota Soares CM (2019) Multi-objective optimization of functionally graded material plates with thermo-mechanical loading. Compos Struct 207:845–857

    Google Scholar 

  56. Gandibleux X, Mezdaoui N, Fr´eville A (1997) A tabu search procedure to solve combinatorial optimisation problems. In: Caballero R, Ruiz F, References 667 Steuer RE (eds) Advances in multiple objective and goal programming, volume 455 of lecture notes in economics and mathematical systems, pp 291–300. Springer-Verlag

  57. Gao Z, Shao X, Jiang P, Wang C, Zhou Q, Cao L, Wang Y (2016) Multi-objective optimization of weld geometry in hybrid fiber laser-arc butt welding using Kriging model and NSGA-II. Appl Phys A 122(6):1–12

    Google Scholar 

  58. Gaudêncio DJH, Almeida FA, Turrioni JB, Costa Quinino R, Balestrassi PP, Paiva AP (2019) A multiobjective optimization model for machining quality in the AISI 12L14 steel turning process using fuzzy multivariate mean square error. Precis Eng 56:303–320

    Google Scholar 

  59. Ghasemi AR, Hajmohammad MH (2016) Multi-objective optimization of laminated composite shells for minimum mass/cost and maximum buckling pressure with failure criteria under external hydrostatic pressure. Struct Multidiscip Optim 55(3):1051–1062

    MathSciNet  Google Scholar 

  60. Gupta SK, Pandey K, Kumar R (2016) Multi-objective optimization of friction stir welding process parameters for joining of dissimilar AA5083/AA6063 aluminum alloys using hybrid approach. Proc Inst Mech Eng Part L J Mater Des Appl 232(4):343–353

    Google Scholar 

  61. Gupta SK, Pandey K, Kumar R (2016) Artificial intelligence-based modelling and multi-objective optimization of friction stir welding of dissimilar AA5083-O and AA6063-T6 aluminium alloys. Proc Inst Mech Eng Part L J Mater Des Appl 232(4):333–342

    Google Scholar 

  62. Ghachi RF, Alnahhal WI, Abdeljaber O, Renno J, Haque ABMT, Shim J, Aref A (2020) Optimization of viscoelastic metamaterials for vibration attenuation properties. Int J Appl Mech

  63. Goicoechea A, Duckstein L, Fogel M (1976) Multi-objective programming in watershed management: a study of the Charleston watershed. Water Resour Res 12(6):1085–1092

    Google Scholar 

  64. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Publishing Company, Reading, Massachusetts

    MATH  Google Scholar 

  65. Gomes GF, Giovani RS (2020) An efficient two-step damage identification method using sunflower optimization algorithm and mode shape curvature (MSDBI–SFO). Eng Comput. https://doi.org/10.1007/s00366-020-01128-2

    Article  Google Scholar 

  66. Gomes GF, Almeida FA, Alexandrino PSL, Cunha SS, Sousa BS, Ancelotti AC (2018) A multi-objective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation. Eng Comput 35(2):519–535

    Google Scholar 

  67. Gomes J (2013) Método dos polinômios canônicos de misturas para otimização multi-objetivo. Itajubá, Minas Gerais, Brasil: Doctoral Thesis - Postgraduate Program in Production Engineering – Universidade Federal de Itajubá

  68. Gunantara N (2018) A review of multi-objective optimization: Methods and its applications. Cogent Eng 5(1):1–16

    Google Scholar 

  69. Guo X, Wu Y, Xie L, Cheng S, Xin J (2015) An adaptive brain storm optimization algorithm for multi-objective optimization problems. Lecture notes in computer science, pp 365–372

  70. Haimes YY, Lasdon LS, Wismer DA (1971) On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans Syst Man Cybern 1(3):296–297

