IEEE/CAA Journal of Automatica Sinica
Citation:  Yicun Hua, Qiqi Liu, Kuangrong Hao and Yaochu Jin, "A Survey of Evolutionary Algorithms for MultiObjective Optimization Problems With Irregular Pareto Fronts," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 303318, Feb. 2021. doi: 10.1109/JAS.2021.1003817 
[1] 
A. M. Zhou, B. Y. Qu, H. Li, S. Z. Zhao, P. N. Suganthan, and Q. F. Zhang, “Multiobjective evolutionary algorithms: A survey of the state of the art,” Swarm Evolut. Comput., vol. 1, no. 1, pp. 32–49, Mar. 2011. doi: 10.1016/j.swevo.2011.03.001

[2] 
H. Jain and K. Deb, “An evolutionary manyobjective optimization algorithm using referencepoint based nondominated sorting approach, part Ⅱ: Handling constraints and extending to an adaptive approach,” IEEE Trans. Evolut. Comput., vol. 18, no. 4, pp. 602–622, Aug. 2014. doi: 10.1109/TEVC.2013.2281534

[3] 
D. K. Saxena, J. A. Duro, A. Tiwari, K. Deb, and Q. F. Zhang, “Objective reduction in manyobjective optimization: Linear and nonlinear algorithms,” IEEE Trans. Evolut. Comput., vol. 17, no. 1, pp. 77–99, Feb. 2013. doi: 10.1109/TEVC.2012.2185847

[4] 
X. L. Ma, Y. Yu, X. D. Li, Y. T. Qi, and Z. X. Zhu, “A survey of weight vector adjustment methods for decompositionbased multiobjective evolutionary algorithms,” IEEE Trans. Evolut. Comput., vol. 24, no. 4, pp. 634–649, Aug. 2020. doi: 10.1109/TEVC.2020.2978158

[5] 
C. J. Zhang, K. C. Tan, L. H. Lee, and L. Gao, “Adjust weight vectors in MOEA/D for biobjective optimization problems with discontinuous Pareto fronts,” Soft Comput., vol. 22, no. 12, pp. 3997–4012, Jun. 2018. doi: 10.1007/s0050001726094

[6] 
H. Ishibuchi, H. Masuda, and Y. Nojima, “Pareto fronts of manyobjective degenerate test problems,” IEEE Trans. Evolut. Comput., vol. 20, no. 5, pp. 807–813, Oct. 2016. doi: 10.1109/TEVC.2015.2505784

[7] 
Q. F. Zhang and H. Li, “MOEA/D: A multiobjective evolutionary algorithm based on decomposition,” IEEE Trans. Evolut. Comput., vol. 11, no. 6, pp. 712–731, Dec. 2007. doi: 10.1109/TEVC.2007.892759

[8] 
R. Cheng, Y. Jin, M. Olhofer, and B. Sendhoff, “A reference vector guided evolutionary algorithm for manyobjective optimization,” IEEE Trans. Evolut. Comput., vol. 20, no. 5, pp. 773–791, Oct. 2016. doi: 10.1109/TEVC.2016.2519378

[9] 
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGAⅡ,” IEEE Trans. Evolut. Comput., vol. 6, no. 2, pp. 182–197, Apr. 2002. doi: 10.1109/4235.996017

[10] 
J. Bader and E. Zitzler, “HypE: An algorithm for fast hypervolumebased manyobjective optimization,” Evolut. Comput., vol. 19, no. 1, pp. 45–76, Feb. 2011. doi: 10.1162/EVCO_a_00009

[11] 
E. Zitzler and S. Künzli, “Indicatorbased selection in multiobjective search, ” in Proc. Int. Conf. Parallel Problem Solving from Nature. Berlin, Heidelberg: Springer, 2004, pp. 832–842.

