Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark (MPB) and show its nonseparable nature irrespective of its number of peaks. We then propose a composite MPB suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower-dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200-D, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems.

中文翻译：

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放大动态优化问题：分而治之的方法

可扩展性是设计高效算法的一个关键方面。尽管它们很普遍，但文献中并未对大规模动态优化问题进行深入研究。本文涉及设计用于研究大规模动态优化问题的基准和框架。我们首先对移动峰值基准 (MPB) 进行正式分析，并显示其不可分离的性质，而不管其峰值数量如何。然后，我们提出了一个具有可利用模块化的复合 MPB 套件，涵盖了广泛的可扩展部分可分离函数，适用于研究大规模动态优化问题。该基准表现出模块化、异质性和不平衡特征，以类似于现实世界的问题。为了处理复杂的大规模动态优化问题，我们提出了一个基于分解的协同进化框架，它将大规模动态优化问题分解为一组低维组件。该框架的一个新颖方面是其高效的双层资源分配机制，该机制控制对负责跟踪多个移动最优值的组件和种群的预算分配。基于对多达 200-D 的各种大规模动态优化问题的综合实证研究，我们展示了问题分解和资源​​分配在处理这些问题中的关键作用。实验结果清楚地表明，所提出的框架在解决大规模动态优化问题方面优于其他三种方法。