基于自变量简约的大规模稀疏多目标优化  

Evolutionary algorithm using dimensionality reduction forsparse multi-objective optimization

作　　者：丘雪瑶 辜方清[1] Qiu Xueyao;Gu Fangqing(School of Mathematics&Statistics,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学数学与统计学院,广州510520

出　　处：《计算机应用研究》2024年第6期1663-1668,共6页Application Research of Computers

基　　金：广东省自然科学基金资助项目(2021A1515011839)。

摘　　要：现有的大多数进化算法在求解大规模优化问题时性能会随决策变量维数的增长而下降。通常,多目标优化的Pareto有效解集是自变量空间的一个低维流形,该流形的维度远小于自变量空间的维度。鉴于此,提出一种基于自变量简约的多目标进化算法求解大规模稀疏多目标优化问题。该算法通过引入局部保持投影降维,保留原始自变量空间中的局部近邻关系,并设计一个归档集,将寻找到的非劣解存入其中进行训练,以提高投影的准确性。将该算法与四种流行的多目标进化算法在一系列测试问题和实际应用问题上进行了比较。实验结果表明,所提算法在解决稀疏多目标问题上具有较好的效果。因此,通过自变量简约能降低问题的求解难度,提高算法的搜索效率,在解决大规模稀疏多目标问题方面具有显著的优势。The performance of most existing evolutionary algorithms tends to decrease as the dimension of the decision variables increases for solving large-scale optimization problems.The Pareto solution set of a multi-objective optimization is a low dimensional manifold in the decision space,whose dimension is much smaller than that of the decision variables space.Accordingly,this paper proposed a multi-objective evolutionary algorithm based on dimensionality reduction of decision variables to solve large-scale sparse multi-objective optimization problems.It preserved local neighborhood information in the original decision variables space by using locality preserving projections,and designed an archive set to train the non-dominated solutions as much as possible to raise the accuracy of projection.The proposed algorithm was compared with four popular evolutionary multi-objective optimization algorithms on a series of test problems and practical application problems.Experimental results show that the proposed algorithm is effective in solving sparse multi-objective problems.Therefore,the reduction of indepen-dent variables can reduce the difficulty of solving the problem,improve the search efficiency of the algorithm,and have significant advantages in solving large-scale sparse multi-objective problems.

关 键 词：局部保持投影 进化算法 大规模稀疏多目标优化问题 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]