[12] 
L. Miguel Antonio and C. A. Coello Coello, “Coevolutionary multiobjective evolutionary algorithms: Survey of the stateoftheart,” IEEE Trans. Evolut. Comput., vol. 22, no. 6, pp. 851–865, Dec. 2018. doi: 10.1109/TEVC.2017.2767023

[13] 
R. Wang, R. C. Purshouse, and P. J. Fleming, “Preferenceinspired coevolutionary algorithms using weight vectors,” Eur. J. Oper. Res., vol. 243, no. 2, pp. 423–441, Jun. 2015. doi: 10.1016/j.ejor.2014.05.019

[14] 
Y. C. Hua, Y. Jin, and K. R. Hao, “A clusteringbased adaptive evolutionary algorithm for multiobjective optimization with irregular Pareto fronts,” IEEE Trans. Cybernet., vol. 49, no. 7, pp. 2758–2770, Jul. 2019. doi: 10.1109/TCYB.2018.2834466

[15] 
H. Ishibuchi, Y. Setoguchi, H. Masuda, and Y. Nojima, “Performance of decompositionbased manyobjective algorithms strongly depends on Pareto front shapes,” IEEE Trans. Evolut. Comput., vol. 21, no. 2, pp. 169–190, Apr. 2017. doi: 10.1109/TEVC.2016.2587749

[16] 
N. Beume, B. Naujoks, and M. Emmerich, “SMSEMOA: Multiobjective selection based on dominated hypervolume,” Eur. J. Oper. Res., vol. 181, no. 3, pp. 1653–1669, Sept. 2007. doi: 10.1016/j.ejor.2006.08.008

[17] 
X. Y. Cai, Z. X. Yang, Z. Fan, and Q. F. Zhang, “Decompositionbasedsorting and anglebasedselection for evolutionary multiobjective and manyobjective optimization,” IEEE Trans. Cybernet., vol. 47, no. 9, pp. 2824–2837, Sept. 2017. doi: 10.1109/TCYB.2016.2586191

[18] 
L. Q. Pan, C. He, Y. Tian, Y. S. Su, and X. Y. Zhang, “A region division based diversity maintaining approach for manyobjective optimization,” Int. Comput.Aid. Eng., vol. 24, no. 3, pp. 279–296, Jun. 2017.

[19] 
Z. P. Liang, K. F. Hu, X. L. Ma, and Z. X. Zhu, “A manyobjective evolutionary algorithm based on a tworound selection strategy,” IEEE Trans. Cybernet., pp. 1–13, 2019. DOI: 10.1109/TCYB.2019.2918087

[20] 
Z. K. Wang, Q. F. Zhang, H. Li, H. Ishibuchi, and L. C. Jiao, “On the use of two reference points in decomposition based multiobjective evolutionary algorithms,” Swarm Evolut. Comput., vol. 34, pp. 89–102, Jun. 2017. doi: 10.1016/j.swevo.2017.01.002

[21] 
Q. Z. Lin, S. B. Liu, K. C. Wong, M. G. Gong, C. A. C. Coello, J. Y. Chen, and J. Zhang, “A clusteringbased evolutionary algorithm for manyobjective optimization problems,” IEEE Trans. Evolut. Comput., vol. 23, no. 3, pp. 391–405, Jun. 2019. doi: 10.1109/TEVC.2018.2866927

[22] 
X. Y. Cai, Z. W. Mei, Z. Fan, and Q. F. Zhang, “A constrained decomposition approach with grids for evolutionary multiobjective optimization,” IEEE Trans. Evolut. Comput., vol. 22, no. 4, pp. 564–577, Aug. 2018. doi: 10.1109/TEVC.2017.2744674

[23] 
Q. Q. Fan and X. F. Yan, “Solving multimodal multiobjective problems through zoning search,” IEEE Trans. Syst. Man Cybernet.:Syst., pp. 1–12, 2019. DOI: 10.1109/TSMC.2019.2944338

[24] 
J. Liang, W. W. Xu, C. T. Yue, K. J. Yu, H. Song, O. D. Crisalle, and B. Y. Qu, “Multimodal multiobjective optimization with differential evolution,” Swarm Evolut. Comput., vol. 44, pp. 1028–1059, Feb. 2019. doi: 10.1016/j.swevo.2018.10.016

[25] 
Q. Z. Lin, W. Lin, Z. X. Zhu, M. G. Gong, J. Q. Li, and C. A. Coello Coello, “Multimodal multiobjective evolutionary optimization with dual clustering in decision and objective spaces,” IEEE Trans. Evolut. Comput., 2020. DOI: 10.1109/TEVC.2020.3008822

[26] 
Y. P. Liu, G. G. Yen, and D. W. Gong, “A multimodal multiobjective evolutionary algorithm using twoarchive and recombination strategies,” IEEE Trans. Evolut. Comput., vol. 23, no. 4, pp. 660–674, Aug. 2019. doi: 10.1109/TEVC.2018.2879406

[27] 
A. Zhou, Q. Zhang, and Y. Jin, “Approximating the set of Paretooptimal solutions in both the decision and objective spaces by an estimation of distribution algorithm,” IEEE Trans. Evolut. Comput., vol. 13, no. 5, pp. 1167–1189, Oct. 2009. doi: 10.1109/TEVC.2009.2021467

[28] 
B. D. Li, J. L. Li, K. Tang, and X. Yao, “Manyobjective evolutionary algorithms,” ACM Comput. Surv., vol. 48, no. 1, Article No. 13, Sep. 2015.

