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Multi-objective optimization techniques: a survey of the state-of-the-art and applications

Multi-objective optimization techniques

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Abstract

In recent years, multi-objective optimization (MOO) techniques have become popular due to their potentiality in solving a wide variety of real-world problems, including bioinformatics, wireless networks, natural language processing, image processing, astronomy and astrophysics, and many more. In the current paper, we have presented a survey of recently developed MOO-based algorithms. Some of the applications, along with possible future research directions, are also discussed.

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Notes

  1. http://www.ntu.edu.sg/home/epnsugan/index_files/cec-benchmarking.htm.

  2. http://crisisnlp.qcri.org/lrec2016/lrec2016.html.

  3. https://pymoo.org/.

  4. http://www.geatbx.com.

References

  1. K. Deb, In Search Methodologies (Springer, Berlin, 2014), pp. 403–449

    Google Scholar 

  2. K. Price, R.M. Storn, J.A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization (Springer Science & Business Media, Berlin, 2006)

    MATH  Google Scholar 

  3. C.C. Coello, M.S. Lechuga, In Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), vol. 2 (IEEE, 2002), vol. 2, pp. 1051–1056

  4. S. Bandyopadhyay, S. Saha, U. Maulik, K. Deb, IEEE Trans. Evol. Comput. 12(3), 269 (2008)

    Google Scholar 

  5. H. Zhang, A. Zhou, S. Song, Q. Zhang, X.Z. Gao, J. Zhang, IEEE Trans. Evol. Comput. 20(5), 792 (2016). https://doi.org/10.1109/TEVC.2016.2521868

    Article  Google Scholar 

  6. R. Sengupta, S. Saha, Inf. Sci. 467, 725 (2018)

    Google Scholar 

  7. R. Sengupta, M. Pal, S. Saha, S. Bandyopadhyay, Swarm Evolut. Comput. 46, 201 (2019)

    Google Scholar 

  8. K. Maity, R. Sengupta, S. Saha, In 2019 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2019), pp. 286–294

  9. M. Pal, S. Saha, S. Bandyopadhyay, Inf. Sci. 423, 200 (2018)

    Google Scholar 

  10. X. Li, H. Zhang, S. Song, Swarm Evolut. Comput. 43, 31 (2018)

    Google Scholar 

  11. B.C. Wang, H.X. Li, J.P. Li, Y. Wang, IEEE Trans. Syst. Man Cybernet. Syst. 49(7), 1482 (2018)

    Google Scholar 

  12. J. Liang, W. Xu, C. Yue, K. Yu, H. Song, O.D. Crisalle, B. Qu, Swarm Evolut. Comput. 44, 1028 (2019)

    Google Scholar 

  13. J. Sun, H. Zhang, A. Zhou, Q. Zhang, K. Zhang, Swarm Evolut. Comput. 44, 304 (2019)

    Google Scholar 

  14. S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Science 220(4598), 671 (1983)

    MathSciNet  ADS  Google Scholar 

  15. K. Deb, In Springer Handbook of Computational Intelligence (Springer, Berlin, 2015), pp. 995–1015

    Google Scholar 

  16. S. Das, S.S. Mullick, P.N. Suganthan, Swarm Evolut. Comput. 27, 1 (2016)

    Google Scholar 

  17. S. Geman, D. Geman, IEEE Trans. Pattern Anal. Mach. Intell. PAMI 6(6), 721–741 (1984)

  18. D. Dasgupta, Z. Michalewicz, Evolutionary Algorithms in Engineering Applications (Springer Science & Business Media, Berlin, 2013)

    MATH  Google Scholar 

  19. R. Storn, K. Price, J. Global Optim. 11(4), 341 (1997)

    MathSciNet  Google Scholar 

  20. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, IEEE Trans. Evol. Comput. 6(2), 182 (2002)

