Handling Imbalance Between Convergence and Diversity in the Decision Space in Evolutionary Multimodal Multiobjective Optimization
Handling Imbalance Between Convergence and Diversity in the Decision Space in Evolutionary Multimodal Multiobjective Optimization
复制标题
进化多模态多目标优化中决策空间收敛性与多样性不平衡的处理
DOI：
10.1109/tevc.2019.2938557
复制
发表时间：
2019
影响因子：
14.3
通讯作者：
Naoki Masuyama
中科院分区：
文献类型：
--
作者：
Yiping Liu;Hisao Ishibuchi;Gary G. Yen;Yusuke Nojima;Naoki Masuyama
多峰多目标优化问题可能存在多个具有相同目标向量的Pareto最优解。找到这样的解决方案的困难可能是不同的。虽然已经提出了一些进化多模式多目标算法(EMMA)，但由于其收敛优先的选择标准，它们无法解决这样的MMOP问题。它们快速收敛到容易找到的帕累托最优解，从而在决策空间中失去多样性。也就是说，这种MMOP的特点是在实现收敛和保持决策空间的多样性之间存在不平衡。在本文中，我们首先提出了一组不平衡距离最小化基准问题。在此基础上，提出了一种基于收敛惩罚密度方法的进化算法。在CPDEA中，根据解的局部收敛性质对决策空间中解之间的距离进行变换。基于变换后的距离估计其密度值，并将其用作选择标准。我们将CPDEA与五个最先进的EMMA在所建议的基准上进行了比较。实验结果表明，CPDEA在解决这些问题上具有明显的优势。
There may exist more than one Pareto optimal solution with the same objective vector to a multimodal multiobjective optimization problem (MMOP). The difficulties in finding such solutions can be different. Although a number of evolutionary multimodal multiobjective algorithms (EMMAs) have been proposed, they are unable to solve such an MMOP due to their convergence-first selection criteria. They quickly converge to the Pareto optimal solutions which are easy to find and therefore lose diversity in the decision space. That is, such an MMOP features an imbalance between achieving convergence and preserving diversity in the decision space. In this article, we first present a set of imbalanced distance minimization benchmark problems. Then we propose an evolutionary algorithm using a convergence-penalized density method (CPDEA). In CPDEA, the distances among solutions in the decision space are transformed based on their local convergence quality. Their density values are estimated based on the transformed distances and used as the selection criterion. We compare CPDEA with five state-of-the-art EMMAs on the proposed benchmarks. Our experimental results show that CPDEA is clearly superior in solving these problems.