Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]

Published: 01 November 2017 Publication History

Abstract

Over the last three decades, a large number of evolutionary algorithms have been developed for solving multi-objective optimization problems. However, there lacks an upto-date and comprehensive software platform for researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve their real-world problems. The demand of such a common tool becomes even more urgent, when the source code of many proposed algorithms has not been made publicly available. To address these issues, we have developed a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes more than 50 multiobjective evolutionary algorithms and more than 100 multi-objective test problems, along with several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files. More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative experiments, embedding new algorithms, creating new test problems, and developing performance indicators. Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.

References

[1]
A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, and C. Coello, “A survey of multiobjective evolutionary algorithms for data mining: Part I,” IEEE Trans. Evol. Comput., vol. 18, no. 1, pp. 4–19, 2014.
[2]
J. Handl and J. Knowles, “An evolutionary approach to multiobjective clustering,” IEEE Trans. Evol. Comput., vol. 11, no. 1, pp. 56–76, 2007.
[3]
B. Lazzerini, F. Marcelloni, and M. Vecchio, “A multi-objective evolutionary approach to image quality/compression trade-off in JPEG baseline algorithm,” Appl. Soft Computing, vol. 10, no. 2, pp. 548–561, 2010.
[4]
F. Pettersson, N. Chakraborti, and H. Saxén, “A genetic algorithms based multi-objective neural net applied to noisy blast furnace data,” Appl. Soft Computing, vol. 7, no. 1, pp. 387–397, 2007.
[5]
S.H. Yeung, K.F. Man, K.M. Luk, and C.H. Chan, “A trapeizform U-slot folded patch feed antenna design optimized with jumping genes evolutionary algorithm,” IEEE Trans. Antennas Propagat., vol. 56, no. 2, pp. 571–577, 2008.
[6]
A. Ponsich, A.L. Jaimes, and C.A.C. Coello, “A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications,” IEEE Trans. Evol. Comput., vol. 17, no. 3, pp. 321–344, 2013.
[7]
J.G. Herrero, A. Berlanga, and J.M.M. López, “Effective evolutionary algorithms for many-specifications attainment: Application to air traffic control tracking filters,” IEEE Trans. Evol. Comput., vol. 13, no. 1, pp. 151–168, 2009.
[8]
H. Ishibuchi and T. Murata, “Multiobjective genetic local search algorithm and its application to flowshop scheduling,” IEEE Trans. Systems, Man, Cybernet. C, vol. 28, no. 3, pp. 392–403, 1998.
[9]
J.D. Schaffer, “Multiple objective optimization with vector evaluated genetic algorithms,” in Proc. 1st Int. Conf. Genetic Algorithms, 1985, pp. 93–100.
[10]
C.M. Fonseca and P.J. Fleming, “Genetic algorithms for multiobjective optimization: Formulation discussion and generalization,” in Proc. 5th Int. Conf. Genetic Algorithms, 1993, vol. 93, pp. 416–423.
[11]
N. Srinivas and K. Deb, “Multiobjective optimization using nondominated sorting in genetic algorithms,” Evol. Comput., vol. 2, no. 3, pp. 221–248, 1995.
[12]
J. Horn, N. Nafpliotis, and D.E. Goldberg, “A niched Pareto genetic algorithm for multiobjective optimization,” in Proc. 1994 IEEE Congr. Evolutionary Computation, 1994, pp. 82–87.
