高效求解百万维多目标问题：一种方向采样与微调方法
Efficiently Tackling Million-Dimensional Multiobjective Problems: A Direction Sampling and Fine-Tuning Approach
AI总结：
针对决策变量超十万的VLSMOPs，本文提出VMOF框架，通过Thompson采样进化方向并微调追踪Pareto最优解，在最高百万维基准与现实问题上优于现有算法。
摘要：
我们将超大规模多目标优化问题定义为优化具有超过100,000个决策变量的多个目标（VLSMOPs）。鉴于现实世界中普遍存在需要优化数十万甚至数百万个变量的场景，这些问题具有重大意义。然而，VLSMOPs中更大的维度加剧了维度灾难，并对现有大规模进化多目标算法构成重大挑战，使其在实际计算资源约束下更难求解。为克服这一问题，我们提出了一种称为超大规模多目标优化框架（VMOF）的新方法。该方法在超大规模空间中高效采样通用且合适的进化方向，随后微调这些方向以定位Pareto最优解。为给不同解采样最合适的进化方向，采用了Thompson采样，因为它能在有限历史评估内从极大量候选项中进行有效推荐。此外，还设计了一种用于微调方向的技术，专门用于追踪Pareto最优解。为理解所设计的框架，我们给出了对该框架的分析，随后使用广泛认可的基准测试和维度从100到1,000,000的现实问题评估VMOF。实验结果表明，与现有算法相比，我们的方法不仅在LSMOPs上，而且在VLSMOPs上均表现出优越性能。
英文摘要：
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.
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