[29] 
I. Das and J. E. Dennis, “Normalboundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems,” Siam J Optimizat., vol. 8, no. 3, pp. 631–657, Mar. 1998. doi: 10.1137/S1052623496307510

[30] 
X. Y. Cai, Z. W. Mei, and Z. Fan, “A decompositionbased manyobjective evolutionary algorithm with two types of adjustments for direction vectors,” IEEE Trans. Cybernet., vol. 48, no. 8, pp. 2335–2348, Aug. 2018. doi: 10.1109/TCYB.2017.2737554

[31] 
H. W. Ge, M. D. Zhao, L. Sun, Z. Wang, G. Z. Tan, Q. Zhang, and C. L. P. Chen, “A manyobjective evolutionary algorithm with two interacting processes: Cascade clustering and reference point incremental learning,” IEEE Trans. Evolut. Comput., vol. 23, no. 4, pp. 572–586, Aug. 2019. doi: 10.1109/TEVC.2018.2874465

[32] 
K. Deb and H. Jain, “An evolutionary manyobjective optimization algorithm using referencepointbased nondominated sorting approach, part I: Solving problems with box constraints,” IEEE Trans. Evolut. Comput., vol. 18, no. 4, pp. 577–601, Aug. 2014. doi: 10.1109/TEVC.2013.2281535

[33] 
Y. Tian, C. He, R. Cheng, and X. Y. Zhang, “A multistage evolutionary algorithm for better diversity preservation in multiobjective optimization,” IEEE Trans. Syst. Man Cybernet.:Syst., pp. 1–15, 2019. DOI: 10.1109/TSMC.2019.2956288

[34] 
M. Q. Li, C. Grosan, S. X. Yang, X. H. Liu, and X. Yao, “Multiline distance minimization: A visualized manyobjective test problem suite,” IEEE Trans. Evolut. Comput., vol. 22, no. 1, pp. 61–78, Feb. 2018. doi: 10.1109/TEVC.2017.2655451

[35] 
K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable test problems for evolutionary multiobjective optimization, ” in Evolutionary Multiobjective Optimization. London: Springer, 2005, pp. 105–145.

[36] 
H. Jain and K. Deb, “An improved adaptive approach for elitist nondominated sorting genetic algorithm for manyobjective optimization, ” in Proc. Int. Conf. Evolutionary MultiCriterion Optimization. Berlin, Heidelberg: Springer, 2013, pp. 307–321.

[37] 
R. Cheng, M. Q. Li, Y. Tian, X. Y. Zhang, S. X. Yang, Y. Jin, and X. Yao, “A benchmark test suite for evolutionary manyobjective optimization,” Complex &Intelligent Systems, vol. 3, no. 1, pp. 67–81, Mar. 2017.

[38] 
S. Huband, P. Hingston, L. Barone, and L. While, “A review of multiobjective test problems and a scalable test problem toolkit,” IEEE Trans. Evolut. Comput., vol. 10, no. 5, pp. 477–506, Oct. 2006. doi: 10.1109/TEVC.2005.861417

[39] 
Y. T. Qi, X. L. Ma, F. Liu, L. C. Jiao, J. Y. Sun, and J. S. Wu, “MOEA/D with adaptive weight adjustment,” Evolut. Comput., vol. 22, no. 2, pp. 231–264, May 2014. doi: 10.1162/EVCO_a_00109

[40] 
H. Li, Q. F. Zhang, and J. D. Deng, “Multiobjective test problems with complicated Pareto fronts: Difficulties in degeneracy, ” in Proc. IEEE Congr. Evolutionary Computation, Beijing, China, 2014, pp. 2156–2163.

