Xiong Lixue, Chen Debao, Zou Feng, Ge Fangzhen, Liu Fuqiang
School of Physics and Electronic Information, Huaibei Normal University, Huaibei, 235000, China.
Anhui Province Key Laboratory of Intelligent Computing and Applications, Huaibei Normal University, Huaibei, 235000, China.
Sci Rep. 2024 Jun 18;14(1):14036. doi: 10.1038/s41598-024-64570-y.
Weighted optimization framework (WOF) achieves variable dimensionality reduction by grouping variables and optimizing weights, playing an important role in large-scale multi-objective optimization problems. However, because of possible problems such as duplicate weight vectors in the selection process and loss of population diversity, the algorithm is susceptible to local optimization. Therefore, this paper develops an algorithm framework called multi-population multi-stage adaptive weighted optimization (MPSOF) to improve the performance of WOF in two aspects. First, the method of using multi-population is employed to address the issue of insufficient algorithmic diversity, while simultaneously reducing the likelihood of converging towards local optima. Secondly, a processing stage is incorporated into MPSOF, where a certain number of individuals are adaptively selected for updating based on the weight information and evolutionary status of different subpopulations, targeting different types of weights. This approach alleviates the impact of repetitive weights on the diversity of newly generated individuals, avoids the drawback of easily converging to local optima when using a single type of weight for updating, and effectively balances the diversity and convergence of subpopulations. Experiments of three types designed on several typical function sets demonstrate that MPSOF exceeds the comparison algorithms in the three metrics for Inverse Generation Distance, Hypervolume and Spacing.
加权优化框架（WOF）通过对变量进行分组和优化权重来实现可变维度降维，在大规模多目标优化问题中发挥着重要作用。然而，由于在选择过程中可能存在权重向量重复以及种群多样性丧失等问题，该算法容易陷入局部优化。因此，本文提出了一种名为多群体多阶段自适应加权优化（MPSOF）的算法框架，从两个方面提高WOF的性能。首先，采用多群体方法来解决算法多样性不足的问题，同时降低收敛到局部最优的可能性。其次，MPSOF引入了一个处理阶段，根据不同子群体的权重信息和进化状态，针对不同类型的权重自适应地选择一定数量的个体进行更新。这种方法减轻了重复权重对新生成个体多样性的影响，避免了使用单一类型权重进行更新时容易收敛到局部最优的缺点，并有效地平衡了子群体的多样性和收敛性。在几个典型函数集上设计的三类实验表明，MPSOF在逆世代距离（Inverse Generation Distance）、超体积（Hypervolume）和间距（Spacing）这三个指标上超过了对比算法。
