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AREA: an adaptive reference-set based evolutionary algorithm for multiobjective optimisation. (English) Zbl 1457.68342
Summary: Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, the performance of these algorithms depends largely on problem characteristics. There is a need to improve these algorithms for wide applicability. References, often specified by the decision maker’s preference in different forms, are very effective to boost the performance of algorithms. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state-of-the-arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.
68W50 Evolutionary algorithms, genetic algorithms (computational aspects)
90C29 Multi-objective and goal programming
90C59 Approximation methods and heuristics in mathematical programming
Full Text: DOI
[1] Cai, X.; Mei, Z.; Fan, Z., A decomposition-based many-objective evolutionary algorithm with two types of adjustments for direction vectors, IEEE Trans. Cybern., 48, 8, 2335-2348 (2018)
[2] 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)
[3] Cheng, R.; Li, M.; Tian, Y.; Zhang, X.; Yang, S.; Jin, Y.; Yao, X., A benchmark test suite for evolutionary many-objective optimization, Complex Intell. Syst., 3, 1, 67-81 (2017)
[4] Das, I.; Dennis, J., 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
[5] Deb, K.; Agrawwal, S.; Pratap, A.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 2, 182-197 (2002)
[6] Deb, K.; Jain, H., 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., 18, 4, 577-601 (2014)
[7] Deb, K.; Thiele, L.; Laumanns, M.; Zitzler, E., Scable test problems for evolutionary multi-objective optimization, in:, Evolutionary Multiobjective Optimization, 105-145 (2005), Springer: Springer London
[8] 2018
[9] Ge, H.; Zhao, M.; Sun, L.; Wang, Z.; Tan, G.; Zhang, Q.; Chen, C. L.P., A many-objective evolutionary algorithm with two interacting processes: cascade clustering and reference point incremental learning, IEEE Trans. Evol. Comput., 23, 4, 572-586 (2019)
[10] Goulart, F.; Campelo, F., Preference-guided evolutionary algorithms for many-objective optimization, Inf. Sci., 329, 236-255 (2016)
[11] 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, 2, 477-506 (2006)
[12] Ishibuchi, H.; Sakane, Y.; Masuda, H.; Nojima, Y., Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes, IEEE Trans. Evol. Comput., 21, 2, 169-190 (2017)
[13] Jain, H.; Deb, K., An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part II: handling constraints and extending to an adaptive approach, IEEE Trans. Evol. Comput., 18, 4, 602-622 (2014)
[14] S. Jiang, M. Torres, D.A. Pelta, D. Krabben, R. Daniel, J.T. Luzardo, M. Kaiser, N. Krasnogor, Improving microbial strain design via multiobjective optimisation and decision making, Proceedings of the AI for Synthetic Biology (IJCAI)2018,.
[15] Jiang, S.; Yang, S., An improved multi-objective optimization evolutionary algorithm based on decomposition for complex pareto fronts, IEEE Trans. Cybern., 46, 2, 421-437 (2016)
[16] Jiang, S.; Yang, S., A strength pareto evolutionary algorithm based on reference direction for multiobjective and many-objective optimisation, IEEE Trans. Evol. Comput., 21, 3, 329-346 (2017)
[17] Jiang, S.; Yang, S.; Wang, Y.; Liu, X., Scalarizing functions in decomposition-based multiobjective evolutionary algorithms, IEEE Trans. Evol. Comput., 22, 2, 296-313 (2018)
[18] M. Li, X. Yao, What weights work for you? adapting weights for any pareto front shape in decomposition-based evolutionary multi-objective optimisation, 2018, arXiv:1709.02679.
