Wang Yuping, Liu Haiyan, Wei Fei, Zong Tingting, Li Xiaodong
School of Computer Science and Technology, Xidian University, Xi'an, 710071, China
School of Computer Science and Technology, Xidian University, Xi'an, 710071, China.
Evol Comput. 2018 Winter;26(4):569-596. doi: 10.1162/evco_a_00214. Epub 2017 Aug 9.
For a large-scale global optimization (LSGO) problem, is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations "", "", "", "" and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being . FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further enhance the efficiency of CCF, a new local search scheme is designed to improve the solution quality. To verify the efficiency of CCF, experiments are conducted on the standard LSGO benchmark suites of CEC'2008, CEC'2010, CEC'2013, and a real-world problem. Our results suggest that the performance of CCF is very competitive when compared with those of the state-of-the-art LSGO algorithms.
对于大规模全局优化（LSGO）问题，通常认为将该问题分解为较小的子问题是一种有效的策略，然后每个子问题都可以单独求解。在这些分解方法中，变量分组近年来被证明很有前景。现有的变量分组方法通常假设问题是黑箱问题（即假设目标函数的解析模型未知），并且它们试图学习合适的变量分组，以便更好地分解问题。在这种情况下，这些变量分组方法不直接使用目标函数的公式。然而，可以认为许多现实世界的问题是白箱问题，也就是说，目标函数的公式通常是先验已知的。这些目标函数的公式提供了丰富的信息，然后可用于设计一种有效的变量分组方法。在本文中，首先提出了一种用于白箱问题的基于公式的分组策略（FBG）。它通过目标函数的公式直接对变量进行分组，目标函数通常由有限数量的运算（即四种算术运算“加”“减”“乘”“除”以及基本初等函数的复合运算）组成。在FBG中，运算被分为两类：一类产生不可分离变量，另一类产生可分离变量。在FBG中，变量可以自动分组为适当数量的非相互作用子组件，每个子组件中的变量是可分离的。FBG可以很容易地应用于任何白箱问题，并且可以集成到协作协同进化框架中。基于FBG，本文提出了一种具有基于公式的变量分组的新型协作协同进化算法（所谓的CCF），用于将大规模白箱问题分解为几个较小的子问题并分别对其进行优化。为了进一步提高CCF的效率，设计了一种新的局部搜索方案来提高解的质量。为了验证CCF的效率，在CEC'2008、CEC'2010、CEC'2013的标准LSGO基准测试套件以及一个实际问题上进行了实验。我们的结果表明，与最先进的LSGO算法相比，CCF的性能非常有竞争力。