    MathSciNet  MATH  Google Scholar 

  71. Hajela P, Lin CY (1992) Genetic search strategies in multicriterion optimal design. Struct Optim 4:99–107

    Google Scholar 

  72. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872

    Google Scholar 

  73. Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  74. Horn J, Nafpliotis N (1993) Multi-objective optimization using the niched pareto genetic algorithm. Technical Report IlliGAl Report 93005, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

  75. Horn J, Nafpliotis N, Goldberg DE (1994) A niched pareto genetic algorithm for multi-objective optimization. In: Proceedings of the first IEEE conference on evolutionary computation, IEEE world congress on computational intelligence, vol 1, pp 82–87, Piscataway, New Jersey. IEEE Service Center

  76. Hwang CL, Yoon KP (1981) Multiple attribute decision making: methods and applications. Springer-Verlag, Berlin/Heidelberg/New York

    MATH  Google Scholar 

  77. Ikeya K, Shimoda M, Shi J-X (2016) Multi-objective free-form optimization for shape and thickness of shell structures with composite materials. Compos Struct 135:262–275

    Google Scholar 

  78. Jaimes AL, Martınez SZ, Coello CAC et al (2009) An introduction to multi-objective optimization techniques. Optim Polym Process, pp 29–57.

  79. Jiang R, Wang D (2016) Optimization of suspension system of self-dumping truck using TOPSIS-based Taguchi method coupled with entropy measurement, SAE Technical Paper, 2016-2001-1385

  80. Jiang R, Wang D (2015) Optimization of vehicle ride comfort and handling stability based on TOPSIS Method, SAE Technical Paper, 2015-200-1348

  81. Jiang P, Wang C, Zhou Q, Shao X, Shu L, Li X (2016) Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II. Adv Eng Softw 99:147–160

    Google Scholar 

  82. Jin Y, Sendhoff B (2002) Fuzzy preference incorporation into evolutionary multi-objective optimization. In: Proceedings of the 4th Asia-pacific conference on simulated evolution and learning, vol 1, pp 26–30

  83. Kalantari M, Dong C, Davies IJ (2016) Multi-objective robust optimisation of unidirectional carbon/glass fibre reinforced hybrid composites under flexural loading. Compos Struct 138:264–275

    Google Scholar 

  84. Karimi M, Hall M, Buckham B, Crawford C (2016) A multi-objective design optimization approach for floating offshore wind turbine support structures. J Ocean Eng Marine Energy 3(1):69–87

    Google Scholar 

  85. Kim G, Park Y (2004) An improved updating parameters method and finite element model updating using multi-objective optimisation technique. Mech Syst Signal Process 18(1):59–78

    Google Scholar 

  86. Kim S, Frangopol DM (2016) Efficient multi-objective optimisation of probabilistic service life management. Struct Infrastruct Eng 13(1):147–159. https://doi.org/10.1080/15732479.2016.1198405

    Article  Google Scholar 

  87. Kitayama S, Miyakawa H, Takano M, Aiba S (2016) Multi-objective optimization of injection molding process parameters for short cycle time and warpage reduction using conformal cooling channel. Int J Adv Manuf Technol 88(5–8):1735–1744

    Google Scholar 

  88. Kitayama S, Yokoyama M, Takano M, Aiba S (2017) Multi-objective optimization of variable packing pressure profile and process parameters in plastic injection molding for minimizing warpage and cycle time. Int J Adv Manuf Technol 92(9–12):3991–3999

    Google Scholar 

  89. Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput 8:149–172

    Google Scholar 

  90. Kumar R, Singh S, Bilga PS, Singh J, Singh S, Scutaru M-L, Pruncu CI (2021) Revealing the benefits of entropy weights method for multi-objective optimization in machining operations: a critical review. J Mater Res Technol 10:1471–1492

    Google Scholar 

  91. Kursawe F (1991) A variant of evolution strategies for vector optimization. In: Schwefel H-P, Manner R (eds) Parallel problem solving from nature. 1st Workshop, PPSN I, pp 193–197, Dortmund, Germany. Springer-Verlag. Lecture notes in computer science No. 496

