Ranking the Pareto frontiers of multi-objective optimization problems by a new quasi-Gaussian evaluation measure

[1] C. Audet, J. Bigeon, D. Cartier, S.L. Digabel, L. Salomon, Performance indicators in multiobjective
optimization, Eur. J. Oper. Res. 292 (2020) 397–422.
[2] Y. Cheng, X. Luo, P. Wang, Z. Yang, J. Huang, J. Gu, W. Zhao, Multi-objective optimization of
thermal-hydraulic performance in a microchannel heat sink with offset ribs using the fuzzy grey
approach, Appl. Therm. Eng. 201 (2022) 117748.
[3] S. Cheng, Y. Shi, Q. Qin, On the performance metrics of multi objective optimization, in:
International-Conference in Swarm Intelligence (2012) 504–512.
[4] Y. Collette, P. Siarry, Optimization multi-objective: Algorithms, Editions Eyrolles, 2011.
[5] I. Das, J.E. Dennis, Normal-boundary intersection: A new method for generating Pareto optimal
points in multicriteria optimization problems, SIAM J. Optim. 8 (1998) 631–657.
[6] K. Deb, L. Thiele, M. Laumanns, E. Zitzler, Scalable multi-objective optimization test problems, In
Proceedings of the 2002 Congress on Evolutionary Computation. 1 (2002) 825–830.
[7] M. Farina, P. Amato, A fuzzy definition of ”optimality” for many-criteria optimization problems,
IEEE T SYST MAN CY A. 34 (2004) 315–326.
[8] K. Guo, L. Zhang, Adaptive multi-objective optimization for emergency evacuation at metro sta-
tions, Reliab. Eng. Syst. Saf. 219 (2022) 108210.
[9] Z. He, G.G. Yen, J. Zhang, Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algo-
rithms,IEEE Trans Evol Comput. 18 (2014) 269–285.
[10] Z. Hou, S. Yang, J. Zou, J. Zheng, G. Yu, G. Ruan, A Performance Indicator for Reference-Point-
Based Multiobjective Evolutionary Optimization, IEEE Symposium Series on Computational Intel-
ligence (SSCI) (2018) 1571–1578. doi: 10.1109/SSCI.2018.8628834
[11] E.H. Houssein, M.A. Mahdy, D. Shebl, A. Manzoor, R. Sarkar, W.M. Mohamed, An efficient slime
mould algorithm for solving multi-objective optimization problems, Expert Syst. Appl. 187 (2022)
115870.
[12] S. Jiang, Y. Ong, J. Zhang, L. Feng, Consistencies and contradictions of performance metrics in
multi-objective optimization, IEEE Trans Cybern. 44 (2014) 2391–2404.

[13] J. Knowles, D. Corne, On metrics for comparing non-dominated sets, IEEE, In Proceedings of the
2002 Congress on Evolutionary Computation. 1 (2002) 711–716.
[14] M. Mattia, A. Nicolini, Multi-Objective Optimization Models to Design a Responsive Built Envi-
ronment: A Synthetic Review, Energies. 15 (2022) 486.
[15] A. Messac, A. Ismail-Yahaya, C. Mattson, The normalized normal constraint method for generating
the Pareto frontier, Struct. Multidisc. Optimal. 25 (2003) 86–98.
[16] K. Miettinen, Some Methods for Nonlinear Multi-objective Optimization, International conference
on evolutionary multi-criterion optimization. Springer, Berlin, Heidelberg, (2001) 1–20.
[17] K. Miettinen, Nonlinear multi objective optimization, Springer Science & Business Media, 2012.
[18] M. Nasir, A.K. Mondal, S. Senguitpta, S. Das, A. Abraham, An improved Multi-objective Evolu-
tionary Algorithm based on decomposition with dominance, IEEE Congress of Evolutionary Com-
putation (CEC), New Orleans, LA (2011) 765–772.
[19] T. Okabe, Y. Jin, B. Sendhoff, A critical survey of performance indices for multi-objective opti-
mization, IEEE, In The 2003 Congress on Evolutionary Computation, 2 (2003) 878–885.
[20] N. Riquelme, C. Von Lucken, B. Baran, Performance metrics in multi-objective optimization, In
2015 Latin American Computing Conference (2015) 1-11. doi: 10.1109/CLEI.2015.7360024.
[21] S. Sharma, V. Chahar, A Comprehensive Review on Multi-objective Optimization Techniques: Past,
Present and Future, Arch. Comput. Methods Eng. 29 (2022) 5605–5633.
[22] H.R. Yousefzadeh, A. Karrabi, A. Heydari, A new two-phase approach to the portfolio optimization
problem based on the prediction of stock price trends, Adv. math. finanace appl. 7 (2021) 849–865.
[23] E. Zahiri, A. Heydari, H.R. Yousefzadeh, A new approach based on Gaussian degree of closeness
for solving multi-objective optimization problem, Journal of Decisions and Operations Research
(2022). doi: 10.22105/dmor.2022.310311.1503.
[24] Q. Zhang, H. Li, MOEA/D: A Multi objective Evolutionary Algorithm Based on Decomposition,
IEEE Trans Evol Comput. 11 (2007) 712–731.
[25] E. Zitzler, K. Deb, L. Thiele, Comparison of multi-objective evolutionary algorithms: Empirical
results, Evol. Comput. 8 (2000) 173–195.
[26] E. Zitzler, L. Thiele, M. Laumanns, C.M. Fonseca, V.G. Da Fonseca, Performance assessment of
multi-objective optimizers: An analysis and review, IEEE Trans Evol Comput. 7 (2003) 117–132.
[27] E. Zitzler, J. Knowles, L. Thiele, Quality assessment of pareto set approximations, Multi-objective
Optimization. (2008) 373–404.