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 optimization framework, on non-separable functions. First, we reveal empirical reasons of why 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 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 functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores.

翻译：鉴于现实世界中广泛存在的不可分离优化问题，本文针对经典的分治优化框架——协同协同进化（CC）在不可分离函数上的大规模版本进行了分析与扩展。首先，我们揭示了在某些不可分离大规模问题中，基于分解的方法在实践中为何被偏好或排斥的实证原因，这在以往的CC文献中尚未明确阐明。随后，我们在不丧失其本质特性的前提下，通过简化将CC形式化为连续博弈模型。不同于先前用于CC的进化博弈理论，我们的新模型提供了更简单但有效的收敛性分析视角，因为只需纯纳什均衡概念，且可显式考虑更通用的适应度景观。基于收敛性分析，我们提出了一种分层分解策略以提升泛化能力，这是由于任何分解都可能面临陷入次优纳什均衡的风险。最后，我们利用强大的分布式计算在多级学习框架下加速该过程，该框架结合了分解的微调能力与CMA-ES的不变性特性。在包含400个CPU核心的集群计算平台上对一组高维函数的实验验证了其搜索性能与可扩展性（相对于CPU核心数）。