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A many-objective population extremal optimization algorithm with an adaptive hybrid mutation operation. (English) Zbl 1451.90171
Summary: Many-objective optimization problems abbreviated as MaOPs with more than three objectives have attracted increasing interests due to their widely existing in a variety of real-world applications. This paper presents a novel many-objective population extremal optimization called MaOPEO-HM algorithm for MaOPs by introducing a reference set based many-objective optimization mechanism into a recently developed population extremal optimization framework and designing an adaptive hybrid mutation operation for updating the population. Despite of the successful applications of extremal optimization in different kinds of numerical and engineering optimization problems, it has never been explored to the many-objective optimization domain so far. Because most of the existing many-objective evolutionary algorithms are usually guided by a single mutation operation, which has insufficient ability to exploit the search space of MaOPs and will get stuck at any local efficient front, it is the first attempt to design a novel hybrid mutation scheme in MaOPEO-HM algorithm by combining the advantages of polynomial mutation operator and multi-non-uniform mutation operator effectively. The experiment results for DTLZ test problems with 3, 5, 8, 10, and 15 objectives and WFG test problems with 3, 5, and 8 objectives have demonstrated the superiority of the proposed MaOPEO-HM to five state-of-the-art decomposition-based many-objective evolutionary algorithms including NSGA-III, RVEA, EFR-RR, \( \theta \)-DEA, and MOEA/DD and two non-decomposition-based algorithms including GrEA and Two\(\_\)Arch2. Furthermore, the great ability of the designed adaptive hybrid mutation operation incorporated into many-objective population extremal optimization (MaOPEO) has also been illustrated by comparing MaOPEO-HM and two MaOPEO algorithms only based on traditional multi-non-uniform mutation or polynomial mutation for DTLZ problems.

90C59 Approximation methods and heuristics in mathematical programming
68W50 Evolutionary algorithms, genetic algorithms (computational aspects)
90C29 Multi-objective and goal programming
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[1] Alcalá-Fdez, J.; Sanchez, L.; Garcia, S., KEEL: a software tool to assess evolutionary algorithms for data mining problems, Soft. Comput., 13, 3, 307-318 (2009)
[2] Bader, J.; Zitzler, E., HypE: an algorithm for fast hypervolume-based many-objective optimization, Evol. Comput., 19, 1, 45-76 (2011)
[3] Boettcher, S.; Percus, A., Optimization with extremal dynamics, Phys. Rev. Lett., 86, 23, 5211-5214 (2001)
[4] Bosman, P.; Thierens, D., The balance between proximity and diversity in multiobjective evolutionary algorithms, IEEE Trans. Evol. Comput., 7, 2, 174-188 (2003)
[5] Chen, J.; Lin, Q.; Ji, Z., A hybrid immune multiobjective optimization algorithm, Eur. J. Oper. Res., 204, 2, 294-302 (2010) · Zbl 1178.90302
[6] Chen, M. R.; Lu, Y. Z., A novel elitist multiobjective optimization algorithm: multiobjective extremal optimization, Eur. J. Oper. Res., 88, 3, 637-651 (2008) · Zbl 1144.90475
[7] Chen, M. R.; Lu, Y. Z.; Yang, G., Multiobjective optimization using population-based extremal optimization, Neural Comput. Appl., 17, 2, 101-109 (2008)
[8] Cheng, R.; Jin, Y.; Olhofer, M.; Sendhoff, B., A reference vector guided evolutionary algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 20, 5, 773-791 (2016)
[9] Das, I.; Dennis, J. E., Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems, SIAM. J. Optimiz., 8, 3, 631-657 (1998) · Zbl 0911.90287
[10] Deb, K.; Goyal, M., A combined genetic adaptive search (GeneAS) for engineering design, Comput. Sci. Inform., 26, 4, 30-45 (1996)
[11] Deb, K.; Jain, H., An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints, IEEE Trans. Evol. Comput., 18, 4, 577-601 (2014)
[12] Deb, K.; Thiele, L.; Laumanns, M.; Zitzler, E., Scalable Multiobjective Optimization Test Problems (2001), Inst. Commun. Inf. Technol: Inst. Commun. Inf. Technol ETH Zurich, Zurich, Switzerland, TIK Tech. Rep 112
[13] Hamdan, M., On the disruption-level of polynomial mutation for evolutionary multi-objective optimisation algorithms, Comput. Inform., 29, 5, 783-800 (2010) · Zbl 1399.68197
[14] He, Z.; Yen, G. G., Visualization and performance metric in many-objective optimization, IEEE Trans. Evol. Comput., 20, 3, 386-402 (2016)
[15] He, Z.; Yen, G. G., Many-objective evolutionary algorithms based on coordinated selection strategy, IEEE Trans. Evol. Comput., 21, 2, 220-233 (2017)
[17] Huband, S.; Hingston, P.; Barone, L.; While, L., A review of multiobjective test problems and a scalable test problem toolkit, IEEE Trans. Evol. Comput., 10, 5, 477-506 (2006)
[18] Li, F., Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information, Appl. Soft. Comput., 11, 4, 3402-3418 (2011)
[19] Li, K.; Deb, K.; Zhang, Q. F.; Kwong, S., An evolutionary many-objective optimization algorithm based on dominance and decomposition, IEEE Trans. Evol. Comput., 19, 5, 694-716 (2015)