  92. Lee D, Morillo C, Bugeda G, Oller S, Onate E (2012) Multilayered composite structure design optimisation using distributed/parallel multi-objective evolutionary algorithms. Compos Struct 94(3):1087–1096

    Google Scholar 

  93. Leguizamón G, Coello CAC (2011) Multi-objective ant colony optimization: a taxonomy and review of approaches. Series in machine perception and artificial intelligence, pp 67–94

  94. Li H, Wang X, Wei Y, Liu T, Gu J, Li Z, Liu Y (2017) Multi-objective optimizations of biodegradable polymer stent structure and stent microinjection molding process. Polymers 9(12):20

    Google Scholar 

  95. Li P, Huang L, Peng J (2018) Sensor distribution optimization for structural impact monitoring based on NSGA-II and wavelet decomposition. Sensors 18(12):4264

    Google Scholar 

  96. Li K, Yan S, Zhong Y, Pan W, Zhao G (2018) Multi-objective optimization of the fiber-reinforced composite injection molding process using Taguchi method, RSM, and NSGA-II. Simulation modelling practice and theory

  97. Li Y, Wei K, Yang W, Wang Q (2020) Improving wind turbine blade based on multi-objective particle swarm optimization. Renew Energy. https://doi.org/10.1016/j.renene.2020.07.067

    Article  Google Scholar 

  98. Lin W, Yu D, Zhang C, Zhang S, Tian Y, Liu S, Luo M (2016) Multi-objective optimization of machining parameters in multi-pass turning operations for low-carbon manufacturing. Proc Inst Mech Eng Part B J Eng Manuf 231(13):2372–2383

    Google Scholar 

  99. Lin J-F, Xu Y-L, Law S-S (2018) Structural damage detection-oriented multi-type sensor placement with multi-objective optimization. J Sound Vib 422:568–589

    Google Scholar 

  100. Liu H, Li Y, Duan Z, Chen C (2020) A review on multi-objective optimization framework in wind energy forecasting techniques and applications. Energy Conv Manage 224:113324

    Google Scholar 

  101. Liu Q, Li X, Liu H, Guo Z (2020) Multi-objective metaheuristics for discrete optimization problems: a review of the state-of-the-art. Appl Soft Comput 93:106382

    Google Scholar 

  102. Long Q, Wu X, Wu C (2021) Non-dominated sorting methods for multi-objective optimization: review and numerical comparison. J Ind Manage Optim 17(2):1001

    MathSciNet  MATH  Google Scholar 

  103. Lostado Lorza R, Escribano García R, Fernandez Martinez R, Martínez Calvo M (2018) Using genetic algorithms with multi-objective optimization to adjust finite element models of welded joints. Metals 8(4):230

    Google Scholar 

  104. Lu C, Gao L, Li X, Zheng J, Gong W (2018) A multi-objective approach to welding shop scheduling for makespan, noise pollution and energy consumption. J Clean Prod 196:773–787

    Google Scholar 

  105. Lu C, Gao L, Li X, Xiao S (2017) A hybrid multi-objective grey wolf optimizer for dynamic scheduling in a real-world welding industry. Eng Appl Artif Intell 57:61–79

    Google Scholar 

  106. Mahfouf M-Y, Linkens DA (2004) Adaptive weighted particle swarm optimisation for multi-objective optimal design of alloy steels. In: Parallel problem solving from nature - PPSN VIII, pp 762–771, Birmingham, UK. Springer-Verlag. Lecture notes in computer science vol 3242

  107. Mane SU, Rao MRN (2017) Many-objective optimization: problems and evolutionary algorithms – a short review. Int J Appl Eng Res 12(20):9774–9793

    Google Scholar 

  108. Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395

    MathSciNet  MATH  Google Scholar 

  109. Mariano CE, Morales E (1999) MOAQ an ant-q algorithm for multiple objective optimization problems. In: Banzhaf W, Daida J, Eiben AE, Garzon MH, Honavar V, Jakiela M, Smith RE (eds) Genetic and evolutionary computing conference (GECCO 99), vol 1, pp 894–901, San Francisco, California, Morgan Kaufmann

