Tian Ye, Lu Chang, Zhang Xingyi, Cheng Fan, Jin Yaochu
IEEE Trans Cybern. 2022 Jul;52(7):6784-6797. doi: 10.1109/TCYB.2020.3041325. Epub 2022 Jul 4.
In real-world applications, there exist a lot of multiobjective optimization problems whose Pareto-optimal solutions are sparse, that is, most variables of these solutions are 0. Generally, many sparse multiobjective optimization problems (SMOPs) contain a large number of variables, which pose grand challenges for evolutionary algorithms to find the optimal solutions efficiently. To address the curse of dimensionality, this article proposes an evolutionary algorithm for solving large-scale SMOPs, which aims to mine the sparse distribution of the Pareto-optimal solutions and, thus, considerably reduces the search space. More specifically, the proposed algorithm suggests an evolutionary pattern mining approach to detect the maximum and minimum candidate sets of the nonzero variables in the Pareto-optimal solutions, and uses them to limit the dimensions in generating offspring solutions. For further performance enhancement, a binary crossover operator and a binary mutation operator are designed to ensure the sparsity of solutions. According to the results on eight benchmark problems and four real-world problems, the proposed algorithm is superior over existing evolutionary algorithms in solving large-scale SMOPs.
在实际应用中，存在许多多目标优化问题，其帕累托最优解是稀疏的，即这些解的大多数变量为0。一般来说，许多稀疏多目标优化问题（SMOP）包含大量变量，这给进化算法高效找到最优解带来了巨大挑战。为了解决维度灾难问题，本文提出了一种用于求解大规模SMOP的进化算法，其旨在挖掘帕累托最优解的稀疏分布，从而显著减少搜索空间。更具体地说，所提出的算法提出了一种进化模式挖掘方法，以检测帕累托最优解中非零变量的最大和最小候选集，并使用它们来限制生成后代解时的维度。为了进一步提高性能，设计了一个二进制交叉算子和一个二进制变异算子以确保解的稀疏性。根据在八个基准问题和四个实际问题上的结果，所提出的算法在求解大规模SMOP方面优于现有的进化算法。
