In recent years, to improve the evolutionary algorithms used to solve optimization problems involving a large number of decision variables, many attempts have been made to simplify the problem solution space of a given problem for the evolutionary search. In the literature, the existing approaches can generally be categorized as decomposition-based methods and dimension-reduction-based methods. The former decomposes a large-scale problem into several smaller subproblems, while the latter transforms the original high-dimensional solution space into a low-dimensional space. However, it is worth noting that a given large-scale optimization problem may not always be decomposable, and it is also difficult to guarantee that the global optimum of the original problem is preserved in the reduced low-dimensional problem space. This paper thus proposes a new search paradigm, namely the multi-space evolutionary search, to enhance the existing evolutionary search methods for solving large-scale optimization problems. In contrast to existing approaches that perform an evolutionary search in a single search space, the proposed paradigm is designed to conduct a search in multiple solution spaces that are derived from the given problem, each possessing a unique landscape. The proposed paradigm makes no assumptions about the large-scale optimization problem of interest, such as that the problem is decomposable or that a certain relationship exists among the decision variables. To verify the efficacy of the proposed paradigm, comprehensive empirical studies in comparison to four state-of-the-art algorithms were conducted using the CEC2013 large-scale benchmark problems.

中文翻译：

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大规模优化的多空间进化搜索

近年来，为了改进用于解决涉及大量决策变量的优化问题的进化算法，已经进行了许多尝试来简化用于进化搜索的给定问题的问题解决空间。在文献中，现有方法通常可分为基于分解的方法和基于降维的方法。前者将一个大型问题分解为几个较小的子问题，而后者将原始的高维解空间转换为一个低维空间。但是，值得注意的是，给定的大规模优化问题可能并不总是可分解的，并且很难保证在缩小的低维问题空间中保留原始问题的全局最优性。因此，本文提出了一种新的搜索范式，即多空间进化搜索，以增强解决大规模优化问题的现有进化搜索方法。与在单个搜索空间中执行进化搜索的现有方法相反，所提出的范例设计为在从给定问题派生的多个解决方案空间中进行搜索，每个解决方案空间均具有唯一的情况。所提出的范例不对感兴趣的大规模优化问题做出任何假设，例如该问题是可分解的，或者决策变量之间存在某种关系。为了验证所提出范例的有效性，使用CEC2013大规模基准测试问题，与四种最新算法进行了全面的经验研究。