[41] 
R. Vlennet, C. Fonteix, and I. Marc, “Multicriteria optimization using a genetic algorithm for determining a Pareto set,” Int. J. Syst. Sci., vol. 27, no. 2, pp. 255–260, Feb. 1996. doi: 10.1080/00207729608929211

[42] 
F. Q. Gu and Y. M. Cheung, “Selforganizing mapbased weight design for decompositionbased manyobjective evolutionary algorithm,” IEEE Trans. Evolut. Comput., vol. 22, no. 2, pp. 211–225, Apr. 2018. doi: 10.1109/TEVC.2017.2695579

[43] 
H. L. Liu, L. Chen, Q. F. Zhang, and K. Deb, “Adaptively allocating search effort in challenging manyobjective optimization problems,” IEEE Trans. Evolut. Comput., vol. 22, no. 3, pp. 433–448, Jan. 2018. doi: 10.1109/TEVC.2017.2725902

[44] 
L. L. Zhen, M. Q. Li, R. Cheng, D. Z. Peng, and X. Yao, Multiobjective test problems with degenerate Pareto fronts. arXiv preprint arXiv: 1806.02706, 2018.

[45] 
H. Xu, W. H. Zeng, D. F. Zhang, and X. X. Zeng, “MOEA/HD: A multiobjective evolutionary algorithm based on hierarchical decomposition,” IEEE Trans. Cybernet., vol. 49, no. 2, pp. 517–526, Feb. 2019. doi: 10.1109/TCYB.2017.2779450

[46] 
R. Wang, Q. F. Zhang, and T. Zhang, “Decompositionbased algorithms using Pareto adaptive scalarizing methods,” IEEE Trans. Evolut. Comput., vol. 20, no. 6, pp. 821–837, Dec. 2016. doi: 10.1109/TEVC.2016.2521175

[47] 
Q. F. Zhang, A. M. Zhou, S. Z. Zhao, P. N. Suganthan, W. D. Liu, and S. Tiwari, “Multiobjective optimization test instances for the CEC 2009 special session and competition, ” Technical Report CES–487, 2008.

[48] 
F. Q. Gu and H. L. Liu, “A novel weight design in multiobjective evolutionary algorithm, ” in Proc. Int. Conf. Computational Intelligence and Security, Nanning, China, 2010, pp. 137–141.

[49] 
F. Q. Gu, H. L. Liu, and K. C. Tan, “A multiobjective evolutionary algorithm using dynamic weight design method,” Int. J. Innovative Computing,Information and Control, vol. 8, no. 5, pp. 3677–3688, May 2012.

[50] 
H. L. Liu, F. Q. Gu, and Y. M. Cheung, “TMOEA/D: MOEA/D with objective transform in multiobjective problems, ” in Proc. Int. Conf. Information Science and Management Engineering, Xi’an, China, 2010, pp. 282–285.

[51] 
C. K. Chi and S. Y. Yue, “A multiobjective evolutionary algorithm that diversifies population by its density,” IEEE Trans. Evolut. Comput., vol. 16, no. 2, pp. 149–172, Apr. 2012. doi: 10.1109/TEVC.2010.2098411

[52] 
H. L. Liu, F. Q. Gu, and Q. F. Zhang, “Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems,” IEEE Trans. Evolut. Comput., vol. 18, no. 3, pp. 450–455, Jun. 2014. doi: 10.1109/TEVC.2013.2281533

[53] 
K. Deb, A. Pratap, and T. Meyarivan, “Constrained test problems for multiobjective evolutionary optimization, ” in Proc. Int. Conf. Evolutionary Multicriterion Optimization. Berlin, Heidelberg: Springer, 2001, pp. 284–298.

[54] 
S. Y. Jiang and S. X. Yang, “An improved multiobjective optimization evolutionary algorithm based on decomposition for complex Pareto fronts,” IEEE Trans. Cybernet., vol. 46, no. 2, pp. 421–437, Feb. 2016. doi: 10.1109/TCYB.2015.2403131

[55] 
D. A. Van Veldhuizen, “Multiobjective evolutionary algorithms: Classifications, analyses, and new innovations, ” Ph.D. dissertation, Air Force Institute of Technology, ENC Wright Patterson AFB, OH, United States, 1999.