  110. Song M-P, Gu G-C (2004) Research on particle swarm optimization: a review. In: Proceedings of 2004 international conference on machine learning and cybernetics (IEEE Cat. No.04EX826)

  111. Messac A, Mattson CA (2002) Generating well-distributed sets of Pareto points for engineering design using physical programming. Optim Eng 3:431–450

    MATH  Google Scholar 

  112. Mia M, Gupta MK, Lozano JA, Carou D, Pimenov DY, Królczyk G, Dhar NR (2018) Multi-objective optimization and life cycle assessment of eco-friendly cryogenic N2 assisted turning of Ti-6Al-4V. J Clean Prod 210:121–133

    Google Scholar 

  113. Miettinen K (1998) No-preference methods. Int Ser Oper Res Manage Sci, pp 67–76

  114. Mirjalili S, Jangir P, Saremi S (2016) Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Appl Intell 46(1):79–95. https://doi.org/10.1007/s10489-016-0825-8

    Article  Google Scholar 

  115. Mirjalili S, Saremi S, Mirjalili SM, Coelho LDS (2016) Grasshopper optimization algorithm for multi-objective optimization problems. Expert Syst Appl 47:106–119

    Google Scholar 

  116. Mirjalili SZ, Mirjalili S, Saremi S, Faris H, Aljarah I (2017) Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48(4):805–820

    Google Scholar 

  117. Moleiro F, Madeira JFA, Carrera E, Reddy JN (2020) Design optimization of functionally graded plates under thermo-mechanical loadings to minimize stress, deformation and mass. Compos Struct p 112360

  118. Monarchi DE, Kisiel CC, Duckstein L (1973) Interactive multi-objective programming in water resources: a case study. Water Resour Res 9(4):837–850

    Google Scholar 

  119. Montalvo-Urquizo J, Niebuhr C, Schmidt A, Villarreal-Marroquín MG (2018) Reducing deformation, stress, and tool wear during milling processes using simulation-based multiobjective optimization. Int J Adv Manuf Technol 96(5–8):1859–1873

    Google Scholar 

  120. Mostaghim S, Teich J (2003) Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: 2003 IEEE swarm intelligence symposium proceedings, pp 26–33, Indianapolis, Indiana, USA, IEEE Service Center

  121. Neumann and Morgenstern (1944) Theory of games and economic behavior. Princeton University Press, Princeton, New Jersey

    MATH  Google Scholar 

  122. Niu Y, Jiao F, Zhao B, Wang D (2017) Multiobjective optimization of processing parameters in longitudinal-torsion ultrasonic assisted milling of Ti-6Al-4V. Int J Adv Manuf Technol 93(9–12):4345–4356

    Google Scholar 

  123. Ojstersek R, Brezocnik M, Buchmeister B (2020) Multi-objective optimization of production scheduling with evolutionary computation: a review. Int J Ind Eng Comput 11(3):359–376

    Google Scholar 

  124. Okabe T, Oya Y, Yamamoto G, Sato J, Matsumiya T, Matsuzaki R, Obayashi S (2017) Multi-objective optimization for resin transfer molding process. Compos A Appl Sci Manuf 92:1–9

    Google Scholar 

  125. Olorunda O, Engelbrecht AP (2008) Measuring exploration/exploitation in particle swarms using swarm diversity. In: IEEE congress on evolutionary computation (IEEE World Congress on Computational Intelligence), IEEE, pp 1128–1134

  126. Omkar S, Mudigere D, Naik GN, Gopalakrishnan S (2008) Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures. Comput Struct 86(1):1–14

    Google Scholar 

  127. Osyczka A (1978) An approach to multicriterion optimization problems for engineering design. Comput Methods Appl Mech Eng 15:309–333