[13]
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multi-objective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182–197, 2002.
[14]
E. Zitzler, M. Laumanns, and L. Thiele, “SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization,” in Proc. 5th Conf. Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, 2001, pp. 95–100.
[15]
D.W. Corne, N.R. Jerram, J.D. Knowles, and M.J. Oates, “PESA-II: Region-based selection in evolutionary multi-objective optimization,” in Proc. 2001 Conf. Genetic and Evolutionary Computation, 2001, pp. 283–290.
[16]
T. Murata, H. Ishibuchi, and M. Gen, “Specification of genetic search directions in cellular multiobjective genetic algorithms,” in Proc. 1st Int. Conf. Evolutionary Multi-Criterion Optimization, 2001, pp. 82–95.
[17]
Q. Zhang and H. Li, “MOEA/D: A multi-objective evolutionary algorithm based on decomposition,” IEEE Trans. Evol. Comput., vol. 11, no. 6, pp. 712–731, 2007.
[18]
H. Li and Q. Zhang, “Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II,” IEEE Trans. Evol. Comput., vol. 13, no. 2, pp. 284–302, 2009.
[19]
H.-L. Liu, F. Gu, and Q. Zhang, “Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems,” IEEE Trans. Evol. Computat., vol. 18, no. 3, pp. 450–455, 2014.
[20]
Y. Yuan, H. Xu, B. Wang, B. Zhang, and X. Yao, “Balancing convergence and diversity in decomposition-based many-objective optimizers,” IEEE Trans. Evol. Comput., vol. 20, no. 2, pp. 180–198, 2016.
[21]
H. Ishibuchi, Y. Setoguchi, H. Masuda, and Y. Nojima, “Performance of decomposition-based many-objective algorithms strongly depends on Pareto front shapes,” IEEE Trans. Evol. Comput., vol. 21, no. 2, pp. 169–190, 2017.
[22]
A. Zhou, B.-Y. Qu, H. Li, S.-Z. Zhao, P.N. Suganthan, and Q. Zhang, “Multiobjective evolutionary algorithms: A survey of the state of the art,” Swarm Evol. Comput., vol. 1, no. 1, pp. 32–49, 2011.
[23]
J.J. Durillo and A.J. Nebro, “jMetal: A java framework for multi-objective optimization,” Adv. Eng. Softw., vol. 42, no. 10, pp. 760–771, 2011.
[24]
M. Lukasiewycz, M. Glaβ, F. Reimann, and J. Teich, “Opt4j: A modular framework for meta-heuristic optimization,” in Proc. 13th Annu. Conf. Genetic and Evolutionary Computation, 2011, pp. 1723–1730.
[25]
R. Shen, J. Zheng, and M. Li, “A hybrid development platform for evolutionary multi-objective optimization,” in Proc. IEEE Congr. Evolutionary Computation, 2015, pp. 1885–1892.
[26]
A. Liefooghe, M. Basseur, L. Jourdan, and E.-G. Talbi, “ParadisEO-MOEO: A framework for evolutionary multi-objective optimization,” in Proc. Int. Conf. Evolutionary Multi-Criterion Optimization, 2007, pp. 386–400.
[27]
S. Bleuler, M. Laumanns, L. Thiele, and E. Zitzler, “PISA-a platform and programming language independent interface for search algorithms,” in Proc. Int. Conf. Evolutionary Multi-Criterion Optimization, 2003, pp. 494–508.
[28]
C. Igel, V. Heidrich-Meisner, and T. Glasmachers, “Shark,” J. Mach. Learn. Res., no. 9, pp. 993–996, 2008.
[29]
D. Izzo, “PyGMO and PyKEP: Open source tools for massively parallel optimization in astrodynamics (the case of interplanetary trajectory optimization),” in Proc. 5th Int. Conf. Astrodynamics Tools and Techniques, 2012.
[30]
L.C. Bezerra, M. López-Ibánez, and T. Stützle, “Automatic component-wise design of multiobjective evolutionary algorithms,” IEEE Trans. Evol. Comput., vol. 20, no. 3, pp. 403–417, 2016.
