Sun Jing, Miao Zhuang, Gong Dunwei, Zeng Xiao-Jun, Li Junqing, Wang Gaige
IEEE Trans Cybern. 2020 Aug;50(8):3444-3457. doi: 10.1109/TCYB.2019.2908485. Epub 2019 Apr 25.
One of the most important and widely faced optimization problems in real applications is the interval multiobjective optimization problems (IMOPs). The state-of-the-art evolutionary algorithms (EAs) for IMOPs (IMOEAs) need a great deal of objective function evaluations to find a final Pareto front with good convergence and even distribution. Further, the final Pareto front is of great uncertainty. In this paper, we incorporate several local searches into an existing IMOEA, and propose a memetic algorithm (MA) to tackle IMOPs. At the start, the existing IMOEA is utilized to explore the entire decision space; then, the increment of the hypervolume is employed to develop an activation strategy for every local search procedure; finally, the local search procedure is conducted by constituting its initial population, whose center is an individual with a small uncertainty and a big contribution to the hypervolume, taking the contribution of an individual to the hypervolume as its fitness function, and performing the conventional genetic operators. The proposed MA is empirically evaluated on ten benchmark IMOPs as well as an uncertain solar desalination optimization problem and compared with three state-of-the-art algorithms with no local search procedure. The experimental results demonstrate the applicability and effectiveness of the proposed MA.
区间多目标优化问题（IMOPs）是实际应用中最重要且广泛面临的优化问题之一。用于IMOPs的最新进化算法（IMOEAs）需要大量的目标函数评估才能找到具有良好收敛性和均匀分布的最终帕累托前沿。此外，最终的帕累托前沿具有很大的不确定性。在本文中，我们将几种局部搜索方法融入现有的IMOEA中，并提出一种Memetic算法（MA）来处理IMOPs。首先，利用现有的IMOEA探索整个决策空间；然后，采用超体积增量为每个局部搜索过程制定激活策略；最后，通过构建其初始种群来执行局部搜索过程，初始种群的中心是一个不确定性小且对超体积贡献大的个体，将个体对超体积的贡献作为其适应度函数，并执行传统的遗传算子。在所提出的MA在十个基准IMOPs以及一个不确定的太阳能海水淡化优化问题上进行了实证评估，并与三种没有局部搜索过程的最新算法进行了比较。实验结果证明了所提出的MA的适用性和有效性。