    Google Scholar 

  21. K.L. Du, M. Swamy, In Search and Optimization by Metaheuristics (Springer, Berlin, 2016), pp. 153–173

    Google Scholar 

  22. R.S. Parpinelli, H.S. Lopes, A.A. Freitas, IEEE Trans. Evol. Comput. 6(4), 321 (2002)

    Google Scholar 

  23. A.K. Abasi, A.T. Khader, M.A. Al-Betar, S. Naim, S.N. Makhadmeh, Z.A.A. Alyasseri, Appl. Soft Comput. 87, 106002 (2020)

    Google Scholar 

  24. J. Carvalho, A. Prado, A. Plastino, In 2014 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT), vol. 2 (IEEE, 2014), vol. 2, pp. 110–117 (2014)

  25. H. Lu, J. Chen, K. Yan, Q. Jin, Y. Xue, Z. Gao, Neurocomputing 256, 56 (2017)

    Google Scholar 

  26. K. Zhang, H. Du, M.W. Feldman, Physica A 478, 20 (2017)

    ADS  Google Scholar 

  27. C.A.C. Coello, G.B. Lamont, Applications of Multi-Objective Evolutionary Algorithms, vol. 1 (World Scientific, Singapore, 2004)

    MATH  Google Scholar 

  28. E. Zitzler, K. Deb, L. Thiele, Evol. Comput. 8(2), 173 (2000)

    Google Scholar 

  29. M.R. Bonyadi, Z. Michalewicz, Evol. Comput. 25(1), 1–54 (2017)

  30. N. Srinivas, K. Deb, Evol. Comput. 2(3), 221 (1994). https://doi.org/10.1162/evco.1994.2.3.221

    Article  Google Scholar 

  31. N. Saini, S. Saha, P. Bhattacharyya, Cogn. Comput. 11(2), 271 (2019)

    Google Scholar 

  32. E. Mezura-Montes, J. Velázquez-Reyes, C.A. Coello Coello, In Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 485–492 (2006)

  33. D. Zhang, B. Wei, In Mechatronics and Automation (ICMA), 2014 IEEE International Conference on (IEEE, 2014), pp. 239–244

  34. J. Vesterstrom, R. Thomsen, In IEEE Congress on Evolutionary Computation, vol. 2, vol. 2, pp. 1980–1987 (2004)

  35. H. Zhang, A. Zhou, S. Song, Q. Zhang, X.Z. Gao, J. Zhang, IEEE Trans. Evol. Comput. 20(5), 792 (2016)

    Google Scholar 

  36. T. Kohonen, Neurocomputing 21(1), 1 (1998)

    Google Scholar 

  37. S.S. Haykin, S.S. Haykin, S.S. Haykin, S.S. Haykin, Neural networks and learning machines, vol. 3 (Pearson Upper Saddle River, NJ, USA:, 2009)

  38. A.L. Jaimes, C.A.C. Coello, J.E.U. Barrientos, In International Conference on Evolutionary Multi-Criterion Optimization (Springer, Berlin, 2009), pp. 423–437

    Google Scholar 

  39. M. Pal, S. Saha, S. Bandyopadhyay, In 2016 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2016), pp. 1131–1138

  40. K. Deb, Comput. Methods Appl. Mech. Eng. 186(2–4), 311 (2000)

    ADS  Google Scholar 

  41. T. Takahama, S. Sakai, In IEEE congress on evolutionary computation (IEEE, 2010), pp. 1–9

  42. T. Takahama, S. Sakai, In IEEE congress on evolutionary computation (IEEE, 2010), pp. 1–8

  43. J.H. Yi, S. Deb, J. Dong, A.H. Alavi, G.G. Wang, Futur. Gener. Comput. Syst. 88, 571 (2018)

    Google Scholar 

  44. C.A.C. Coello, S.G. Brambila, J.F. Gamboa, M.G.C. Tapia, R.H. Gómez, Complex Intell. Syst. 6(2), 221 (2020)

    Google Scholar 

  45. J.J. Rowland, Biosystems 72(1–2), 187 (2003)

    Google Scholar 

  46. B. Zhang, A.K. Qin, T. Sellis, Proceedings of the Genetic and Evolutionary Computation Conference , 577–584 (2018)

  47. F. Jiménez, C. Martínez, E. Marzano, J.T. Palma, G. Sánchez, G. Sciavicco, IEEE Trans. Fuzzy Syst. 27(5), 1085 (2019)