[31]
J. Humeau, A. Liefooghe, E.-G. Talbi, and S. Verel, “ParadisEO-MO: From fitness landscape analysis to efficient local search algorithms,” J. Heuristics, vol. 19, no. 6, pp. 881–915, 2013.
[32]
K. Deb, M. Mohan, and S. Mishra, “Towards a quick computation of well-spread Pareto-optimal solutions,” in Proc. 2003 Int. Conf. Evolutionary Multi-Criterion Optimization, 2003, pp. 222–236.
[33]
E. Zitzler and S. Künzli, “Indicator-based selection in multiobjective search,” in Proc. 8th Int. Conf. Parallel Problem Solving from Nature, 2004, pp. 832–842.
[34]
N. Beume, B. Naujoks, and M. Emmerich, “SMS-EMOA: Multiobjective selection based on dominated hypervolume,” Eur. J. Oper. Res., vol. 181, no. 3, pp. 1653–1669, 2007.
[35]
E.J. Hughes, “MSOPS-II: A general-purpose many-objective optimiser,” in Proc. 2007 IEEE Congr. Evolutionary Computation. 2007, pp. 3944–3951.
[36]
L.-Y. Tseng and C. Chen, “Multiple trajectory search for unconstrained/constrained multi-objective optimization,” in Proc. 2009 IEEE Congr. Evolutionary Computation, 2009, pp. 1951–1958.
[37]
M. Wagner and F. Neumann, “A fast approximation-guided evolutionary multi-objective algorithm,” in Proc. 15th Annu. Conf. Genetic and Evolutionary Computation, 2013, pp. 687–694.
[38]
B. Chen, W. Zeng, Y. Lin, and D. Zhang, “A new local search-based multiobjective optimization algorithm,” IEEE Trans. Evol. Comput., vol. 19, no. 1, pp. 50–73, 2015.
[39]
M. Li, S. Yang, and X. Liu, “Pareto or non-Pareto: Bi-criterion evolution in multi-objective optimization,” IEEE Trans. Evol. Comput., vol. 20, no. 5, pp. 645–665, 2015.
[40]
Y. Tian, X. Zhang, R. Cheng, and Y. Jin, “A multiobjective evolutionary algorithm based on an enhanced inverted generational distance metric,” in Proc. IEEE Congr. Evolutionary Computation, 2016, pp. 5222–5229.
[41]
J. Bader and E. Zitzler, “HypE: An algorithm for fast hypervolume-based many-objective optimization,” Evol. Comput., vol. 19, no. 1, pp. 45–76, 2011.
[42]
R. Wang, R.C. Purshouse, and P.J. Fleming, “Preference-inspired coevolutionary algorithms for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 17, no. 4, pp. 474–494, 2013.
[43]
S. Yang, M. Li, X. Liu, and J. Zheng, “A grid-based evolutionary algorithm for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 17, no. 5, pp. 721–736, 2013.
[44]
K. Deb and H. Jain, “An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part I: Solving problems with box constraints,” IEEE Trans. Evol. Comput., vol. 18, no. 4, pp. 577–601, 2014.
[45]
H. Jain and K. Deb, “An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach,” IEEE Trans. Evol. Comput., vol. 18, no. 4, pp. 602–622, 2014.
[46]
M. Li, S. Yang, and X. Liu, “Shift-based density estimation for pareto-based algorithms in many-objective optimization,” IEEE Trans. Evol. Comput., vol. 18, no. 3, pp. 348–365, 2014.
[47]
M. Li, S. Yang, and X. Liu, “Bi-goal evolution for many-objective optimization problems,” Artif. Intell., vol. 228, pp. 45–65, 2015.
[48]
M. Asafuddoula, T. Ray, and R. Sarker, “A decomposition based evolutionary algorithm for many objective optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 3, pp. 445–460, 2015.
[49]
X. Zhang, Y. Tian, and Y. Jin, “A knee point driven evolutionary algorithm for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 6, pp. 761–776, 2015.
[50]
