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A region search evolutionary algorithm for many-objective optimization. (English) Zbl 1451.90145
Summary: Achieving a balance between convergence and diversity in many-objective optimization is a great challenge. This paper suggests an evolutionary algorithm based on a region search strategy to deal with different kinds of benchmark problems. In the proposed algorithm, each solution is associated with a region, and the region search strategy is applied to constrain the updating process; this strategy will enhance the diversity of population without losing convergence. A new normalization procedure is used for dealing with scaled problems. Moreover, the comparison of two solutions is based on both dominance relation and perpendicular distance; the result shows the algorithm’s reliability for solving both convex and concave problems. The performance of the proposed algorithm is validated by several well-known benchmark problems with different properties. Seven state-of-the-art algorithms are compared and the experimental results demonstrate that the introduced algorithm performs the best on almost all benchmark problems. Furthermore, the proposed strategy depicts a high computational efficiency for solving the problems with a high dimension of objectives.
Reviewer: Reviewer (Berlin)
90C29 Multi-objective and goal programming
90C59 Approximation methods and heuristics in mathematical programming
Full Text: DOI
[1] Bader, J.; Zitzler, E., HypE: an algorithm for fast hypervolume-based many-objective optimization, Evol. Comput., 19, 1, 45-76 (2011)
[2] Bai, H.; Zheng, J.; Yu, G.; Yang, S.; Zou, J., A pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation, Inf. Sci., 478, 186-207 (2019)
[3] Brest, J.; Greiner, S.; Boskovic, B.; Mernik, M.; Zumer, V., Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems, IEEE Trans. Evol. Comput., 10, 646-657 (2006)
[4] Cai, X.; Sun, H.; Fan, Z., A diversity indicator based on reference vectors for many-objective optimization, Inf. Sci., 430-431, 467-486 (2019)
[5] Chikumbo, O.; Goodman, E.; Deb, K., Approximating a multidimensional Pareto front for a land use management problem: a modified MOEA with an epigenetic silencing metaphor, (Evolutionary Computation (CEC), 2012 IEEE Congress on (2012), IEEE), 1-9
[6] Coello, C. A.C.; Pulido, G. T.; Lechuga, M. S., Handling multiple objectives with particle swarm optimization, IEEE Trans. Evol. Comput., 8, 256-279 (2004)
[7] Das, I.; Dennis, J. E., Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems, SIAM J. Optim., 8, 631-657 (1998) · Zbl 0911.90287
[8] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 182-197 (2002)
[9] 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, 577-601 (2014)
[10] Deb, K.; Agrawal, R. B., Simulated binary crossover for continuous search space, Complex Syst., 9, 115-148 (1994) · Zbl 0843.68023
[11] Deb, K.; Goyal, M., A combined genetic adaptive search (GeneAS) for engineering design, Comput. Sci. Inf., 26, 30-45 (1996)
[12] Deb, K.; Thiele, L.; Laumanns, M.; Zitzler, E., Scalable test problems for evolutionary multiobjective optimization, Evolutionary Multiobjective Optimization (Advanced Information and Knowledge Processing), 105-145 (2005), Springer: Springer London, U.K. · Zbl 1078.90567
[13] Farokhi, A.; Mahmoodabadi, M. J., Optimal fuzzy inverse dynamics control of a parallelogram mechanism based on a new multi-objective PSO, Cogent Eng., 5, 1 (2018)
[14] Fonseca, C. M.; Fleming, P. J., Genetic algorithms for multiobjective optimization: formulation discussion and generalization, (International Conference on Genetic Algorithms (1999)), 416-423
[15] Gómez, R. H.; Coello, C. A.C., Improved metaheuristic based on the R2 indicator for many-objective optimization, (Genet. Evol. Comput. Conf.. Genet. Evol. Comput. Conf., Madrid, Spain (2015)), 679-686
[16] He, Z.; Yen, G. G.; Zhang, J., Fuzzy-based pareto optimality for many-objective evolutionary algorithms, IEEE Trans. Evol. Comput., 18, 269-285 (2014)
[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, 477-506 (2006)
[18] Ishibuchi, H.; Setoguchi, Y.; Masuda, H.; Nojima, Y., Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes, IEEE Trans. Evol. Comput., 21, 169-190 (2017)
[19] Kaisa, M., Nonlinear Multiobjective Optimization (1999), Springer: Springer New York, NY, USA · Zbl 0949.90082
[20] Khan, B.; Hanoun, S.; Johnstone, M.; Lim, C. P.; Creighton, D.; Nahavandi, S., A scalarization-based dominance evolutionary algorithm for many-objective optimization, Inf. Sci., 474, 236-252 (2019)
[21] Lai, X.; Li, C.; Zhou, J., A Multi-objective Artificial Sheep Algorithm (2018), Neural Comput & Applic
[22] Laumanns, M.; Thiele, L.; Deb, K.; Zitzler, E., Combining convergence and diversity in evolutionary multiobjective optimization, Evol. Comput., 10, 263-282 (2002)
