Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education, Wuhan University of Science and Technology, 947 Heping Avenue, Wuhan 430081, China.
Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, 947 Heping Avenue, Wuhan 430081, China.
Comput Intell Neurosci. 2020 Jul 18;2020:7179647. doi: 10.1155/2020/7179647. eCollection 2020.
Multiobjective evolutionary algorithms (MOEAs) with higher population diversity have been extensively presented in literature studies and shown great potential in the approximate Pareto front (PF). Especially, in the recent development of MOEAs, the reference line method is increasingly favored due to its diversity enhancement nature and auxiliary selection mechanism based on the uniformly distributed reference line. However, the existing reference line method ignores the nadir point and consequently causes the Pareto incompatibility problem, which makes the algorithm convergence worse. To address this issue, a multiobjective evolutionary algorithm based on the adaptive cross-reference line method, called MOEA-CRL, is proposed under the framework of the indicator-based MOEAs. Based on the dominant penalty distance (DPD) indicator, the cross-reference line method can not only solve the Pareto incompatibility problem but also enhance the population diversity on the convex PF and improve the performances of MOEA-CRL for irregular PF. In addition, the MOEA-CRL adjusts the distribution of the cross-reference lines directly defined by the DPD indicator according to the contributing solutions. Therefore, the adaptation of cross-reference lines will not be affected by the population size and the uniform distribution of cross-reference lines can be maintained. The MOEA-CRL is examined and compared with other MOEAs on several benchmark problems. The experimental results show that the MOEA-CRL is superior to several advanced MOEAs, especially on the convex PF. The MOEA-CRL exhibits the flexibility in population size setting and the great versatility in various multiobjective optimization problems (MOPs) and many-objective optimization problems (MaOPs).
多目标进化算法（MOEAs）具有更高的种群多样性，在文献研究中得到了广泛的展示，并在近似 Pareto 前沿（PF）中显示出巨大的潜力。特别是在 MOEAs 的最新发展中，由于其多样性增强的性质和基于均匀分布参考线的辅助选择机制，参考线方法越来越受到青睐。然而，现有的参考线方法忽略了极点，从而导致 Pareto 不兼容性问题，这使得算法的收敛性变差。为了解决这个问题，在基于指标的 MOEAs 框架下，提出了一种基于自适应交叉参考线方法的多目标进化算法，称为 MOEA-CRL。基于支配惩罚距离（DPD）指标，交叉参考线方法不仅可以解决 Pareto 不兼容性问题，而且可以增强凸 PF 上的种群多样性，提高 MOEA-CRL 在不规则 PF 上的性能。此外，MOEA-CRL 根据贡献解直接调整由 DPD 指标定义的交叉参考线的分布。因此，交叉参考线的自适应不会受到种群大小的影响，并且可以保持交叉参考线的均匀分布。在几个基准问题上对 MOEA-CRL 进行了检验和比较。实验结果表明，MOEA-CRL 优于几个先进的 MOEAs，特别是在凸 PF 上。MOEA-CRL 在种群大小设置上具有灵活性，在各种多目标优化问题（MOPs）和多目标优化问题（MaOPs）中具有很强的通用性。