    Google Scholar 

  48. H. Ullah, T. Saba, N. Islam, N. Abbas, A. Rehman, Z. Mehmood, A. Anjum, Microsc. Res. Tech. 82(4), 361 (2019)

    Google Scholar 

  49. H. Al-Sahaf, Y. Bi, Q. Chen, A. Lensen, Y. Mei, Y. Sun, B. Tran, B. Xue, M. Zhang, J. R. Soc. New Zealand 49(2), 205 (2019)

    Google Scholar 

  50. J.M. Moyano, E.L. Gibaja, K.J. Cios, S. Ventura, Inf. Fusion 50, 168 (2019)

    Google Scholar 

  51. A.A. Bidgoli, H. Ebrahimpour-Komleh, S. Rahnamayan, In 2019 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2019), pp. 1588–1595

  52. C.E. da Silva Santos, R.C. Sampaio, L. dos Santos Coelho, G.A. Bestard, C.H. Llanos, Pattern Recogn. 110, 107649 (2021)

    Google Scholar 

  53. Y. Zhang, D. Gong, X. Sun, Y. Guo, Sci. Rep. 7(1), 1 (2017)

    ADS  Google Scholar 

  54. A. Onan, S. Korukoğlu, H. Bulut, Inf. Process. Manag. 53(4), 814 (2017)

    Google Scholar 

  55. R. Xu, D. Wunsch, Clustering, vol. 10 (Wiley, Hoboken, 2008)

    Google Scholar 

  56. A. Likas, N. Vlassis, J.J. Verbeek, Pattern Recogn. 36(2), 451 (2003)

    ADS  Google Scholar 

  57. N.K. Kaur, U. Kaur, D.D. Singh, Int. J. Comput. Appl. Technol. (IJCAT) 1(1), 2349 (2014)

    Google Scholar 

  58. F. Murtagh, P. Contreras, Wiley interdisciplinary reviews. Data Min. Knowl. Disc. 2(1), 86 (2012)

    Google Scholar 

  59. C. Legány, S. Juhász, A. Babos, In Proceedings of the 5th WSEAS international conference on artificial intelligence, knowledge engineering and data bases (World Scientific and Engineering Academy and Society (WSEAS) Stevens Point..., 2006), pp. 388–393 (2006)

  60. S. Saha, S. Bandyopadhyay, Pattern Recogn. 43(3), 738 (2010)

    ADS  Google Scholar 

  61. M.K. Pakhira, S. Bandyopadhyay, U. Maulik, Pattern Recogn. 37(3), 487 (2004)

    ADS  Google Scholar 

  62. M. Sharma, J.K. Chhabra, Sustain. Comput.: Inform. Syst. 23, 144 (2019)

    Google Scholar 

  63. M. Shojafar, R. Taheri, Z. Pooranian, R. Javidan, A. Miri, Y. Jararweh, In 2019 IEEE/ACS 16th International Conference on Computer Systems and Applications (AICCSA) (IEEE, 2019), pp. 1–8

