Cooperative coevolutionary Modified Differential Evolution with Distance-based Selection for Large-Scale Optimization Problems in noisy environments through an automatic Random Grouping
Cooperative coevolutionary Modified Differential Evolution with Distance-based Selection for Large-Scale Optimization Problems in noisy environments through an automatic Random Grouping
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DOI：
10.48550/arxiv.2209.00777
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Rui Zhong;M. Munetomo
中科院分区：
文献类型：
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作者：
Rui Zhong;M. Munetomo
许多优化问题都受到噪声的影响，基于非线性检查的分解方法（例如差分分组）将完全无法检测乘性噪声环境中变量之间的相互作用，因此很难分解噪声环境中的大规模优化问题（LSOP）。在本文中，我们提出了一种自动随机分组（aRG），它不需要用户指定任何显式超参数。仿真实验和数学分析表明，aRG可以在没有适应度景观知识的情况下检测变量之间的相互作用，并且aRG分解的子问题规模更小，更容易被EA优化。基于协作协同进化（CC）框架，我们引入了一种名为基于距离选择的改进差分进化（MDE-DS）的高级优化器，以增强噪声环境中的搜索能力。与典型DE相比，MDE-DS的参数自适应、多样化与集约化的平衡以及基于距离的概率选择赋予了MDE-DS更强的探索和开发能力。为了评估我们提案的性能，我们基于 CEC2013 LSGO Suite 设计了在噪声环境中具有各种可分离性的 $500$-D 和 $1000$-D 问题。数值实验表明，我们的建议在解决噪声环境中的 LSOP 方面具有广阔的前景，并且可以轻松扩展到更高维度的问题。
Many optimization problems suffer from noise, and nonlinearity check-based decomposition methods (e.g. Differential Grouping) will completely fail to detect the interactions between variables in multiplicative noisy environments, thus, it is difficult to decompose the large-scale optimization problems (LSOPs) in noisy environments. In this paper, we propose an automatic Random Grouping (aRG), which does not need any explicit hyperparameter specified by users. Simulation experiments and mathematical analysis show that aRG can detect the interactions between variables without the fitness landscape knowledge, and the sub-problems decomposed by aRG have smaller scales, which is easier for EAs to optimize. Based on the cooperative coevolution (CC) framework, we introduce an advanced optimizer named Modified Differential Evolution with Distance-based Selection (MDE-DS) to enhance the search ability in noisy environments. Compared with canonical DE, the parameter self-adaptation, the balance between diversification and intensification, and the distance-based probability selection endow MDE-DS with stronger ability in exploration and exploitation. To evaluate the performance of our proposal, we design $500$-D and $1000$-D problems with various separability in noisy environments based on the CEC2013 LSGO Suite. Numerical experiments show that our proposal has broad prospects to solve LSOPs in noisy environments and can be easily extended to higher-dimensional problems.