Opposition-based learning OBL

在 Tizhoosh(2005)[1]中首次引入了 OBL 作为一种新的计算智能方案。在过去的几年里，OBL 已经成功地应用于各种基于种群的进化算法中 [2]-[10]。众所周知，从当前种群中随机生成一个解决方案，往往会导致重新访问搜索空间中没有希望的区域[11]-[12]，这是一种低效的探索模式。OBL 的主要想法同时考虑候选的解决方案及其相反的解决方案。实验表明,如果没有先验知识优化问题,相反的候选解决方案比随机解能够到达全局最优的概率更高[8]。因此，引入一个随机解及其对应的反解比引入两个独立的随机生成解更有希望。
在本文中，我们推广了 OBL 的概念来解决 MFO 问题，并利用多任务环境中的多组上界和下界来产生相反的解决方案。
反解的数学定义如下:

参考资料 Liang, Z., Zhang, J., Feng, L. & Zhu, Z. A hybrid of genetic transform and hyper-rectangle search strategies for evolutionary multi-tasking. Expert Systems with Applications 138, 112798 (2019).

[1]Tizhoosh, H. R. (2005). Opposition-based learning: A new scheme for machine in- telligence. In International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce: 1 (pp. 695–701). doi: 10.1109/CIMCA.2005. 1631345 .

[2]El-Abd, M. (2011). Opposition-based artificial bee colony algorithm. In Proceedings of the 13th annual conference on genetic and evolutionary computation (pp. 109–116). New York, NY, USA: ACM. doi: 10.1145/2001576.2001592 .

[3] Rahnamayan, S., Tizhoosh, H. R., & Salama, M. M. A. (2006). Opposition-based dif- ferential evolution for optimization of noisy problems. In 2006 IEEE international conference on evolutionary computation (pp. 1865–1872). doi: 10.1109/CEC.2006. 1688534 .

[4] Rahnamayan, S., Tizhoosh, H. R., & Salama, M. M. A. (2008a). Opposition-based dif- ferential evolution. IEEE Transactions on Evolutionary Computation, 12 (1), 64–79. doi: 10.1109/TEVC.20 07.89420 0 .

[5] Rahnamayan, S., Tizhoosh, H. R., & Salama, M. M. A. (2008b). Opposition versus ran- domness in soft computing techniques. Applied Soft Computing, 8 (2), 906–918. doi: 10.1016/j.asoc.2007.07.010 .

[6] Rahnamayan, S., Wang, G. G., & Ventresca, M. (2012). An intuitive distance-based explanation of opposition-based sampling. Applied Soft Computing, 12 (9), 2828–2839. doi: 10.1016/j.asoc.2012.03.034 .

[7] Wang, H., Li, H., Liu, Y., Li, C., & Zeng, S. (2007). Opposition-based particle swarm algorithm with cauchy mutation. In 2007 IEEE congress on evolutionary compu- tation (pp. 4750–4756). doi: 10.1109/CEC.2007.4425095 .

[8] Wang, H., Wu, Z., Rahnamayan, S., Liu, Y., & Ventresca, M. (2011). Enhancing par- ticle swarm optimization using generalized opposition-based learning. Informa- tion Sciences, 181 (20), 4699–4714. doi: 10.1016/j.ins.2011.03.016 .

[9] Wang, W., Wang, H., Sun, H., & Rahnamayan, S. (2016). Using opposition-based learning to enhance differential evolution: A comparative study. In 2016 IEEE congress on evolutionary computation (pp. 71–77). doi: 10.1109/CEC.2016.7743780 .

[10] Zhou, Y., Hao, J., & Duval, B. (2017). Opposition-based memetic search for the max- imum diversity problem. IEEE Transactions on Evolutionary Computation, 21 (5), 731–745. doi: 10.1109/TEVC.2017.2674800

[11] Ma, X., Liu, F., Qi, Y., Gong, M., Yin, M., Li, L., . . . Wu, J. (2014). MOEA/D with opposition-based learning for multiobjective optimization problem. Neurocom- puting, 146 (C), 48–64. doi: 10.1016/j.neucom.2014.04.068 .

[12] Ma, X., Zhang, Q., Tian, G., Yang, J., & Zhu, Z. (2018). On Tchebycheffdecomposi- tion approaches for multiobjective evolutionary optimization. IEEE Transactions on Evolutionary Computation, 22 (2), 226–244. doi: 10.1109/TEVC.2017.2704118 .

反向学习，相对基学习 opposition-based learning 简介

Opposition-based learning OBL