J. Cheng, G. Yen, and G. Zhang, “A many-objective evolutionary algorithm with enhanced mating and environmental selections,” IEEE Trans. Evol. Comput., vol. 19, no. 4, pp. 592–605, 2015.
[51]
K. Li, K. Deb, Q. Zhang, and S. Kwong, “Combining dominance and decomposition in evolutionary many-objective optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 5, pp. 694–716, 2015.
[52]
R. Hernández Gómez and C.A. Coello, “Improved metaheuristic based on the R2 indicator for many-objective optimization,” in Proc. Genetic and Evolutionary Computation Conf., 2015, pp. 679–686.
[53]
H. Wang, L. Jiao, and X. Yao, “Two_Arch2: An improved two-archive algorithm for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 4, pp. 524–541, 2015.
[54]
Z. He and G.G. Yen, “Many-objective evolutionary algorithm: Objective space reduction and diversity improvement,” IEEE Trans. Evol. Comput., vol. 20, no. 1, pp. 145–160, 2016.
[55]
Y. Liu, D. Gong, X. Sun, and Z. Yong, “Many-objective evolutionary optimization based on reference points,” Appl. Soft Comput., vol. 50, pp. 344–355, 2017.
[56]
R. Cheng, Y. Jin, M. Olhofer, and B. Sendhoff, “A reference vector guided evolutionary algorithm for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 20, no. 5, pp. 773–791, 2016.
[57]
S. Jiang and S. Yang, “A strength Pareto evolutionary algorithm based on reference direction for multi-objective and many-objective optimization,” IEEE Trans. Evol. Comput., vol. 21, no. 3, pp. 329–346, 2017.
[58]
Y. Yuan, H. Xu, B. Wang, and X. Yao, “A new dominance relation-based evolutionary algorithm for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 20, no. 1, pp. 16–37, 2016.
[59]
X. Ma, F. Liu, Y. Qi, X. Wang, L. Li, L. Jiao, M. Yin, and M. Gong, “A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables,” IEEE Trans. Evol. Comput., vol. 20, no. 2, pp. 275–298, 2016.
[60]
X. Zhang, Y. Tian, R. Cheng, and Y. Jin, “A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization,” IEEE Trans. Evol. Comput., to be published.
[61]
J. Molina, L.V. Santana, A.G. Hernández-Díaz, C.A.C. Coello, and R. Caballero, “G-Dominance: Reference point based dominance for multiobjective metaheuristics,” Eur. J. Oper. Res., vol. 197, no. 2, pp. 685–692, 2009.
[62]
L.B. Said, S. Bechikh, and K. Ghédira, “The r-dominance: A new dominance relation for interactive evolutionary multicriteria decision making,” IEEE Trans. Evol. Comput., vol. 14, no. 5, pp. 801–818, 2010.
[63]
X. Zhang, X. Jiang, and L. Zhang, “A weight vector based multi-objective optimization algorithm with preference,” Acta Electron. Sin., vol. 44, no. 11, pp. 2639–2645, 2016.
[64]
S. Kukkonen and J. Lampinen, “GDE3: The third evolution step of generalized differential evolution,” in Proc. IEEE Congr. Evolutionary Computation, 2005, vol. 1, pp. 443–450.
[65]
C.C. Coello and M.S. Lechuga, “MOPSO: A proposal for multiple objective particle swarm optimization,” in Proc. 2002 IEEE Congr. Evolutionary Computation, 2002, vol. 2, pp. 1051–1056.
[66]
A.J. Nebro, J.J. Durillo, J. Garcia-Nieto, C.C. Coello, F. Luna, and E. Alba, “SMPSO: A new PSO-based metaheuristic for multi-objective optimization,” in Proc. IEEE Symp. Computational Intelligence in Multi-Criteria Decision-Making, 2009, pp. 66–73.
[67]
S. Zapotecas Martínez and C.A. Coello, “A multiobjective particle swarm optimizer based on decomposition,” in Proc. 13th Annu. Conf. Genetic and Evolutionary Computation, 2011, pp. 69–76.