  64. A. Alexeyenko, I. Tamas, G. Liu, E.L. Sonnhammer, Bioinformatics 22(14), e9 (2006)

    Google Scholar 

  65. P. Dutta, S. Saha, Comput. Biol. Med. 89, 31 (2017)

    Google Scholar 

  66. M. Garza-Fabre, J. Handl, J. Knowles, IEEE Trans. Evol. Comput. 22(4), 515 (2017)

    Google Scholar 

  67. A.K. Paul, P.C. Shill, Inf. Sci. 448, 112 (2018)

    Google Scholar 

  68. R. Wang, S. Lai, G. Wu, L. Xing, L. Wang, H. Ishibuchi, Inf. Sci. 450, 128 (2018)

    Google Scholar 

  69. D. Dutta, J. Sil, P. Dutta, Expert Syst. Appl. 137, 357 (2019)

    Google Scholar 

  70. S. Zhu, L. Xu, E.D. Goodman, Knowl.-Based Syst. 188, 105018 (2020)

    Google Scholar 

  71. S. Saha, S. Bandyopadhyay, Appl. Soft Comput. 13(1), 89 (2013)

    Google Scholar 

  72. N. Saini, S. Saha, A. Jangra, P. Bhattacharyya, Knowl.-Based Syst. 164, 45 (2019)

    Google Scholar 

  73. N. Saini, S. Saha, D. Chakraborty, P. Bhattacharyya, PLoS One 14(11), e0223477 (2019)

    Google Scholar 

  74. N. Saini, S. Saha, A. Kumar, P. Bhattacharyya, In International Conference on Neural Information Processing (Springer, Berlin, 2019), pp. 670–678

    Google Scholar 

  75. N. Saini, S. Saha, S. Mansoori, P. Bhattacharyya, Soft Computing pp. 1–13 (2020)

  76. N. Saini, S. Kumar, S. Saha, P. Bhattacharyya, In 2020 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2020), pp. 1–8

  77. N. Saini, S. Saha, P. Bhattacharyya, H. Tuteja, A.C.M. Trans, Multimedia Comput. Commun. Appl. (TOMM) 16(1s), 1 (2020)

    Google Scholar 

  78. N. Saini, S. Saha, V. Potnuru, R. Grover, P. Bhattacharyya, IEEE Intell. Syst. 34(6), 43 (2019)

    Google Scholar 

  79. N. Saini, S. Kumar, S. Saha, P. Bhattacharyya, In 2020 IEEE International Conference on Pattern Recognition (ICPR) (IEEE, 2020)

  80. J.M. Sanchez-Gomez, M.A. Vega-Rodríguez, C.J. Perez, Expert Syst. Appl. 140, 112904 (2020)

    Google Scholar 

  81. J.M. Sanchez-Gomez, M.A. Vega-Rodríguez, C.J. Pérez, Appl. Soft Comput. 91, 106231 (2020)

    Google Scholar 

  82. R. Alqaisi, W. Ghanem, A. Qaroush, IEEE Access 8, 228206 (2020)

    Google Scholar 

  83. M.A. Mosa, Appl. Soft Comput. 90, 106189 (2020)

    Google Scholar 

  84. A. Jangra, S. Saha, A. Jatowt, M. Hasanuzzaman, In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval (2020), pp. 1745–1748

  85. L. Wang, X. Fu, M.I. Menhas, M. Fei, In Life System Modeling and Intelligent Computing (Springer, Berlin, 2010), pp. 49–57

    Google Scholar 

  86. S. Agarwal, H. Yu, In AMIA Annual Symposium Proceedings, vol. 2009 (American Medical Informatics Association, 2009), vol. 2009, p. 6

  87. B.P. Ramesh, R.J. Sethi, H. Yu, PLoS One 10(2), e0115671 (2015)

    Google Scholar 

  88. N. Saini, S. Saha, P. Bhattacharyya, IEEE Trans. Comput. Soc. Syst. 6(6), 1219 (2019)

    Google Scholar 

  89. M. Kusner, Y. Sun, N. Kolkin, K. Weinberger, International Conference on Machine Learning , 957–966 (2015)

  90. S.H. Liu, K.Y. Chen, Y.L. Hsieh, B. Chen, H.M. Wang, H.C. Yen, W.L. Hsu, INTERSPEECH , 670–674 (2016)

  91. T. Mikolov, K. Chen, G. Corrado, J. Dean, arXiv preprint arXiv:1301.3781 (2013)

  92. J. Ramos, et al., In Proceedings of the first instructional conference on machine learning, vol. 242, vol. 242, pp. 133–142 (2003)

  93. G. Erkan, D.R. Radev, J. Artif. Intell. Res. 22, 457 (2004)

    Google Scholar 

  94. S. Mitra, M. Hasanuzzaman, S. Saha, A. Way, In Proceedings of the 27th International Conference on Computational Linguistics, pp. 3793–3805 (2018)

