  We define very large-scale multiobjective optimization problems as optimizing
multiple objectives (VLSMOPs) with more than 100,000 decision variables. These
problems hold substantial significance, given the ubiquity of real-world
scenarios necessitating the optimization of hundreds of thousands, if not
millions, of variables. However, the larger dimension in VLSMOPs intensifies
the curse of dimensionality and poses significant challenges for existing
large-scale evolutionary multiobjective algorithms, rendering them more
difficult to solve within the constraints of practical computing resources. To
overcome this issue, we propose a novel approach called the very large-scale
multiobjective optimization framework (VMOF). The method efficiently samples
general yet suitable evolutionary directions in the very large-scale space and
subsequently fine-tunes these directions to locate the Pareto-optimal
solutions. To sample the most suitable evolutionary directions for different
solutions, Thompson sampling is adopted for its effectiveness in recommending
from a very large number of items within limited historical evaluations.
Furthermore, a technique is designed for fine-tuning directions specific to
tracking Pareto-optimal solutions. To understand the designed framework, we
present our analysis of the framework and then evaluate VMOF using widely
recognized benchmarks and real-world problems spanning dimensions from 100 to
1,000,000. Experimental results demonstrate that our method exhibits superior
performance not only on LSMOPs but also on VLSMOPs when compared to existing
algorithms.