[56] 
E. Zitzler, K. Deb, and L. Thiele, “Comparison of multiobjective evolutionary algorithms: Empirical results,” Evolut. Comput., vol. 8, no. 2, pp. 173–195, Feb. 2000. doi: 10.1162/106365600568202

[57] 
Y. Jin, “Effectiveness of weighted aggregation of objectivesfor evolutionary multiobjective optimization: Methods, analysis and applications,” 2002, [Online]. Available: http://www.softcomputing.de/edwa2002.pdf.

[58] 
G. Yu, T. Y. Chai, and X. C. Luo, “Multiobjective production planning optimization using hybrid evolutionary algorithms for mineral processing,” IEEE Trans. Evolut. Comput., vol. 15, no. 4, pp. 487–514, Aug. 2011. doi: 10.1109/TEVC.2010.2073472

[59] 
H. Li and D. LandaSilva, “An adaptive evolutionary multiobjective approach based on simulated annealing,” Evolut. Comput., vol. 19, no. 4, pp. 561–595, Nov. 2011. doi: 10.1162/EVCO_a_00038

[60] 
Q. Xu, Z. Q. Xu, and T. Ma, “A survey of multiobjective evolutionary algorithms based on decomposition: Variants, challenges and future directions,” IEEE Access, vol. 8, pp. 41588–41614, Feb. 2020. doi: 10.1109/ACCESS.2020.2973670

[61] 
M. Q. Li, S. X. Yang, and X. H. Liu, “Pareto or nonPareto: Bicriterion evolution in multiobjective optimization,” IEEE Trans. Evolut. Comput., vol. 20, no. 5, pp. 645–665, Oct. 2016. doi: 10.1109/TEVC.2015.2504730

[62] 
H. Li, J. D. Deng, Q. F. Zhang, and J. Y. Sun, “Adaptive epsilon dominance in decompositionbased multiobjective evolutionary algorithm,” Swarm Evolut. Comput., vol. 45, pp. 52–67, Mar. 2019. doi: 10.1016/j.swevo.2018.12.007

[63] 
C. Liu, Q. Zhao, B. Yan, S. Elsayed, T. Ray, and R. Sarker, “Adaptive sortingbased evolutionary algorithm for manyobjective optimization,” IEEE Trans. Evolut. Comput., vol. 23, no. 2, pp. 247–257, Apr. 2019. doi: 10.1109/TEVC.2018.2848254

[64] 
Y. R. Zhou, Y. Xiang, Z. F. Chen, J. He, and J. H. Wang, “A scalar projection and anglebased evolutionary algorithm for manyobjective optimization problems,” IEEE Trans. Cybernet., vol. 49, no. 6, pp. 2073–2084, Jun. 2019. doi: 10.1109/TCYB.2018.2819360

[65] 
M. Y. Wu, K. Li, S. Kwong, and Q. F. Zhang, “Evolutionary manyobjective optimization based on adversarial decomposition,” IEEE Trans. Cybernet., vol. 50, no. 2, pp. 753–764, Feb. 2020. doi: 10.1109/TCYB.2018.2872803

[66] 
K. S. Bhattacharjee, H. K. Singh, T. Ray, and Q. F. Zhang, “Decomposition based evolutionary algorithm with a dual set of reference vectors, ” in Proc. IEEE Congr. Evolutionary Computation, San Sebastian, Spain, 2017, pp. 105–112.

[67] 
R. Cheng, Y. Jin, and K. Narukawa, “Adaptive reference vector generation for inverse model based evolutionary multiobjective optimization with degenerate and disconnected Pareto fronts, ” in Proc. Int. Conf. Evolutionary MultiCriterion Optimization. Guimarães, Portugal: Springer, 2015, pp. 127–140.

[68] 
X. Y. He, Y. R. Zhou, and Z. F. Chen, “An evolution pathbased reproduction operator for manyobjective optimization,” IEEE Trans. Evolut. Comput., vol. 23, no. 1, pp. 29–43, Feb. 2019. doi: 10.1109/TEVC.2017.2785224

[69] 
Y. H. Zhang, Y. J. Gong, T. L. Gu, H. Q. Yuan, W. Zhang, S. Kwong, and J. Zhang, “DECAL: Decompositionbased coevolutionary algorithm for manyobjective optimization,” IEEE Trans. Cybernet., vol. 49, no. 1, pp. 27–41, Jan. 2019. doi: 10.1109/TCYB.2017.2762701

