A multi-stage knowledge-guided evolutionary algorithm

论文-62-A multi-stage knowledge-guided evolutionary algorithm for large-scale sparse multi-objective optimization problems

1.论文总览

To address these issues, this paper proposes a multi-stage knowledge-guided evolutionary algorithm for large-scale sparse multi-objective optimization problems, which aims to enhance the optimization capability by incorporating diversified sparsity knowledge into the evolutionary process. 为了解决这些问题，本文提出了一种用于大规模稀疏多目标优化问题的多阶段知识引导进化算法，旨在通过将多样化的稀疏知识引入进化过程来增强优化能力。 Specifically, three kinds of the knowledge are designed and an effective multi-stage evolutionary strategy based on knowledge fusion is developed to make full use of three kinds of knowledge. 具体而言，设计了三种知识，并开发了一种有效的基于知识融合的多阶段进化策略，以充分利用三种知识。

具体步骤：

The first knowledge is the prior guidance vector (called 𝑝𝑣), which seeks to analyze the prior fitness contribution of each decision variable to the objective functions before evolution ; this prior knowledge is then adaptively refined by the evolution. 设计了三种不同的知识来估计帕累托最优解的稀疏分布。 第一个知识是先验引导向量（称为𝑝𝑣), 其试图在进化之前分析每个决策变量对目标函数的先验适应度贡献；然后，该先验知识被进化自适应地细化。 The filter guidance vector (called 𝑓𝑣) is the second knowledge that is obtained from the current population based on the filter method of feature selection. 滤波器引导矢量（称为𝑓𝑣) 是基于特征选择的滤波方法从当前人群获得的第二知识。 i是维度，j是个体数，R代表非支配解个数，x=dec*mask 通常，在滤波方法中，如果特征的方差很小，则该特征中的样本之间基本上没有差异；因此，这一特性对于分类任务通常是无用的。类似地，我们假设具有较大离散度的决策变量更有可能是非零决策变量，这对应于特征选择问题中的有用特征。为此，𝑓𝑣 有助于筛选𝑚𝑎𝑠𝑘 以标记可能翻转的元素。

The statistical guidance vector (called 𝑠𝑣) is the last knowledge, which is captured by counting the concentration degree of the accumulated elite individuals during the evolution based on a voting method. Based on the above analysis, the three kinds of knowledge contain different categories of sparse information, and utilizing them appropriately is key to enhancing the optimization capability. 统计引导向量（称为𝑠𝑣) 是最后一个知识，通过基于投票方法计算进化过程中积累的精英个体的集中度来获取。 基于以上分析，这三种知识包含不同类别的稀疏信息，适当利用它们是提高优化能力的关键。 统计引导向量𝑠𝑣 从二进制文件中挖掘𝑚𝑎𝑠𝑘 解决方案和滤波器引导矢量𝑓𝑣 从解的实际变量中挖掘。

A multi-stage evolutionary strategy based on knowledge fusion is developed in MSKEA. In stage I, the prior guidance vector and the filter guidance vector are used to guide the genetic operators. In stage II, the three kinds of knowledge are adopted to guide the evolution. In stage III, only the statistical guidance vector is employed to guide the search. Thus, the multi-stage evolutionary strategy makes full use of the three types of knowledge and maintains a good balance between exploration and exploitation to achieve promising performance. 在MSKEA中开发了一种基于知识融合的多阶段进化策略。 在第一阶段，使用先验引导向量和滤波器引导向量来引导遗传算子。 在第二阶段，采用三种知识来指导进化。 在阶段III中，仅使用统计引导向量来引导搜索。因此，多阶段进化策略充分利用了这三种类型的知识，并在探索和开发之间保持了良好的平衡，以实现有希望的绩效。

展望：

尽管MSKEA在解决大规模SMOP方面表现出优异的性能，但它与两层编码方法的混合表示有时会显示出它的弱点，因为它未能考虑二进制编码层和实编码层之间的相互作用。在优化或设计新的编码方法时有效地结合它们仍然是一个重要的问题。 此外，挖掘的知识和设计的具有知识融合的遗传算子也可以嵌入到其他现有的MOEA框架中，以提高其性能