    MATH  Google Scholar 

  128. Paiva AP, Gomes JHF, Peruchi RS, Leme RC, Balestrassi PP (2014) A multivariate robust parameter optimization approach based on principal component analysis with combined arrays. Comput Ind Eng 74:186–198

    Google Scholar 

  129. Panagant N, Pholdee N, Wansasueb K, Bureerat S, Yildiz AR, Sait SM (2019) Comparison of recent algorithms for many-objective optimisation of an automotive floor-frame. Int J Vehicle Des 80(2/3/4):176

    Google Scholar 

  130. Panagant N, Pholdee N, Bureerat S et al (2021) A comparative study of recent multi-objective metaheuristics for solving constrained truss optimisation problems. Arch Computat Methods Eng. https://doi.org/10.1007/s11831-021-09531-8

    Article  Google Scholar 

  131. Paula TI, Gomes GF, Freitas Gomes JH, Paiva AP (2019). A mixture design of experiments approach for genetic algorithm tuning applied to multi-objective optimization. Optim Complex Syst Theory Models Algorithms Appl, pp 600–610.

  132. Peng Y, Wang X, Xiong X, Xu P (2016) Crashing analysis and multi-objective optimisation of duplex energy-absorbing structure for subway vehicle. Int J Crashworthiness 21(4):338–352

    Google Scholar 

  133. Perera R, Ruiz A (2008) A multistage FE updating procedure for damage identification in large-scale structures based on multi-objective evolutionary optimization. Mech Syst Signal Process 22(4):970–991. https://doi.org/10.1016/j.ymssp.2007.10.004

    Article  Google Scholar 

  134. Parsopoulos K, Vrahatis M (2002) Particle swarm optimization method in multi-objective problems. In: Proceedings of the 2002 ACM symposium on applied computing (SAC’2002), pp 603–607, Madrid, Spain, ACM Press, New York

  135. Park H-S, Nguyen T-T, Dang X-P (2016) Multi-objective optimization of turning process of hardened material for energy efficiency. Int J Precis Eng Manuf 17(12):1623–1631

    Google Scholar 

  136. Parkinson AR, Balling RJ, Hedengren JD (2013) Optimization methods for engineering design: applications and theory. Brigham Young University

  137. Prakash C, Singh S, Singh M, Antil P, Aliyu AAA, Abdul-Rani AM, Sidhu SS (2018) Multi-objective optimization of MWCNT mixed electric discharge machining of Al–30SiCp MMC using particle swarm optimization. materials horizons: From Nature to Nanomaterials, pp 145–164

  138. Prakash C, Kansal HK, Pabla BS, Puri S (2016) Multi-objective optimization of powder mixed electric discharge machining parameters for fabrication of biocompatible layer on β-Ti alloy using NSGA-II coupled with Taguchi based response surface methodology. J Mech Sci Technol 30(9):4195–4204

    Google Scholar 

  139. Qu S, Zhao J, Wang T (2016) Experimental study and machining parameter optimization in milling thin-walled plates based on NSGA-II. Int J Adv Manuf Technol 89(5–8):2399–2409

    Google Scholar 

  140. Rangaiah GP, Zemin F, Hoadley AF (2020) Multi-objective optimization applications in chemical process engineering: tutorial and review. J Process. https://doi.org/10.3390/pr8050508

    Article  Google Scholar 

  141. Rao RV, Rai DP, Balic J (2016) Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm. J Intell Manuf 29(8):1715–1737

    Google Scholar 

  142. Rao RV, Saroj A, Ocloń P, Taler J, Taler D (2017) Single- and multi-objective design optimization of plate-fin heat exchangers using jaya algorithm. Heat Transfer Eng 39(13–14):1201–1216

    Google Scholar 

  143. Rao RV, Rai DP (2017) Optimization of submerged arc welding process parameters using quasi-oppositional based jaya algorithm. J Mech Sci Technol 31(5):2513–2522

