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.

翻译：近些年来,为了改进用于解决涉及大量决策变量的优化问题的演进算法,已经多次尝试简化一个特定问题的解决问题空间,以便进行演进搜索;在文献中,现有方法一般可以分为分解法和降低维度方法;前者将一个大规模问题分解成几个较小的子问题,而后者则将原有的高维解决方案空间转换成一个低维空间;然而,值得注意的是,一个大型优化问题不一定总是可以分解,而且也很难保证最初问题的全球最佳程度在较低的问题空间得到维护;在文献中,现有方法一般可以归类为分解法和降低维度的方法;前者将一个大规模问题分解成几个较小的子问题,而后者则将原有的高维度解决方案空间转化为一个低维空间;然而,拟议的模式旨在对从特定问题衍生出来的多种解决方案空间进行搜索,每个问题都具有独特的地貌;拟议的模式没有对大规模规模的欧洲价值链进行假设;因此,对大规模规模的模型化决策效率的模型研究,即对大规模规模化的模型的变式关系进行这种变式研究是某种感兴趣的。