Abstract
1by1EA is a competitive method among existing many-objective evolutionary algorithms. However, we find that it may fail to find boundary solutions depending on the Pareto front shape. In this study, we present an improved version of 1by1EA, named 1by1EA-II, to enhance the flexibility in handling various shapes of Pareto fronts. In 1by1EA-II, the Chebyshev distances from a solution to the nadir and ideal points are alternately employed as two convergence indicators. Using the first convergence indicator, boundary solutions are preferred for a wide spread in the objective space. With the other convergence indicator, non-boundary solutions are preferred to promote diversity. We empirically compare the proposed 1by1EA-II with its original version as well as four other state-of-the-art algorithms on DTLZ and Minus-DTLZ test problems. The results show that 1by1EA-II is the most flexible algorithm.
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Bhattacharjee, K.S., Singh, H.K., Ray, T., Zhang, Q.: Decomposition based evolutionary algorithm with a dual set of reference vectors. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 105–112. IEEE (2017)
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)
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 (2013)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization, pp. 105–145. Springer, London (2005). https://doi.org/10.1007/1-84628-137-7_6
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)
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(2), 169–190 (2017)
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)
Li, M., Yang, S., Liu, X.: Bi-goal evolution for many-objective optimization problems. Artif. Intell. 228, 45–65 (2015)
Liu, Y., Gong, D., Sun, J., Jin, Y.: A many-objective evolutionary algorithm using a one-by-one selection strategy. IEEE Trans. Cybern. 47(9), 2689–2702 (2017)
Liu, Y., Gong, D., Sun, X., Zhang, Y.: Many-objective evolutionary optimization based on reference points. Appl. Soft Comput. 50(1), 344–355 (2017)
Tian, Y., Cheng, R., Zhang, X., Jin, Y.: PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput. Intell. Mag. 12(4), 73–87 (2017)
Wang, Z., Zhang, Q., Li, H., Ishibuchi, H., Jiao, L.: On the use of two reference points in decomposition based multiobjective evolutionary algorithms. Swarm Evol. Comput. 34, 89–102 (2017)
Yang, S., Li, M., Liu, X., Zheng, J.: A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 17(5), 721–736 (2013)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Zhang, X., Tian, Y., Jin, Y.: A knee point driven evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 19(6), 761–776 (2015)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm. Technical report, Eidgenössische Technische Hochschule Zürich (ETH), Institut für Technische Informatik und Kommunikationsnetze (TIK) (2001)
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(2), 117–132 (2003)
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This work was supported by the Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284).
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Liu, Y., Ishibuchi, H., Nojima, Y., Masuyama, N., Shang, K. (2018). Improving 1by1EA to Handle Various Shapes of Pareto Fronts. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_25
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