    Google Scholar 

  144. Rao RV, Rai DP, Balic J (2017) Multi-objective optimization of abrasive waterjet machining process using Jaya algorithm and PROMETHEE Method. J Intell Manuf 30(5):2101–2127

    Google Scholar 

  145. Rao S (1984) Multi-objective optimization in structural design with uncertain parameters and stochastic processes. AIAA J 22(11):1670–1678

    MATH  Google Scholar 

  146. Rao S (1986) Game theory approach for multi-objective structural optimization. Comput Struct 25(1):119–127

    Google Scholar 

  147. Rao SS, Rao SS (2009) Engineering optimization: theory and practice. John Wiley and Sons, New Jersey

    Google Scholar 

  148. Ridha HM, Gomes C, Hizam H, Ahmadipour M, Heidari AA, Chen H (2021) Multi-objective optimization and multi-criteria decision-making methods for optimal design of standalone photovoltaic system: a comprehensive review. Renew Sustain Energy Rev 135:110202

    Google Scholar 

  149. Rivas D, Quiza R, Rivas M, Haber RE (2020) Towards sustainability of manufacturing processes by multi-objective optimization: a case study on a submerged arc welding process. IEEE Access 8:212904–212916

    Google Scholar 

  150. Sadollah A, Eskandar H, Kim JH (2015) Water cycle algorithm for solving constrained multi-objective optimization problems. Appl Soft Comput 27:279–298

    Google Scholar 

  151. Saha A, Mondal SC (2017) Multi-objective optimization of manual metal arc welding process parameters for nano-structured hardfacing material using hybrid approach. Measurement 102:80–89

    Google Scholar 

  152. Sahu NK, Andhare AB (2018) Multiobjective optimization for improving machinability of Ti-6Al-4V using RSM and advanced algorithms. J Comput Des Eng 6(1):1–12

    Google Scholar 

  153. Sailender M, Reddy GC, Venkatesh S (2018) Influences of process parameters on weld strength of low carbon alloy steel in purged SAW. Mater Today Proc 5(1):2928–2937

    Google Scholar 

  154. Silva MM, Batista VR, Maciel TM, dos Santos MA, Brasileiro TL (2018) Optimization of submerged arc welding process parameters for overlay welding. Weld Int 32(2):122–129

    Google Scholar 

  155. Schlieter T, Dlugosz A (2020) Structural optimization of aerofoils for many criteria. 26°International Conference. Engineering Mechanics 2020. Brno, Czech Republic

  156. Senthil SM, Parameshwaran R, Ragu Nathan S, Bhuvanesh Kumar M, Deepandurai K (2020) A multi-objective optimization of the friction stir welding process using RSM-based-desirability function approach for joining aluminum alloy 6063–T6 pipes. Struct Multidiscip Optim 62(3):1117–1133

    Google Scholar 

  157. Serafini P (1994) Simulated annealing for multiple objective optimization problems. In: Tzeng G, Wang H, Wen U, Yu P (eds) Proceedings of the tenth international conference on multiple criteria decision making: expand and enrich the domains of thinking and application, vol 1, pp 283–292, Springer-Verlag, Berlin

  158. Sivaiah P, Chakradhar D (2018) Performance improvement of cryogenic turning process during machining of 17–4 PH stainless steel using multi objective optimization techniques. Measurement. https://doi.org/10.1016/j.measurement.2018.12.094

    Article  Google Scholar 

  159. Schaffer JD (1984) Multiple objective optimization with vector evaluated genetic algorithms. PhD thesis, Vanderbilt University, Nashville, Tennessee

  160. Shanjeevi C, Satish Kumar S, Sathiya P (2014) Multi-objective optimization of friction welding parameters in AISI 304L austenitic stainless steel and copper joints. Proc Inst Mech Eng Part B J Eng Manuf 230(3):449–457

    Google Scholar 

  161. Shao Q, Xu T, Yoshino T, Song N (2017) Multi-objective optimization of gas metal arc welding parameters and sequences for low-carbon steel (Q345D) T-joints. J Iron Steel Res Int 24(5):544–555

