Abstract
The performance of multimodal multi-objective evolutionary algorithms (MMEAs) is determined by not only the convergence to the Pareto front in the objective space, but also the distribution spread to the Pareto set in the decision space. Comparing with the performance matrix applied in the objective space, the performance assessment in the decision space should pay more attention to the distribution spread of solutions. This paper presents a novel diversity metric (PSCR) to reveal the distribution spread of a solution set to the pareto set in the decision space. In addition, in order to avoid the influence of boundary individuals, the grid-partition method is adopted. Through adjusting the scale of the grid, the proposed PSCR could evaluate the MMEAs on both coarse-grained and fine-grained way. The test is carried out on 6 test functions and the reasonable range of parameters is discussed. Moreover, the results of 21 experiments were measured with metrics, and PSCR was compared with other metrics. It was proved that PSCR could not only accurately measure the performance of the algorithm, but also had a higher degree of differentiation than the other metrics.
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References
Deb, K., Pratap, A., Agarwal, S., et al.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Trivedi, A., Srinivasan, D., Sanyal, K., et al.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans. Evol. Comput. 21(3), 440–462 (2016)
Liang, J., Yue, C., Qu, B.: Multimodal multi-objective optimization: a preliminary study. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 2454–2461 (2016)
Van Veldhuizen, D.A., Lamont, G.B.: On measuring multiobjective evolutionary algorithm performance. In: Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No. 00TH8512), pp. 1: 204–211(2000)
Wu, J., Azarm, S.: Metrics for quality assessment of a multiobjective design optimization solution set. J. Mech. Des. 123(1), 18–25 (2001)
Schott, J.R.: Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. cellular immunology (1995)
Zhou, A., Jin, Y., Zhang, Q., et al.: Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: 2006 IEEE International Conference on Evolutionary Computation, pp. 892–899(2006)
While, L., Hingston, P., Barone, L., et al.: A faster algorithm for calculating hypervolume. IEEE Trans. Evol. Comput. 10(1), 29–38 (2006)
Tan, K., Lee, T., Khor, E.: Evolutionary algorithms for multi-objective optimization: performance assessments and comparisons. Artif. Intell. Rev. 17(4), 251–290 (2002)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)
Wang, H., Jin, Y., Yao, X.: Diversity assessment in many-objective optimization. IEEE Trans. Cybern. 47(6), 1510–1522 (2016)
Yue, C., Qu, B., Yu, K., et al.: A novel scalable test problem suite for multimodal multiobjective optimization. Swarm Evolut. Comput. 48, 62–71 (2019)
Yue, C., Liang, J., Qu, B., et al.: Multimodal multiobjective optimization in feature selection. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp. 302–309 (2019)
Zhou, A., Zhang, Q., Jin, Y.: Approximating the set of Pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Trans. Evol. Comput. 13(5), 1167–1189 (2009)
Tian, Y., Cheng, R., Zhang, X., et al.: Diversity assessment of multi-objective evolutionary algorithms: performance metric and benchmark problems. IEEE Comput. Intell. Mag. 14(3), 61–74 (2019)
Yue, C., Qu, B., Liang, J.: A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems. IEEE Trans. Evol. Comput. 22(5), 805–817 (2017)
Zhang, Q., Zhou, A., Jin, Y.: RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans. Evol. Comput. 12(1), 41–63 (2008)
Liu, Y., Yen, G., Gong, D.: A multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies. IEEE Trans. Evol. Comput. 23(4), 660–674 (2018)
Schütze, O., Mostaghim, S., Dellnitz, M., et al.: Covering Pareto sets by multilevel evolutionary subdivision techniques. In: International Conference on Evolutionary Multi-Criterion Optimization, pp. 118–132 (2003)
Gong, M., Jiao, L., Du, H., et al.: Multiobjective immune algorithm with nondominated neighbor-based selection. Evolut. Comput. 16(2), 225–255 (2008)
Qu, B., Li, C., Liang, J., et al.: A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems. Appl. Soft Comput. 86, 105886 (2020)
Acknowledgment
The paper is supported by the National Natural Science Foundation of China (No. 51905494, 61501405), Funding program for key scientific research projects of universities in Henan province (No. 20A520004), science and technology key project of Henan province (No. 212102210154), Training plan of young backbone teachers in Colleges and universities of Henan Province (No. 2019GGJS138).
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Zhang, W., Fan, Y., Zhang, N., Zhang, W. (2022). An Adjustable Diversity Metric for Multimodal Multi-objective Evolutionary Algorithms. In: Li, B., et al. Advanced Data Mining and Applications. ADMA 2022. Lecture Notes in Computer Science(), vol 13087. Springer, Cham. https://doi.org/10.1007/978-3-030-95405-5_27
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DOI: https://doi.org/10.1007/978-3-030-95405-5_27
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