[19] 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)
[20] Liu, H.; Gu, F.; Zhang, Q., Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems, IEEE Trans. Evol. Comput., 18, 3, 450-455 (2014)
[21] Liu, H.; Li, X., The multiobjective evolutionary algorithm based on determined weight and sub-regional search, in:, Proc. Congr. Evol. Comput., 15, 361-384 (2009)
[22] Liu, Z.; Wang, Y.; Huang, P., And: a many-objective evolutionary algorithm with angle-based selection and shift-based density estimation, Inf. Sci., 509, 400-419 (2020)
[23] Molina, J.; Santana, L. V.; Hernndez-Daz, A. G.; Coello, C. A.C.; Caballero, R., G-dominance: reference point based dominance for multiobjective metaheuristics, Eur. J. Oper. Res., 197, 2, 685-692 (2009) · Zbl 1159.90424
[24] Qi, T.; Ma, X.; Liu, F.; Jiao, L.; Sun, J.; Wu, J., MOEA/D with adaptive weight adjustment, Evol. Comput., 22, 2, 231-264 (2014)
[25] Rostami, S.; OŔeilly, D.; Shenfield, A.; Bowring, N., A novel preference articulation operator for the evolutionary multi-objective optimisation of classifiers in concealed weapons detection, Inf. Sci., 295, 494-520 (2015)
[26] Rostami, S.; Neri, F.; Epitropakis, M., Progressive preference articulation for decision making in multi-objective optimisation problems, Int. Comput. Aided Eng., 24, 4, 315-335 (2017)
[27] Said, L. B.; Bechikh, S.; Ghedira, K., The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making, IEEE Trans. Evol. Comput, 14, 5, 801-818 (2010)
[28] Sato, H., Analysis of inverted PBI and comparison with other scalarizing functions in decomposition based MOEAs, J. Heuristics, 21, 6, 819-849 (2015)
[29] Schott, J. R., Fault Tolerant Design Using Single And Multicriteria Genetic Algorithm Optimization, M.S. Thesis (1995), Massachusetts Institute of Technology: Massachusetts Institute of Technology Cambridge, Massachusetts
[30] Tian, Y.; Cheng, R.; Yang, X.; Cheng, F.; Jin, Y., An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility, IEEE Trans. Evol. Comput., 22, 4, 609-622 (2018)
[31] N.K. Visalakshi, J. Suguna, K-Means clustering using max-min distance measure, in:, Proceedings of the Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2009) (2009). 1-6. IEEE
[32] R. Wang, H. Ishibuchi, Y. Zhang, X. Zheng, T. Zhang, On the effect of localized PBI method in MOEA/d for multi-objective optimization in:, Proceedings of the IEEE Symposium Series on Computational Intelligence (2016).
[33] Wang, Z.; Ong, Y. S.; Ishibuchi, H., On scalable multiobjective test problems with hardly dominated boundaries, IEEE Trans. Evol. Comput., 23, 2, 217-231 (2019)
[34] Wilcoxon, F., Individual comparisons by ranking methods, Biometrics, 1, 6, 80-83 (1945)
[35] Wolpert, D. H.; Macready, W. G., No free lunch theorems for optimization, IEEE Trans. Evol. Comput., 1, 1, 67-82 (1997)
[36] Wu, M.; Li, K.; Kwong, S.; Zhang, Q.; Zhang, J., Learning to decompose: a paradigm for decomposition-based multiobjective optimization, IEEE Trans. Evol. Comput., 23, 3, 376-390 (2019)
[37] Yan, B.; Zhao, Q.; Wang, Z.; Zhang, J. A., Adaptive decomposition-based evolutionary approach for multiobjective sparse reconstruction, Inf. Sci., 462, 141-159 (2008)
[38] Yang, S.; Jiang, S.; Jiang, Y., Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes, Soft Comput., 21, 16, 4677-4691 (2017)
[39] Zhang, X.; Jiang, X.; Zhang, L., Parameter multiobjective optimization method based on weight vector, Acta Electron. J., 44, 11, 2639-2645 (2016)
[40] Zhang, C.; Tan, K. C.; Lee, L. H.; Gao, L., Adaptive weight vectors in MOEA/d for bi-objective optimization problems with discontinuous pareto fronts, Soft Comput., 22, 3997-4012 (2018)
[41] Zhang, Q.; Li, H., MOEA/D: a multiobjective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput., 11, 6, 712-731 (2007)
[42] IEEE
[43] Zhang, Q.; Zhou, A.; Zhao, S.; Suganthan, P. N.; Liu, W.; Tiwari, S., Multiobjective optimization test instances for the CEC 2009 sepcial session and competition technical report CES-487, the shool of computer science and electronic engineering, Technical Report. (2008)
[44] Zhou, A.; Zhang, Q., Are all the subproblems equally important? resource allocation in decomposition-based multiobjective evolutionary algorithms, IEEE Trans. Evol. Comput., 20, 1, 52-64 (2016)
[45] E. Zitzler, S. Kunzli, Indicator-based selection in multiobjective search, in:, Proceedings of the 8th International Conference Parallel Problem Solving from Nature (PPSN VIII) 3242 (2004) 832-842. LNCS.
[46] Zitzler, E.; Thiele, L., Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach, IEEE Trans. Evol. Comput., 3, 4, 257-271 (1999)
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