    Google Scholar 

  162. Sowrirajan M, Koshy Mathews P, Vijayan S (2018) Simultaneous multi-objective optimization of stainless steel clad layer on pressure vessels using genetic algorithm. J Mech Sci Technol 32(6):2559–2568

    Google Scholar 

  163. Srinivas N, Deb K (1994) Multi-objective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Google Scholar 

  164. Teughels A, Maeck J, Roeck G (2002) Damage assessment by FE model updating using damage functions. Comput Struct 80:1869–1879

    Google Scholar 

  165. Tamaki H, Kita H, Kobayashi S (1996). Multi-objective optimization by genetic algorithms: a review. In: Proceedings of IEEE international conference on evolutionary computation, pp 517–522

  166. Tawhid MA, Savsani V (2017) Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems. Neural Comput Appl 31(2):915–929

    Google Scholar 

  167. Thiele L, Miettinen K, Korhonen PJ, Molina J (2009) A preference-based evolutionary algorithm for multi-objective optimization. Evol Comput 17(3):411–436

    Google Scholar 

  168. Torres AF, Rocha FB, Almeida FA, Gomes JHF, Paiva AP, Balestrassi PP (2020) Multivariate stochastic optimization approach applied in a flux-cored arc welding process. IEEE Access 8:61267–61276

    Google Scholar 

  169. Tripathy S, Tripathy DK (2017) Multi-response optimization of machining process parameters for powder mixed electro-discharge machining of H-11 die steel using grey relational analysis and topsis. Mach Sci Technol 21(3):362–384

    Google Scholar 

  170. Vo-Duy T, Duong-Gia D, Ho-Huu V, Vu-Do HC, Nguyen-Thoi T (2017) Multi-objective optimization of laminated composite beam structures using NSGA-II algorithm. Compos Struct 168:498–509. https://doi.org/10.1016/j.compstruct.2017.02.038

    Article  Google Scholar 

  171. Xin-Gang Z, Ji L, Jin M, Ying Z (2020) An improved quantum particle swarm optimization algorithm for environmental economic dispatch. Exp Syst Appl 152:113370

    Google Scholar 

  172. Wakchaure KN, Thakur AG, Gadakh V, Kumar A (2018) Multi-objective optimization of friction stir welding of aluminium alloy 6082–T6 using hybrid taguchi-grey relation analysis- ANN method. Mater Today Proc 5(2):7150–7159

    Google Scholar 

  173. Wang H, Olhofer M, Jin Y (2017) A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges. Complex Intell Syst 3(4):233–245

    Google Scholar 

  174. Wang J, Yan Z, Wang M, Li M, Dai Y (2013) Multi-objective optimization of an organic Rankine cycle (ORC) for low grade waste heat recovery using evolutionary algorithm. Energy Convers Manage 71:146–158

    Google Scholar 

  175. Wang L, Wang T, Wu J, Chen G (2017) Multi-objective differential evolution optimization based on uniform decomposition for wind turbine blade design. Energy 120:346–361

    Google Scholar 

  176. Wang Y, Ma Q, Li W (2012) Structural damage detection by multi-objective intelligent algorithm. In: The 15th world conference on earthquake engineering, Lisbon

  177. Wang Y, Huo X (2018) Multiobjective optimization design and performance prediction of centrifugal pump based on orthogonal test. Adv Mater Sci Eng 2018:1–10

    Google Scholar 

  178. Warsi SS, Agha MH, Ahmad R, Jaffery SHI, Khan M (2018) Sustainable turning using multi-objective optimization: a study of Al 6061 T6 at high cutting speeds. Int J Adv Manuf Technol 100(1–4):843–855

    Google Scholar 

  179. Yang X-S (2014) Nature-inspired optimization algorithms. Elsevier, Amsterdam

    MATH  Google Scholar 

  180. Yang Y, Cao L, Zhou Q, Wang C, Wu Q, Jiang P (2018) Multi-objective process parameters optimization of Laser-magnetic hybrid welding combining Kriging and NSGA-II. Robot Comput Integr Manuf 49:253–262