[68]
J.D. Knowles and D.W. Corne, “M-PAES: A memetic algorithm for multiobjective optimization,” in Proc. IEEE Congr. Evolutionary Computation, 2000, pp. 325–332.
[69]
C. Igel, N. Hansen, and S. Roth, “Covariance matrix adaptation for multi-objective optimization,” Evol. Comput., vol. 15, no. 1, pp. 1–28, 2007.
[70]
Q. Zhang, A. Zhou, and Y. Jin, “RM-MEDA: A regularity model-based multiobjective estimation of distribution algorithm,” IEEE Trans. Evol. Comput., vol. 12, no. 1, pp. 41–63, 2008.
[71]
R. Cheng, Y. Jin, K. Narukawa, and B. Sendhoff, “A multiobjective evolutionary algorithm using Gaussian process based inverse modeling,” IEEE Trans. Evol. Comput., vol. 19, no. 6, pp. 838–856, 2015.
[72]
J. Knowles, “ParEGO: A hybrid algorithm with online landscape approximation for expensive multiobjective optimization problems,” IEEE Trans. Evol. Comput., vol. 10, no. 1, pp. 50–66, 2006.
[73]
W. Ponweiser, T. Wagner, D. Biermann, and M. Vincze, “Multiobjective optimization on a limited budget of evaluations using model-assisted S-metric selection,” in Proc. 2008 Int. Conf. Parallel Problem Solving from Nature, 2008, pp. 784–794.
[74]
T. Chugh, Y. Jin, K. Miettinen, J. Hakanen, and K. Sindhya, “A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization,” IEEE Trans. Evol. Comput., to be published.
[75]
E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach,” IEEE Trans. Evol. Comput., vol. 3, no. 4, pp. 257–271, 1999.
[76]
H. Ishibuchi, N. Akedo, and Y. Nojima, “Behavior of multiobjective evolutionary algorithms on many-objective knapsack problems,” IEEE Trans. Evol. Comput., vol. 19, no. 2, pp. 264–283, 2015.
[77]
K.D.E. Zitzler and L. Thiele, “Comparison of multiobjective evolutionary algorithms: Empirical results,” Evol. Comput., vol. 8, no. 2, pp. 173–195, 2000.
[78]
J. Knowles and D. Corne, “Instance generators and test suites for the multiobjective quadratic assignment problem,” in Proc. 2003 Int. Conf. Evolutionary Multi-Criterion Optimization, 2003, pp. 295–310.
[79]
K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable test problems for evolutionary multiobjective optimization,” in Proc. Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, 2005, pp. 105–145.
[80]
S. Huband, P. Hingston, L. Barone, and L. While, “A review of multiobjective test problems and a scalable test problem toolkit,” IEEE Trans. Evol. Comput., vol. 10, no. 5, pp. 477–506, 2006.
[81]
H. Ishibuchi, H. Masuda, and Y. Nojima, “Pareto fronts of many-objective degenerate test problems,” IEEE Trans. Evol. Comput., vol. 20, no. 5, pp. 807–813, 2016.
[82]
Y. Zhang, M. Harman, and S.A. Mansouri, “The multi-objective next release problem,” in Proc. 9th Annu. Conf. Genetic and Evolutionary Computation, 2007, pp. 1129–1137.
[83]
D.W. Corne and J.D. Knowles, “Techniques for highly multiobjective optimisation: Some nondominated points are better than others,” in Proc. 9th Conf Genetic and Evolutionary Computation, 2007, pp. 773–780.
[84]
M. Köppen and K. Yoshida, “Substitute distance assignments in NSGA-II for handling many-objective optimization problems,” in Proc. 2007 Int. Conf. Evolutionary Multi-criterion Optimization, 2007, pp. 727–741.
[85]
Q. Zhang, A. Zhou, S. Zhao, P.N. Suganthan, W. Liu, and S. Tiwari, “Multiobjective optimization test instances for the CEC 2009 special session and competition,” Univ. Essex, Colchester, U.K., and Nanyang Technol. Univ., Tech. Rep. CES-487. 2008.