[20] Li, H.; Deb, K.; Zhang, Q. F.; Suganthan, P. N.; Chen, L., Comparison between MOEA/D and NSGA-III on a set of novel many and multi-objective benchmark problems with challenging difficulties, Swarm Evol. Comput., 46, 104-117 (2019)
[21] Li, B.; Li, J.; Tang, K.; Yao, X., Many-objective evolutionary algorithms: a survey, ACM Comput. Surv., 48, 1, 13 (2015)
[22] Li, F.; Wan, P., Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information, Appl Soft. Comput., 13, 11, 4333-4348 (2013)
[23] Li, M.; Yang, S.; Liu, X., Shift-based density estimation for pareto-based algorithms in many-objective optimization, IEEE Trans. Evol. Comput., 18, 3, 348-365 (2014)
[24] Li, H.; Zhang, Q., Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II, IEEE Trans. Evol. Comput., 13, 2, 284-302 (2009)
[25] Li, M.; Zhen, L.; Yao, Y., How to read many-objective solution sets in parallel coordinates, IEEE Comput. Intell. Mag., 12, 4, 88-100 (2017)
[26] Liu, Z.; Wang, Y.; Huang, P., AnD: a many-objective evolutionary algorithm with angle-based selection and shift-based density estimation, Inf. Sci. (2018), (Published online)
[27] Lu, Y. Z.; Chen, Y. W.; Chen, M. R.; Chen, P.; Zeng, G. Q., Extremal Optimization: Fundamentals, Algorithms, and Applications (2016), CRC Press & Chemical Industry Press
[28] Mainentilopes, I.; Souza, L. C.G.; De Sousa, F. L., Design of a nonlinear controller for a rigid-flexible satellite using multi-objective generalized extremal optimization with real codification, Shock. Vib., 19, 5, 947-956 (2013)
[29] Mashwani, W. K.; Salhi, A., A decomposition-based hybrid multiobjective evolutionary algorithm with dynamic resource allocation, Appl. Soft Comput., 12, 9, 2765-2780 (2012)
[30] Pistolesi, F.; Lazzerini, B.; Mura, M. D.; Dini, G., EMOGA: a hybrid genetic algorithm with extremal optimization core for multiobjective disassembly line balancing, IEEE Trans. Ind. Inform., 14, 3, 1089-1098 (2018)
[31] Randall, M.; Lewis, A., Population extremal optimisation for discrete multi-objective optimization problems, Inf. Sci., 367, 390-402 (2016)
[32] Shim, V. A.; Tan, K. C.; Tang, H., Adaptive memetic computing for evolutionary multiobjective optimization, IEEE Trans. Cybern., 45, 4, 610-621 (2015)
[33] Tang, P. H.; Tseng, M. H., Adaptive directed mutation for real-coded genetic algorithms, Appl. Soft. Comput., 13, 1, 600-614 (2013)
[34] Tian, Y.; Cheng, R.; Zhang, X. Y.; Jin, Y. C., PlatEMO: a MATLAB Platform for evolutionary multi-objective optimization [Educational Forum], IEEE Comput. Intell. Mag., 12, 4, 73-87 (2017)
[35] Vallero, A.; Di Carlo, S., ReDO: cross-layer multi-objective design-exploration framework for efficient soft error resilient systems, IEEE Trans. Comput. (2018) · Zbl 06940734
[36] Wan, P.; Li, F., Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees, Inf. Sci., 325, 484-503 (2015) · Zbl 1390.91119
[37] Wang, H.; Jiao, L.; Yao, X., Two_Arch2: an improved two-archive algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 19, 4, 524-541 (2015)
[38] Wang, H.; Jin, Y.; Yao, X., Diversity assessment in many-objective optimization, IEEE Trans. Cybern., 47, 6, 1510-1522 (2017)
[39] Wang, H.; Zeng, G. Q.; Dai, Y. X.; Bi, D. Q.; Sun, J. L.; Xie, X. Q., Design of a fractional order frequency PID controller for an islanded microgrid: a multi-objective extremal optimization method, Energies, 10, 10, 1502 (2017)
[40] While, R. L.; Hingston, P.; Barone, L.; Huband, S., A faster algorithm for calculating hypervolume, IEEE Trans. Evol. Comput., 10, 1, 29-38 (2006)
[41] Yang, J.; Li, F.; Lai, B., Parameterized bilinear programming methodology for solving triangular intuitionistic fuzzy number bimatrix games, J. Intell. Fuzzy. Syst., 31, 1, 115-125 (2016) · Zbl 1366.90236
[42] Yang, S.; Li, M.; Liu, X.; Li, M.; Liu, X.; Zheng, J., A grid-based evolutionary algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 17, 5, 721-736 (2013)
[43] Yuan, Y.; Xu, H.; Wang, B.; Xin, Y., A new dominance relation-based evolutionary algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 20, 1, 16-37 (2016)
[44] Yuan, Y.; Xu, H.; Wang, B.; Zhao, B.; Xin, Y., Balancing convergence and diversity in decomposition-based many-objective optimizers, IEEE Trans. Evol. Comput., 20, 2, 180-198 (2016)
[45] Zeng, G. Q.; Chen, J.; Li, L. M.; Chen, M. R.; Wu, L.; Dai, Y. X.; Zheng, C. W., An improved multi-objective population-based extremal optimization algorithm with polynomial mutation, Inf. Sci., 330, 49-73 (2016)
[46] Zeng, G. Q.; Chen, J.; Dai, Y. X.; Li, L. M.; Zheng, C. W.; Chen, M. R., Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization, Neurocomputing, 160, 173-184 (2015)
[47] Zeng, G. Q.; Xie, X. Q.; Chen, M. R.; Weng, J., Adaptive population extremal optimization based PID neural network for multivariable nonlinear control systems, Swarm Evol. Comput. (2018), (In press)
[48] Zhang, Q.; Li, H., MOEA/D: a multiobjective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput., 11, 6, 712-731 (2007)
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