  95. S. Saha, S. Mitra, S. Kramer, ACM Trans. Knowl. Disc. Data (TKDD) 12(4), 1 (2018)

    Google Scholar 

  96. N. Saini, D. Bansal, S. Saha, P. Bhattacharyya, Expert Syst. Appl. 168, 114299 (2021)

    Google Scholar 

  97. U.K. Sikdar, A. Ekbal, S. Saha, In 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI) (IEEE, 2014), pp. 1039–1044

  98. S. Yadav, A. Ekbal, S. Saha, Soft. Comput. 22(20), 6881 (2018)

    Google Scholar 

  99. Y. Zhang, D. Gong, X. Gao, T. Tian, X. Sun, Inf. Sci. 507, 67 (2020)

    Google Scholar 

  100. U.K. Sikdar, A. Ekbal, S. Saha, O. Uryupina, M. Poesio, Soft. Comput. 19(8), 2149 (2015)

    Google Scholar 

  101. L. Rundo, A. Tangherloni, M.S. Nobile, C. Militello, D. Besozzi, G. Mauri, P. Cazzaniga, Expert Syst. Appl. 119, 387 (2019)

    Google Scholar 

  102. S.S. Rajput, K. Arya, V.K. Bohat, In Computational Intelligence: Theories, Applications and Future Directions, vol. II (Springer, Berlin, 2019), pp. 635–644

    Google Scholar 

  103. E.J. Carmona, J.M. Molina-Casado, Neural Comput. Appl. 33(6), 1903–1921 (2021)

  104. A. Khan, A.S. Qureshi, N. Wahab, M. Hussain, M.Y. Hamza, arXiv preprint arXiv:1901.07387 (2019)

  105. P. Dutta, S. Saha, S. Chopra, V. Miglani, IEEE/ACM Trans. Comput. Biol. Bioinform. 17(6), 2005–2016 (2019)

  106. P. Dutta, S. Saha, In 2019 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2019), pp. 2521–2528 (2019)

  107. P. Dutta, P. Mishra, S. Saha, Comput. Biol. Med. 125, 103965 (2020)

  108. P. Dutta, S. Saha, S. Naskar, Multimedia Tools and Applications pp. 1–21 (2020)

  109. P. Dutta, S. Saha, S. Pai, A. Kumar, Sci. Rep. 10(1), 1 (2020)

    Google Scholar 

  110. R. Pearce, X. Huang, D. Setiawan, Y. Zhang, J. Mol. Biol. 431(13), 2467 (2019)

    Google Scholar 

  111. S. Rasti, C. Vogiatzis, Ann. Oper. Res. 276(1–2), 35 (2019)

    MathSciNet  Google Scholar 

  112. S. Saha, A.K. Alok, A. Ekbal, IEEE J. Biomed. Health Inform. 20(4), 1171 (2015)

    Google Scholar 

  113. A.K. Alok, N. Kanekar, S. Saha, A. Ekbal, In 2014 9th International Conference on Industrial and Information Systems (ICIIS) (IEEE, 2014), pp. 1–6

  114. A.K. Alok, P. Gupta, S. Saha, V. Sharma, Int. J. Mach. Learn. Cybern. 11, 2541–2563 (2020)

  115. R.K. Sanodiya, M. Tiwari, J. Mathew, S. Saha, S. Saha, Soft. Comput. 24(24), 18713 (2020)

    Google Scholar 

  116. J. Kennedy, R. Eberhart, In Proceedings of ICNN’95-International Conference on Neural Networks, vol. 4 (IEEE, 1995), vol. 4, pp. 1942–1948 (1995)