    Google Scholar 

  181. Yang Y, Cao L, Wang C, Zhou Q, Jiang P (2018) Multi-objective process parameters optimization of hot-wire laser welding using ensemble of metamodels and NSGA-II. Robot Comput Integr Manuf 53:141–152

    Google Scholar 

  182. Yifei T, Meng Z, Jingwei L, Dongbo L, Yulin W (2018) Research on intelligent welding robot path optimization based on GA and PSO algorithms. IEEE Access 6:65397–65404

    Google Scholar 

  183. Yoon KP, Kim WK (2017) The behavioral TOPSIS. Expert Syst Appl 89:266–272

    Google Scholar 

  184. Zadeh LA (1963) Optimality and nonscalar-valued performance criteria. IEEE Trans Autom Control 8(1):59–60

    Google Scholar 

  185. Zhou GD, Yi T-H, Xie M-X, Li H-N, Xu J-H (2021) Optimal wireless sensor placement in structural health monitoring emphasizing information effectiveness and network performance. J Aerosp Eng 34(2):04020112

    Google Scholar 

  186. Zhang H, Peng Y, Hou L, Tian G, Li Z (2019) A hybrid multi-objective optimization approach for energy-absorbing structures in train collisions. Inf Sci 481:491–506

    Google Scholar 

  187. Zhang J, Zhu H, Yang C, Li Y, Wei H (2011) Multi-objective shape optimization of helico-axial multiphase pump impeller based on NSGA-II and ANN. Energy Convers Manage 52(1):538–546

    Google Scholar 

  188. Zhang L, Zhang S, Zhang W (2019) Multi-objective optimization design of in-wheel motors drive electric vehicle suspensions for improving handling stability. Proc Inst Mech Eng Part D J Autom Eng 233:2232–2245

    Google Scholar 

  189. Zhang Q, Li H (2007) MOEA/D: a multi-objective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731

    Google Scholar 

  190. Zhang R, Wang X (2019) Parameter study and optimization of a half-vehicle suspension system model integrated with an arm-teeth regenerative shock absorber using Taguchi method. Mech Sys Signal Process 126:65–81

    Google Scholar 

  191. Zhang Y, Xu Y, Zheng Y, Fernandez-Rodriguez E, Sun A, Yang C, Wang J (2019) Multiobjective optimization design and experimental investigation on the axial flow pump with orthogonal test approach. Complexity 2019:1–14

    Google Scholar 

  192. Zhang J, Wang J, Lin J, Guo Q, Chen K, Ma L (2015) Multiobjective optimization of injection molding process parameters based on Opt LHD, EBFNN, and MOPSO. Int J Adv Manuf Technol 85(9–12):2857–2872

    Google Scholar 

  193. Zitzler E, Deb K, Thiele L (2000) Comparison of multi-objective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Google Scholar 

  194. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm. In: Giannakoglou K, Tsahalis D, Periaux J, Papailou P, Fogarty T (eds) EUROGEN 2001. Evolutionary methods for design, optimization and control with applications to industrial problems, pp 95–100, Athens, Greece

  195. Zitzler E, Thiele L (1999) Multi-objective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Google Scholar 

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Acknowledgements

The authors would like to acknowledge the financial support from the Brazilian agency CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais—APQ-00385-18).

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    João Luiz Junho Pereira, Guilherme Antônio Oliver, Matheus Brendon Francisco, Sebastião Simões Cunha Jr & Guilherme Ferreira Gomes

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Pereira, J.L.J., Oliver, G.A., Francisco, M.B. et al. A Review of Multi-objective Optimization: Methods and Algorithms in Mechanical Engineering Problems. Arch Computat Methods Eng 29, 2285–2308 (2022). https://doi.org/10.1007/s11831-021-09663-x

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