[86]
T. Okabe, Y. Jin, M. Olhofer, and B. Sendhoff, “On test functions for evolutionary multi-objective optimization,” in Proc. 2004 Int. Conf. Parallel Problem Solving from Nature, 2004, pp. 792–802.
[87]
H. Li, Q. Zhang, and J. Deng, “Biased multiobjective optimization and decomposition algorithm,” IEEE Trans. Cybernetics, vol. 47, no. 1, pp. 52–66, 2017.
[88]
R. Cheng, Y. Jin, M. Olhofer, and B. Sendhoff, “Test problems for large-scale multiobjective and many-objective optimization,” IEEE Trans. Cybernetics, to be published.
[89]
D.A.V. Veldhuizen and G.B. Lamont, “Multiobjective evolutionary algorithm research: A history and analysis,” Dept. Electr. Computer Eng. Graduate School of Eng., Air Force Inst. Technol, Wright Patterson, Tech. Rep. TR-98-03, 1998.
[90]
L. While, P. Hingston, L. Barone, and S. Huband, “A faster algorithm for calculating hypervolume,” IEEE Trans. Evol. Comput., vol. 10, no. 1, pp. 29–38, 2006.
[91]
A. Zhou, Y. Jin, Q. Zhang, B. Sendhoff, and E. Tsang, “Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion,” in Proc. IEEE Congr. Evolutionary Computation, 2006, pp. 892–899.
[92]
H. Wang, Y. Jin, and X. Yao, “Diversity assessment in many-objective optimization,” IEEE Trans. Cybernet., vol. 47, no. 6, pp. 1510–1522, 2017.
[93]
J.R. Schott, “Fault tolerant design using single and multicriteria genetic algorithm optimization,” M.S. thesis, Massachusetts Inst. Technol., Cambridge, 1995.
[94]
Y. Wang, L. Wu, and X. Yuan, “Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure,” Soft Comput., vol. 14, no. 3, pp. 193–209, 2010.
[95]
Z. He and G.G. Yen, “Performance metric ensemble for multiobjective evolutionary algorithms,” IEEE Trans. Evol. Comput., vol. 18, no. 1, pp. 131–144, 2014.
[96]
K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms. New, York: Wiley, 2001.
[97]
K. Deb and M. Goyal, “A combined genetic adaptive search (GeneAS) for engineering design,” Computer Sci. Informat., vol. 26, no. 4, pp. 30–45, 1996.
[98]
L. Davis, “Applying adaptive algorithms to epistatic domains,” in Proc. Int. Joint Conf. Artificial Intelligence, vol. 1, 1985, pp. 162–164.
[99]
D.B. Fogel, “An evolutionary approach to the traveling salesman problem,” Biol. Cybernet., vol. 60, no. 2, pp. 139–144, 1988.
[100]
K. Price, R.M. Storn, and J.A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization. Springer Science & Business Media, 2006.
[101]
J. Kennedy, J.F. Kennedy, R.C. Eberhart, and Y. Shi, Swarm Intelligence. San Mateo, CA: Morgan Kaufmann, 2001.
[102]
X. Yao, Y. Liu, and G. Lin, “Evolutionary programming made faster,” IEEE Trans. Evol. Comput., vol. 3, no. 2, pp. 82–102, 1999.
[103]
X. Zhang, Y. Tian, R. Cheng, and Y. Jin, “An efficient approach to non-dominated sorting for evolutionary multi-objective optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 2, pp. 201–213, 2015.
[104]
X. Zhang, Y. Tian, R. Cheng, and Y. Jin, “Empirical analysis of a tree-based efficient non-dominated sorting approach for many-objective optimization,” in Proc. IEEE Symp. Series on Computational Intelligence, 2016, pp. 1–8.
[105]
D. Brockhoff, “A bug in the multiobjective optimizer IBEA: Salutary lessons for code release and a performance re-assessment,” in Proc. Int. Conf Evolutionary Multi-Criterion Optimization, 2015, pp. 187–201.