  117. S. Yadav, A. Ekbal, S. Saha, Knowl. Inf. Syst. 60(3), 1453 (2019)

    Google Scholar 

  118. K. Jha, S. Saha, Appl. Soft Comput. 98, 106823 (2021)

  119. K. Nag, N.R. Pal, In Evolutionary and Swarm Intelligence Algorithms (Springer, Berlin, 2019), pp. 119–141

    Google Scholar 

  120. D.A. Anushya, Int. J. Comput. Sci. Eng. 7, 2 (2019)

    Google Scholar 

  121. R. Guha, M. Ghosh, S. Kapri, S. Shaw, S. Mutsuddi, V. Bhateja, R. Sarkar, Evolut. Intell. 14(2), 357–367 (2021)

  122. C.B. Gokulnath, S. Shantharajah, Clust. Comput. 22(6), 14777 (2019)

    Google Scholar 

  123. B. Xue, M. Zhang, W.N. Browne, X. Yao, IEEE Trans. Evol. Comput. 20(4), 606 (2015)

    Google Scholar 

  124. N. Abd-Alsabour, In 2014 European Modelling Symposium (IEEE, 2014), pp. 20–26

  125. H. Li, F. He, Y. Liang, Q. Quan, Soft Comput. 24(9), 6851–6870 (2020)

  126. P. Charbonneau, Astrophys. J. Suppl. Ser. 101, 309 (1995)

    ADS  Google Scholar 

  127. M.R. Sentinella, L. Casalino, Celest. Mech. Dyn. Astron. 105(1–3), 211 (2009)

    ADS  Google Scholar 

  128. S. Makhija, S. Saha, S. Basak, M. Das, Astro. Comput. 29, 100313 (2019)

    Google Scholar 

  129. K. Bora, S. Saha, S. Agrawal, M. Safonova, S. Routh, A. Narasimhamurthy, Astro. Comput. 17, 129 (2016)

    ADS  Google Scholar 

  130. G.M. Jacquez, Stat. Med. 15(18), 1935 (1996)

    Google Scholar 

  131. S. Saha, S. Basak, M. Safonova, K. Bora, S. Agrawal, P. Sarkar, J. Murthy, Astro. Comput. 23, 141 (2018)

    ADS  Google Scholar 

  132. A. Konstantinidis, K. Yang, Q. Zhang, D. Zeinalipour-Yazti, Comput. Netw. 54(6), 960 (2010)

    Google Scholar 

  133. P.J. Angeline, G.M. Saunders, J.B. Pollack, IEEE Trans. Neural Networks 5(1), 54 (1994)

    Google Scholar 

  134. H.Q. Nguyen, H.B. Ly, V.Q. Tran, T.A. Nguyen, T.T. Le, B.T. Pham, Materials 13(5), 1205 (2020)

    ADS  Google Scholar 

  135. J. Maturana, F. Lardeux, F. Saubion, J. Heuristics 16(6), 881 (2010)

    Google Scholar 

  136. F. Ramezani, J. Lu, J. Taheri, F.K. Hussain, World Wide Web 18(6), 1737 (2015)

    Google Scholar 

  137. A. Slowik, H. Kwasnicka, Neural Comput. Appl. 32, 12363–12379 (2020)

  138. H. Pohlheim, URL: http://www.geatbx.com/. Last access: Jun 24 (2012)

  139. S. Mishra, S. Mondal, S. Saha, C.A.C. Coello, Swarm Evolut. Comput. 43, 244 (2018)

    Google Scholar 

  140. S. Mishra, S. Saha, S. Mondal, C.A.C. Coello, Swarm Evolut. Comput. 44, 748 (2019)

    Google Scholar 

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Acknowledgements

Dr. Naveen Saini would like to acknowledge the support received from the Woosong University Academic research in 2021. Dr. Sriparna Saha would like to acknowledge the support received from the Young Faculty Research Fellowship program of Visvesvaraya Ph.D. Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation (Formerly Media Lab Asia) for conducting this research.

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  1. Technology Studies Department, Endicott College of International Studies, Woosong University, Daejeon, 34606, South Korea

    Naveen Saini

  2. Department of Computer Science and Engineering, Indian Institute of Technology Patna, Bihar, 801103, India

    Sriparna Saha

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  1. Naveen Saini
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Saini, N., Saha, S. Multi-objective optimization techniques: a survey of the state-of-the-art and applications. Eur. Phys. J. Spec. Top. 230, 2319–2335 (2021). https://doi.org/10.1140/epjs/s11734-021-00206-w

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