Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer black-box optimization framework, on non-separable functions. First, we reveal empirical reasons of when decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous-game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition, there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the recent multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional test functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores.

翻译：鉴于现实世界中不可分离优化问题的普遍性，本文分析并扩展了经典的分治黑箱优化框架——协同协同进化在大规模不可分离函数上的应用。首先，我们揭示了在实际中基于分解的方法为何在某些不可分离大规模问题上具有优势或局限性，这一经验性原因在以往许多CC论文中并未明确阐明。随后，我们将CC通过简化建模为连续博弈模型，同时保留其本质特性。与先前针对CC的进化博弈论方法不同，我们的新模型提供了更简单但有用的收敛性分析视角——仅需纯纳什均衡概念，且能明确考虑更一般的适应度景观。基于收敛性分析，我们提出一种分层分解策略以增强泛化能力，因为任何分解都存在陷入次优纳什均衡的风险。最后，利用最近的多层学习框架，结合分布式计算实现加速：该框架融合了分解的微调能力与CMA-ES的不变性特性。在包含400个CPU核的集群计算平台上，对一组高维测试函数的实验验证了其搜索性能及可扩展性（关于CPU核心数）。