Abstract
Weight adaptation methods can enhance the diversity of solutions obtained by decomposition-based approaches when addressing irregular Pareto front shapes. Generally, these methods adapt the location of each weight vector during the search process. However, early adaptation could be unnecessary and ineffective because the population does not provide a good Pareto front approximation at early generations. In order to improve its performance, a better approach would be to trigger such adaptation only when the population has reached the Pareto front. In this paper, we introduce a performance indicator to assist weight adaptation methods, called the median of dispersion of the population (MDP). The proposed indicator provides a general snapshot of the progress of the population toward the Pareto front by analyzing the local progress of each subproblem. When the population becomes steady according to the proposed indicator, the adaptation of weight vectors starts. We evaluate the performance of the proposed approach in both regular and irregular test problems. Our experimental results show that the proposed approach triggers the weight adaptation when it is needed.
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References
Bradstreet, L., While, L., Barone, L.: A fast many-objective hypervolume algorithm using iterated incremental calculations. In: IEEE Congress on Evolutionary Computation, pp. 1–8, July 2010. https://doi.org/10.1109/CEC.2010.5586344
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). https://doi.org/10.1109/TEVC.2016.2519378
Coello, C., Lamont, G., Veldhuizen, D.V.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, Heidelberg (2007). https://doi.org/10.1007/978-0-387-36797-2
Das, I., Dennis, J.: Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8(3), 631–657 (1998). https://doi.org/10.1137/S1052623496307510
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). https://doi.org/10.1109/TEVC.2013.2281535
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). https://doi.org/10.1109/4235.996017
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: Theoretical Advances and Applications. AI&KP, pp. 105–145. Springer, London (2005). https://doi.org/10.1007/1-84628-137-7_6
Eiben, A., Smith, J.: Introduction to Evolutionary Computing. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-44874-8
Havbro, M.: Statistics and Probability Theory. Springer, Heidelberg (2012). https://doi.org/10.1007/978-94-007-4056-3
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. PP(99), 1 (2016). https://doi.org/10.1109/TEVC.2016.2587749
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: a short review. In: 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), pp. 2419–2426, June 2008. https://doi.org/10.1109/CEC.2008.4631121
Jain, H., Deb, K.: An improved adaptive approach for elitist nondominated sorting genetic algorithm for many-objective optimization. Technical report, Indian Institute of Technology, Kanpur, India. Department of Mechanical Engineering (2013)
Jain, H., Deb, K.: An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, Part II: Handling constraints and extending to an adaptive approach. IEEE Trans. Evol. Comput. 18(4), 602–622 (2014). https://doi.org/10.1109/TEVC.2013.2281534
Lee, H.: Foundations of Applied Statistical Methods. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-319-02402-8
Li, B., Li, J., Tang, K., Yao, X.: Many-objective evolutionary algorithms: a survey. ACM Comput. Surv. 48(1), 13:1–13:35 (2015). https://doi.org/10.1145/2792984
Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015). https://doi.org/10.1109/TEVC.2014.2373386
Li, M., Yao, X.: What weights work for you? Adapting weights for any Pareto front shape in decomposition-based evolutionary multi-objective optimisation. CoRR abs/1709.02679 (2017). http://arxiv.org/abs/1709.02679
Miettinen, K.: On the methodology of multiobjective optimization with applications. Ph.D. thesis, University of Jyväskylä, Department of Mathematics (1994)
Solow, A., Polasky, S.: Measuring biological diversity. Environ. Ecol. Stat. 1(2), 95–103 (1994). https://doi.org/10.1007/BF02426650
Tian, Y., Cheng, R., Zhang, X., Cheng, F., Jin, Y.: An indicator based multi-objective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans. Evol. Comput. PP(99), 1 (2017). https://doi.org/10.1109/TEVC.2017.2749619
Ulrich, T., Thiele, L.: Maximizing population diversity in single-objective optimization. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, GECCO 2011, pp. 641–648. ACM, New York (2011). https://doi.org/10.1145/2001576.2001665
Wang, R., Zhang, Q., Zhang, T.: Decomposition-based algorithms using Pareto adaptive scalarizing methods. IEEE Trans. Evol. Comput. 20(6), 821–837 (2016). https://doi.org/10.1109/TEVC.2016.2521175
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). https://doi.org/10.1109/TEVC.2016.2587808
Yuan, Y., Xu, H., Wang, B., Yao, X.: A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 20(1), 16–37 (2016). https://doi.org/10.1109/TEVC.2015.2420112
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007). https://doi.org/10.1109/TEVC.2007.892759
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). https://doi.org/10.1109/TEVC.2015.2424251
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). https://doi.org/10.1109/4235.797969
Acknowledgment
Auraham Camacho acknowledges support from CONACyT through a scholarship to pursue his studies. Gregorio Toscano and Ricardo Landa gratefully acknowledge support from SEP-Cinvestav project No. 262. Hisao Ishibuchi would like to thank the Shenzhen Peacock Plan (Grant No. KQTD2016112514355531), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No. 2017ZT07X386), the Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284), and the Program for University Key Laboratory of Guangdong Province (Grant No. 2017KSYS008).
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Camacho, A., Toscano, G., Landa, R., Ishibuchi, H. (2019). Indicator-Based Weight Adaptation for Solving Many-Objective Optimization Problems. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_18
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