For large-scale multi-objective problems (LSMOPs), it is necessary to get a good grouping strategy or another way to reduce dimensions because of “the curse of dimensions”. In this paper, a weighted optimization framework with random dynamic grouping is proposed for large-scale problems. A weight optimization framework utilizes a problem transformation scheme in which weights are chosen to be optimized instead of the decision variables in order to reduce the dimensionality of the search space. Random dynamic grouping is used to determine sizes of each group adaptively. And multi-objective particle swarm optimization with multiple search strategies (MMOPSO) is employed as an optimizer for both original variables and weight variables. The proposed algorithm is performed on 28 benchmark test problems with 1000 dimensions, and the experimental results show that it can get better performance than some the-state-of-art algorithms in fewer function evaluations. In addition, it can be extended to solve LSMOPs with 5000 dimensions.

对于大型多目标问题（LSMOP），由于“维数的诅咒”，有必要获得一种良好的分组策略或减少维数的另一种方法。本文针对大规模问题提出了一种具有随机动态分组的加权优化框架。权重优化框架利用问题转换方案，其中选择权重来优化而不是决策变量，以减少搜索空间的维数。随机动态分组用于自适应地确定每个组的大小。并采用具有多种搜索策略（MMOPSO）的多目标粒子群算法作为原始变量和权重变量的优化器。该算法在1000个维度的28个基准测试问题上执行，实验结果表明，在较少的函数评估中，它可以获得比某些最新算法更好的性能。另外，它可以扩展为解决具有5000个尺寸的LSMOP。