[70] 
S. Y. Jiang, S. X. Yang, Y. Wang, and X. B. Liu, “Scalarizing functions in decompositionbased multiobjective evolutionary algorithms,” IEEE Trans. Evolut. Comput., vol. 22, no. 2, pp. 296–313, Apr. 2018. doi: 10.1109/TEVC.2017.2707980

[71] 
R. Wang, Z. B. Zhou, H. Ishibuchi, T. J. Liao, and T. Zhang, “Localized weighted sum method for manyobjective optimization,” IEEE Trans. Evolut. Comput., vol. 22, no. 1, pp. 3–18, Feb. 2018. doi: 10.1109/TEVC.2016.2611642

[72] 
R. Wang, T. Zhang, and B. Guo, “An enhanced MOEA/D using uniform directions and a preorganization procedure, ” in Proc. IEEE Congr. Evolutionary Computation, Cancun, Mexico, 2013, pp. 2390–2397.

[73] 
S. W. Jiang, L. Feng, D. Z. Yang, C. K. Heng, Y. S. Ong, A. N. Zhang, P. S. Tan, and Z. H. Cai, “Towards adaptive weight vectors for multiobjective evolutionary algorithm based on decomposition, ” in Proc. IEEE Congr. Evolutionary Computation, Vancouver, BC, Canada, 2016, pp. 500–507.

[74] 
M. Q. Li and X. Yao, “What weights work for you? Adapting weights for any Pareto front shape in decompositionbased evolutionary multiobjective optimisation” Evolut. Comput., vol. 28, no. 2, pp. 227–253, Jun. 2020. doi: 10.1162/evco_a_00269

[75] 
L. R. C. de Farias, P. H. M. Braga, H. F. Bassani, and A. F. Araújo, “MOEA/D with uniformly randomly adaptive weights, ” in Proc. GECCO’18: Genetic and Evolutionary Computation Conf., Kyoto, Japan, 2018, pp. 641–648.

[76] 
Y. Y. Lin, H. Liu, and Q. Y. Jiang, “Dynamic reference vectors and biased crossover use for inverse model based evolutionary multiobjective optimization with irregular Pareto fronts,” Appl. Intell., vol. 48, no. 9, pp. 3116–3142, Sep. 2018. doi: 10.1007/s1048901711337

[77] 
C. Zhou, G. M. Dai, C. J. Zhang, X. P. Li, and K. Ma, “Entropy based evolutionary algorithm with adaptive reference points for manyobjective optimization problems,” Inform. Sci., vol. 465, pp. 232–247, Oct. 2018. doi: 10.1016/j.ins.2018.07.012

[78] 
A. R. Sánchez, A. Ponsich, and A. L. Jaimes, “Generation techniques and a novel online adaptation strategy for weight vectors within decompositionbased MOEAs, ” in Proc. Genetic and Evolutionary Computation Conf. Companion, Prague, Czech Republic, 2019, pp. 229–230.

[79] 
Y. P. Liu, D. W. Gong, J. Sun, and Y. Jin, “A manyobjective evolutionary algorithm using a onebyone selection strategy,” IEEE Trans. Cybernet., vol. 47, no. 9, pp. 2689–2702, Sep. 2017. doi: 10.1109/TCYB.2016.2638902

[80] 
X. Yi, Y. R. Zhou, M. Q. Li, and Z. F. Chen, “A vector anglebased evolutionary algorithm for unconstrained manyobjective optimization,” IEEE Trans. Evolut. Comput., vol. 21, no. 1, pp. 131–152, Feb. 2017. doi: 10.1109/TEVC.2016.2587808

[81] 
Y. C. Hua, Y. Jin, K. R. Hao, and Y. Cao, “Generating multiple reference vectors for a class of manyobjective optimization problems with degenerate Pareto fronts,” Comp. Intell. Syst., vol. 6, pp. 275–285, Jul. 2020. doi: 10.1007/s40747020001365

[82] 
S. W. Jiang, J. Zhang, and Y. S. Ong, “Asymmetric Paretoadaptive scheme for multiobjective optimization, ” in Proc. Australasian Joint Conf. Artificial Intelligence. Berlin, Heidelberg: Springer, 2011, pp. 351–360.