[23] Li, C.; Wang, W.; Chen, D., Multi-objective complementary scheduling of Hydro-Thermal-RE power system via a multi-objective hybrid grey wolf optimizer, Energy, 171, 241-255 (2019)
[24] Li, H.; Zhang, Q., Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II, IEEE Trans. Evol. Comput., 13, 284-302 (2009)
[25] Li, K.; Deb, K.; Zhang, Q.; Kwong, S., An evolutionary many-objective optimization algorithm based on dominance and decomposition, IEEE Trans. Evol. Comput., 19, 694-716 (2015)
[26] Li, K.; Zhang, Q.; Kwong, S.; Li, M.; Wang, R., Stable matching-based selection in evolutionary multiobjective optimization, IEEE Trans. Evol. Comput., 18, 909-923 (2014)
[27] Liu, H.; Gu, F.; Zhang, Q., Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems, IEEE Trans. Evol. Comput., 18, 450-455 (2014)
[28] Liu, Y.; Qin, H.; Mo, L.; Wang, Y.; Chen, D.; Pang, S.; Yin, X., Hierarchical flood operation rules optimization using multi-objective cultured evolutionary algorithm based on decomposition, Water Resour. Manage., 33, 1, 337-354 (2019)
[29] Liu, Y.; Ye, L.; Qin, H.; Hong, X.; Ye, J.; Yin, X., Monthly streamflow forecasting based on hidden Markov model and Gaussian mixture regression, J. Hydrol., 561, 146-159 (2018)
[30] Lygoe, R. J.; Cary, M.; Fleming, P. J., A real-world application of a many-objective optimisation complexity reduction process, Evolutionary Multi-Criterion Optimization, 641-655 (2013), Springer
[31] Mahmoodabadi, M. J.; Taherkhorsandi, M.; Maafi, R. A.; Castillovillar, K. K., “A novel multi-objective optimisation algorithm: artificial bee colony in conjunction with bacterial foraging, Int. J. Intell. Eng. Inf., 3, 4, 369-386 (2015)
[32] Mezura-Montes, E.; Coello, C. A.C., Constraint-handling in nature-inspired numerical optimization: past, present and future, Swarm and Evol. Comput., 1, 173-194 (2011)
[33] Qi, Y.; Ma, X.; Liu, F.; Jiao, L.; Sun, J.; Wu, J., MOEA/D with adaptive weight adjustment, Evol. Comput., 22, 231-264 (2014)
[34] Storn, R.; Price, K., Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., 11, 341-359 (1997) · Zbl 0888.90135
[35] Tanabe, R.; Fukunaga, A., Success-history based parameter adaptation for differential evolution, (Evolutionary Computation 2013 IEEE Congress on Evolutionary Computation (2013), IEEE), 71-78
[36] Wang, R.; Zhou, Z.; Ishibuchi, H.; Liao, T.; Zhang, T., Localized weighted sum method for many-objective optimization, IEEE Trans. Evol. Comput., 22, 3-18 (2018)
[37] Wang, Z.; Zhang, Q.; Gong, M.; Zhou, A., A replacement strategy for balancing convergence and diversity in MOEA/D, IEEE Congress on Evolutionary Computation (CEC), 2132-2139 (2014), PEOPLES R CHINA: PEOPLES R CHINA Beijing
[38] While, L.; Bradstreet, L.; Barone, L., A Fast way of calculating exact hypervolumes, IEEE Trans. Evol. Comput., 16, 86-95 (2012)
[39] Wilcoxon, F., Individual comparisons by ranking methods, Biometrics, 1, 6, 80-83 (1945)
[40] Xiang, Y.; Zhou, Y.; Li, M.; Chen, Z., A vector angle-based evolutionary algorithm for unconstrained many-objective optimization, IEEE Trans. Evol. Comput., 21, 1, 131-152 (2017)
[41] Yang, S.; Li, M.; Liu, X.; Zheng, J., A grid-based evolutionary algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 17, 721-736 (2013)
[42] Yuan, Y.; Xu, H.; Wang, B.; Zhang, B.; Yao, X., Balancing convergence and diversity in decomposition-based many-objective optimizers, IEEE Trans. Evol. Comput., 20, 180-198 (2016)
[43] Yuan, Y.; Xu, H.; Wang, B.; Yao, X., A new dominance relation-based evolutionary algorithm for many-objective optimization, IEEE Trans. Evol. Comput., 20, 16-37 (2016)
[44] Zhang, Q.; Li, H., MOEA/D: a multiobjective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput. (2007)
[45] Zhou, A.; Wang, Y.; Zhang, J., Objective extraction via fuzzy clustering in evolutionary many-objective optimization, Inf. Sci. (2018)
[46] Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C. M.; Da Fonseca, V. G., Performance assessment of multiobjective optimizers: an analysis and review, IEEE Trans. Evol. Comput., 7, 117-132 (2003)
[47] Zitzler, E.; Thiele, L., Multiobjective evolutionary algorithms: a comparative case study and the Strength Pareto approach, IEEE Trans. Evol. Comput., 3, 257-271 (1999)
[48] Zitzler, E.; Künzli, S., Indicator-based selection in multiobjective search, Lect. Notes Comput. Sci., 3242, 832-842 (2004)
[49] Zitzler, E.; Laumanns, M.; Thiele, L., SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization, Evolutionary Methods for Design, Optimisation, and Control, 95-100 (2002), CIMNE: CIMNE Barcelona, Spain
[50] Zou, X.; Chen, Y.; Liu, M.; Kang, L., A new evolutionary algorithm for solving many-objective optimization problems, IEEE Trans. Syst. Man Cybern. Part B (Cybernetics), 38, 5, 1402-1412 (2008)
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