Cited By

View all
  • (2025)A novel multi-state reinforcement learning-based multi-objective evolutionary algorithmInformation Sciences: an International Journal10.1016/j.ins.2024.121397688:COnline publication date: 1-Jan-2025
  • (2025)A two-stage accelerated search strategy for large-scale multi-objective evolutionary algorithmInformation Sciences: an International Journal10.1016/j.ins.2024.121347686:COnline publication date: 1-Jan-2025
  • (2025)Many-objective optimization algorithm based on the similarity principle and multi-mechanism collaborative searchThe Journal of Supercomputing10.1007/s11227-024-06553-481:1Online publication date: 1-Jan-2025
  • Show More Cited By

Index Terms

  1. PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]
            Index terms have been assigned to the content through auto-classification.

            Recommendations

            Comments

            Information & Contributors

            Information

            Published In

            cover image IEEE Computational Intelligence Magazine
            IEEE Computational Intelligence Magazine  Volume 12, Issue 4
            Nov. 2017
            106 pages

            Publisher

            IEEE Press

            Publication History

            Published: 01 November 2017

            Qualifiers

            • Research-article

            Contributors

            Other Metrics

            Bibliometrics & Citations

            Bibliometrics

            Article Metrics

            • Downloads (Last 12 months)0
            • Downloads (Last 6 weeks)0
            Reflects downloads up to 14 Jan 2025

            Other Metrics

            Citations

            Cited By

            View all
            • (2025)A novel multi-state reinforcement learning-based multi-objective evolutionary algorithmInformation Sciences: an International Journal10.1016/j.ins.2024.121397688:COnline publication date: 1-Jan-2025
            • (2025)A two-stage accelerated search strategy for large-scale multi-objective evolutionary algorithmInformation Sciences: an International Journal10.1016/j.ins.2024.121347686:COnline publication date: 1-Jan-2025
            • (2025)Many-objective optimization algorithm based on the similarity principle and multi-mechanism collaborative searchThe Journal of Supercomputing10.1007/s11227-024-06553-481:1Online publication date: 1-Jan-2025
            • (2025)An adaptive transfer strategy guided by reference vectors for many-objective optimization problemsThe Journal of Supercomputing10.1007/s11227-024-06547-281:1Online publication date: 1-Jan-2025
            • (2025)A clustering and vector angle-based adaptive evolutionary algorithm for multi-objective optimization with irregular Pareto frontsThe Journal of Supercomputing10.1007/s11227-024-06496-w81:1Online publication date: 1-Jan-2025
            • (2024)An Improved Coevolutionary Algorithm for Constrained Multi-Objective Optimization ProblemsInternational Journal of Cognitive Informatics and Natural Intelligence10.4018/IJCINI.35576618:1(1-16)Online publication date: 16-Oct-2024
            • (2024)A Grey Prediction-Based Reproduction Strategy for Many-Objective Evolutionary AlgorithmInternational Journal of Intelligent Systems10.1155/2024/89949382024Online publication date: 1-Jan-2024
            • (2024)An Improved Particle Swarm Optimization Method for Nonlinear OptimizationInternational Journal of Intelligent Systems10.1155/2024/66281102024Online publication date: 1-Jan-2024
            • (2024)Using Generative Adversarial Networks for Efficient Constrained Multi-objective OptimizationProceedings of the 2024 3rd International Conference on Frontiers of Artificial Intelligence and Machine Learning10.1145/3653644.3664966(135-138)Online publication date: 26-Apr-2024
            • (2024)A Population Initialization Method Based on Similarity and Mutual Information in Evolutionary Algorithm for Bi-Objective Feature SelectionACM Transactions on Evolutionary Learning and Optimization10.1145/36530254:3(1-21)Online publication date: 19-Mar-2024
            • Show More Cited By

            View Options

            View options

            Media

            Figures

            Other

            Tables

            Share

            Share

            Share this Publication link

            Share on social media