Abstract
Rich works have been done on brain storm optimization algorithm solving static single- or multi-objective optimization problems, but less reports for dynamic multi-objective optimization problems. Based on this, a grid-based multi-objective brain storming algorithm with hybrid mutation operation is proposed to find the robust Pareto-optimal solution set over time. Grid-based clustering method partitions the objective space evenly along each objective and classifies the individuals located in the same grid into a cluster. Its computational complexity is less than k-means- and group-based clustering strategies. Traditional Gaussian-, Cauchy- and Chaotic-based mutation operators have different mutation steps and generate the new individuals with various diversity. In order to enhance the diversity and avoiding the premature convergence, a hybrid mutation strategy integrating above three mutation operators is presented. Experimental results for eight dynamic multi-objective benchmark functions show that the proposed algorithm can find robust Pareto-optimal solutions approximating the true Pareto front under more subsequent environments with the acceptable fitness threshold. The longer survival time also indicates that grid-based clustering method and hybrid mutation strategy are apt to better robustness.
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References
Azzouz R, Bechikh S, Said LB (2017) A dynamic multi-objective evolutionary algorithm using a change severity-based adaptive population management strategy. Soft Comput 21(4):1–22
Chen GY, Rogers KJ (2010) Proposition of two multiple criteria models applied to dynamic multi-objective facility layout problem based on ant colony optimization. In: IEEE international conference on industrial engineering and engineering management, pp. 1553–1557
Chen MR, Guo YN, Gong DW, Yang Z (2017) A novel dynamic multi-objective robust evolutionary optimization method. Acta Autom Sin 43(11):2014–2032
Cheng S, Shi Y, Qin Q, Zhang Q, Bai R (2014) Population diversity maintenance in brain storm optimization algorithm. J Artif Intell Soft Comput Res 4(2):83–97
Deb K, Udaya Bhaskara RN, Karthik S (2007) Dynamic multi-objective optimization and decision-making using modified nsga-ii: a case study on hydro-thermal power scheduling. In: International conference on evolutionary multi-criterion optimization, pp 803–817
Farina M, Deb K, Amato P (2004) Dynamic multiobjective optimization problems: test cases, approximations, and applications. IEEE Trans Evolut Comput 8(5):425–442
Fu H, Sendhoff B, Tang K, Yao X (2015) Robust optimization over time: problem difficulties and benchmark problems. IEEE Trans Evolut Comput 19(5):731–745
Goh CK, Tan KC (2009) A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans Evolut Comput 13(1):103–127
Goh C K, Ong Y-S, Tan KC, Teoh EJ (2008) An investigation on evolutionary gradient search for multi-objective optimization. In: 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence). IEEE, pp 3741–3746
Guo X, Wu Y, Xie L, Cheng S, Xin J (2015) An adaptive brain storm optimization algorithm for multiobjective optimization problems. In: International conference in swarm intelligence, pp 365–372
Guo Y-N, Cheng J, Luo S, Gong D (2018) Robust dynamic multi-objective vehicle routing optimization method. IEEE/ACM Trans Comput Biol Bioinform 15(6):1891–1903
Guo Y, Yang H, Chen M, Cheng J, Gong D (2019) Ensemble prediction-based dynamic robust multi-objective optimization methods. Swarm Evolut Comput 48:156–171
Jiang M, Huang Z, Qiu L, Huang W, Yen GG (2018) Transfer learning based dynamic multiobjective optimization algorithms. IEEE Trans Evolut Comput 22(4):501–514
Jin Y, Tang K, Xin Y, Sendhoff B, Yao X (2013) A framework for finding robust optimal solutions over time. Memet Comput 5(1):3–18
Li X, Branke J, Kirley M (2007) On performance metrics and particle swarm methods for dynamic multiobjective optimization problems. In: 2007 IEEE congress on evolutionary computation. IEEE, pp 576–583
Li Q, Zou J, Yang S, Zheng J, Gan R (2018) A predictive strategy based on special points for evolutionary dynamic multi-objective optimization. Soft Comput 1:1–17
Liang J J, Qu B-Y (2013) Large-scale portfolio optimization using multiobjective dynamic mutli-swarm particle swarm optimizer. In: 2013 IEEE symposium on swarm intelligence (SIS). IEEE, pp 1–6
Nguyen TT, Yao X (2012) Continuous dynamic constrained optimization—the challenges. IEEE Trans Evolut Comput 16(6):769–786
Palaniappan S, Zein-Sabatto S, Sekmen A (2001) Dynamic multiobjective optimization of war resource allocation using adaptive genetic algorithms. In: Southeastcon IEEE, pp 160–165
Schott JR (1995) Fault tolerant design using single and multi-criteria genetic algorithms. Masters Thesis Massachusetts Institute of Technology, vol 37, no 1, p 1C13
Shang R, Jiao L, Ren Y, Li L, Wang L (2014) Quantum immune clonal coevolutionary algorithm for dynamic multiobjective optimization. Soft Comput 18(4):743–756
Shi Y (2011) Brain storm optimization algorithm. IEEE Congr Evolut Comput 6728(CEC):1–14
Shi Y, Xue J, Wu Y (2013) Multi-objective optimization based on brain storm optimization algorithm. Int J Swarm Intell Res (IJSIR) 4(3):1–21
Wilcoxon F (1945) Individual comparisons by ranking methods. Biom Bull 1(6):80–83
Xie L, Wu Y (2014) A modified multi-objective optimization based on brain storm optimization algorithm. In: International conference in swarm intelligence. Springer, pp 328–339
Xu B, Zhang Y, Gong D, Guo Y, Rong M (2018) Environment sensitivity-based cooperative co-evolutionary algorithms for dynamic multi-objective optimization. IEEE/ACM Trans Comput Biol Bioinform 15(6):1877–1890
Xue J, Wu Y, Shi Y, Cheng S (2012) Brain storm optimization algorithm for multi-objective optimization problems. In: Lecture notes in computer science, vol 7331, no 4, pp 513–519
Yang S (2015) Evolutionary computation for dynamic optimization problems. In: Companion publication of the 2015 conference on genetic and evolutionary computation, pp 629–649
Yu X, Jin Y, Tang K, Yao X (2010) Robust optimization over time—a new perspective on dynamic optimization problems. In: Evolutionary computation, pp 1–6
Acknowledgements
This work is supported by National Natural Science Foundation of China under Grant 61573361, National Key Research and Development Program under Grant 2016YFC0801406 and Six Talent Peaks Project in Jiangsu Province under Grant 2017-DZXX-046.
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Guo, Y., Yang, H., Chen, M. et al. Grid-based dynamic robust multi-objective brain storm optimization algorithm. Soft Comput 24, 7395–7415 (2020). https://doi.org/10.1007/s00500-019-04365-w
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DOI: https://doi.org/10.1007/s00500-019-04365-w