[83] 
M. Asafuddoula, H. K. Singh, and T. Ray, “An enhanced decompositionbased evolutionary algorithm with adaptive reference vectors,” IEEE Trans. Cybernet., vol. 48, no. 8, pp. 2321–2334, Aug. 2018. doi: 10.1109/TCYB.2017.2737519

[84] 
Q. Q. Liu, Y. Jin, M. Heiderich, and T. Rodemann, “Adaptation of reference vectors for evolutionary manyobjective optimization of problems with irregular Pareto fronts, ” in Proc. IEEE Congr. Evolutionary Computation, Wellington, New Zealand, 2019, pp. 1726–1733.

[85] 
I. Giagkiozis, R. C. Purshouse, and P. J. Fleming, “Towards understanding the cost of adaptation in decompositionbased optimization algorithms, ” in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, Manchester, UK, 2013, pp. 615–620.

[86] 
S. Liu, Q. Lin, K.C. Wong, C. C. A. Coello, J. Li, Z. Ming, and J. Zhang, “A selfguided reference vector strategy for manyobjective optimization,” IEEE Trans. Cybernetics, pp. 1–15, 2020. DOI: 10.1109/TCYB.2020.2971638

[87] 
C. Y. Zhu, X. Y. Cai, Z. Fan, and M. Sulaman, “A twophase manyobjective evolutionary algorithm with penalty based adjustment for reference lines, ” in Proc. IEEE Congr. Evolutionary Computation, Vancouver, BC, Canada, 2016, pp. 2161–2168.

[88] 
A. Camacho, G. Toscano, R. Landa, and H. Ishibuchi, “Indicatorbased weight adaptation for solving manyobjective optimization problems, ” in Proc. Int. Conf. Evolutionary MultiCriterion Optimization. East Lansing, MI, USA: Springer, 2019, pp. 216–228.

[89] 
Q. S. Zhang, W. Zhu, B. Liao, X. T. Chen, and L. J. Cai, “A modified PBI approach for multiobjective optimization with complex Pareto fronts,” Swarm Evolut. Comput., vol. 40, pp. 216–237, Jun. 2018. doi: 10.1016/j.swevo.2018.02.001

[90] 
Y. P. Liu, H. Ishibuchi, N. Masuyama, and Y. Nojima, “Adapting reference vectors and scalarizing functions by growing neural gas to handle irregular Pareto fronts,” IEEE Trans. Evolut. Comput., vol. 24, no. 3, pp. 439–453, Jun. 2020.

[91] 
Q. Q. Liu, Y. Jin, M. Heiderich, T. Rodemann, and G. Yu, “An adaptive reference vectorguided evolutionary algorithm using growing neural gas for manyobjective optimization of irregular problems,” IEEE Trans. Cybernet., pp. 1–14, 2020. DOI: 10.1109/TCYB.2020.3020630

[92] 
K. Harada, S. Hiwa, and T. Hiroyasu, “Adaptive weight vector assignment method for MOEA/D, ” in Proc. IEEE Symp. Series on Computational Intelligence, Honolulu, HI, USA, 2017, pp. 1–9.

[93] 
M. Y. Wu, S. Kwong, Y. H. Jia, K. Li, and Q. F. Zhang, “Adaptive weights generation for decompositionbased multiobjective optimization using Gaussian process regression, ” in Proc. Genetic and Evolutionary Computation Conf., Berlin, Germany, 2017, pp. 641–648.

[94] 
M. Y. Wu, K. Li, S. Kwong, Q. F. Zhang, and J. Zhang, “Learning to decompose: A paradigm for decompositionbased multiobjective optimization,” IEEE Trans. Evolut. Comput., vol. 23, no. 3, pp. 376–390, Jun. 2019. doi: 10.1109/TEVC.2018.2865931

[95] 
L. J. He, Y. Nan, K. Shang, and H. Ishibuchi, “A study of the naïve objective space normalization method in MOEA/D, ” in Proc. IEEE Symp. Series on Computational Intelligence, Xiamen, China, 2019, pp. 1834–1840.

