Sparse large-scale multi-objective optimization problems (LSMOPs) widely exist in real-world applications, which have the properties of involving a large number of decision variables and sparse Pareto optimal solutions, i.e., most decision variables of these solutions are zero. In recent years, sparse LSMOPs have attracted increasing attentions in the evolutionary computation community. However, all the recently tailored algorithms for sparse LSMOPs put the sparsity detection and maintenance in the first place, where the nonzero variables can hardly be optimized sufficiently within a limited budget of function evaluations. To address this issue, this paper proposes to enhance the connection between real variables and binary variables within the two-layer encoding scheme with the assistance of variable grouping techniques. In this way, more efforts can be devoted to the real part of nonzero variables, achieving the balance between sparsity maintenance and variable optimization. According to the experimental results on eight benchmark problems and three real-world applications, the proposed algorithm is superior over existing state-of-the-art evolutionary algorithms for sparse LSMOPs.

稀疏大规模多目标优化问题（LSMOPs）广泛存在于实际应用中，其具有涉及大量决策变量和稀疏帕累托最优解的特性，即这些解的大部分决策变量为零。近年来，稀疏 LSMOP 在进化计算社区中引起了越来越多的关注。然而，最近所有针对稀疏 LSMOP 定制的算法都将稀疏检测和维护放在首位，在有限的函数评估预算内，非零变量很难得到充分优化。为了解决这个问题，本文提出在变量分组技术的帮助下，在两层编码方案中增强实变量和二进制变量之间的联系。通过这种方式，可以在非零变量的实部投入更多的精力，实现稀疏性维护和变量优化之间的平衡。根据八个基准问题和三个实际应用的实验结果，所提出的算法优于现有的最先进的稀疏 LSMOP 进化算法。