帕累托集合预测辅助的双层多目标优化
Pareto Set Prediction Assisted Bilevel Multi-objective Optimization
AI总结：
针对黑箱双层多目标优化中嵌套搜索评估成本高的问题，提出用神经网络直接预测下层帕累托集合作为初始化，构建PSP-BLEMO框架，实验证明其在欺骗性与非欺骗性问题上的竞争力。
摘要：
双层优化问题包含一个上层优化任务，该任务将下层优化任务作为约束。尽管利用进化计算求解上下层均为单目标的双层问题已有大量且不断增长的文献，但针对上下层均为多目标的问题（BLMOP）的研究相对较少。对于黑箱BLMOP，现有的进化技术通常采用嵌套搜索，其原生形式会消耗大量的函数评估次数。在这项工作中，我们提出通过直接为候选上层解预测下层帕累托集合来减少这一开销，而不是从头开始进行优化。这种预测对BLMOP而言极具挑战性，因为它涉及一对多的映射场景。我们通过使用辅助变量补充数据集并构建神经网络来解决这一瓶颈，该网络随后可被训练以有意义的方式映射变量。然后，我们将此初始化嵌入到一个双层优化框架中，称为帕累托集合预测辅助的进化双层多目标优化（PSP-BLEMO）。文中给出了与现有最先进方法的系统实验以证明其优势。实验表明，所提出的方法在一系列问题上具有竞争力，包括欺骗性和非欺骗性问题。
英文摘要：
Bilevel optimization problems comprise an upper level optimization task that contains a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single objective at both levels using evolutionary computation, there is relatively scarce work done to address problems with multiple objectives (BLMOP) at both levels. For black-box BLMOPs, the existing evolutionary techniques typically utilize nested search, which in its native form consumes large number of function evaluations. In this work, we propose to reduce this expense by predicting the lower level Pareto set for a candidate upper level solution directly, instead of conducting an optimization from scratch. Such a prediction is significantly challenging for BLMOPs as it involves one-to-many mapping scenario. We resolve this bottleneck by supplementing the dataset using a helper variable and construct a neural network, which can then be trained to map the variables in a meaningful manner. Then, we embed this initialization within a bilevel optimization framework, termed Pareto set prediction assisted evolutionary bilevel multi-objective optimization (PSP-BLEMO). Systematic experiments with existing state-of-the-art methods are presented to demonstrate its benefit. The experiments show that the proposed approach is competitive across a range of problems, including both deceptive and non-deceptive problems
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