[96] 
Y. Tian, H. D. Wang, X. Y. Zhang, and Y. Jin, “Effectiveness and efficiency of nondominated sorting for evolutionary multi and manyobjective optimization,” Comp. Intell. Syst., vol. 3, no. 4, pp. 247–263, Dec. 2017. doi: 10.1007/s4074701700575

[97] 
Y. Tian, R. Cheng, X. Y. Zhang, F. Cheng, and Y. Jin, “An indicatorbased multiobjective evolutionary algorithm with reference point adaptation for better versatility,” IEEE Trans. Evolut. Comput., vol. 22, no. 4, pp. 609–622, Aug. 2018. doi: 10.1109/TEVC.2017.2749619

[98] 
S. Y. Jiang, H. R. Li, J. L. Guo, M. J. Zhong, S. X. Yang, M. Kaiser, and N. Krasnogor, “AREA: An adaptive referenceset based evolutionary algorithm for multiobjective optimisation,” Inform. Sci., vol. 515, pp. 365–387, Apr. 2020. doi: 10.1016/j.ins.2019.12.011

[99] 
Y. P. Liu, D. W. Gong, X. Y. Sun, and Y. Zhang, “Manyobjective evolutionary optimization based on reference points,” Appl. Soft Comput., vol. 50, pp. 344–355, Jan. 2017. doi: 10.1016/j.asoc.2016.11.009

[100] 
W. Q. Feng and D. W. Gong, “Multiobjective evolutionary optimization with objective space partition based on online perception of Pareto front,” Acta Autom. Sinica, vol. 46, no. 8, pp. 1628–1643, Sep. 2020.

[101] 
H. Zhang, S. M. Song, A. M. Zhou, and X. Z. Gao, “A clustering based multiobjective evolutionary algorithm, ” in Proc. IEEE Congr. Evolutionary Computation, Beijing, China, 2014, pp. 723–730.

[102] 
S. S. Das, M. M. Islam, and N. A. Arafat, “Evolutionary algorithm using adaptive fuzzy dominance and reference point for manyobjective optimization,” Swarm Evolut. Comput., vol. 44, pp. 1092–1107, Feb. 2019. doi: 10.1016/j.swevo.2018.11.003

[103] 
R. Denysiuk, L. Costa, and I. E. Santo, “Clusteringbased selection for evolutionary manyobjective optimization, ” in Proc. Int. Conf. Parallel Problem Solving from Nature. Ljubljana, Slovenia: Springer, 2014, pp. 538–547.

[104] 
C. He, L. H. Li, Y. Tian, X. Y. Zhang, R. Cheng, Y. Jin, and X. Yao, “Accelerating largescale multiobjective optimization via problem reformulation,” IEEE Trans. Evolut. Comput., vol. 23, no. 6, pp. 949–961, 2019. doi: 10.1109/TEVC.2019.2896002

[105] 
Z. Yang, Y. Jin, and K. R. Hao, “A bioinspired selflearning coevolutionary dynamic multiobjective optimization algorithm for internet of things services,” IEEE Trans. Evolut. Comput., vol. 23, no. 4, pp. 675–688, Aug. 2019. doi: 10.1109/TEVC.2018.2880458

[106] 
Y. Jin, H. D. Wang, T. Chugh, D. Guo, and K. Miettinen, “Datadriven evolutionary optimization: An overview and case studies,” IEEE Trans. Evolut. Comput., vol. 23, no. 3, pp. 442–458, Jun. 2019. doi: 10.1109/TEVC.2018.2869001

[107] 
T. Chugh, K. Sindhya, J. Hakanen, and K. Miettinen, “A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms,” Soft Comput., vol. 23, no. 9, pp. 3137–3166, May 2019. doi: 10.1007/s0050001729650

[108] 
C. He, S. H. Huang, R. Cheng, K. C. Tan, and Y. Jin, “Evolutionary multiobjective optimization driven by generative adversarial networks (GANs),” IEEE Trans. Cybernet., pp. 1–14, 2020. DOI: 10.1109/TCYB.2020.2985081

[109] 
X. Y. Sun, D. W. Gong, Y. Jin, and S. S. Chen, “A new surrogateassisted interactive genetic algorithm with weighted semisupervised learning,” IEEE Trans. Cybernet., vol. 43, no. 2, pp. 685–698, Apr. 2013. doi: 10.1109/TSMCB.2012.2214382

[110] 
X. J. Zhu and A. B. Goldberg, “Introduction to semisupervised learning,” Synthesis Lectures on Artificial Intelligence and Machine Learning, vol. 3, no. 1, pp. 1–130, 2009.

[111] 
Q. Yang, Y. Zhang, W. Y. Dai, and S. J. Pan, Transfer Learning. Cambridge: Cambridge University Press, 2020.

JAS20200976supp.pdf 