In dealing with the expensive multiobjective optimization problem, some algorithms convert it into a number of single-objective subproblems for optimization. At each iteration, these algorithms conduct surrogate-assisted optimization on one or multiple subproblems. However, these subproblems may be unnecessary or resolved. Operating on such subproblems can cause server inefficiencies, especially in the case of expensive optimization. To overcome this shortcoming, we propose an adaptive subproblem selection (ASS) strategy to identify the most promising subproblems for further modeling. To better leverage the cross information between the subproblems, we use the collaborative multioutput Gaussian process surrogate to model them jointly. Moreover, the commonly used acquisition functions (also known as infill criteria) are investigated in this article. Our analysis reveals that these acquisition functions may cause severe imbalances between exploitation and exploration in multiobjective optimization scenarios. Consequently, we develop a new acquisition function, namely, adaptive lower confidence bound (ALCB), to cope with it. The experimental results on three different sets of benchmark problems indicate that our proposed algorithm is competitive. Beyond that, we also quantitatively validate the effectiveness of the ASS strategy, the CoMOGP model, and the ALCB acquisition function.

中文翻译：

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为昂贵的多目标优化中的协同建模选择合适的子问题

在处理代价高昂的多目标优化问题时，一些算法将其转化为多个单目标子问题进行优化。在每次迭代中，这些算法对一个或多个子问题进行代理辅助优化。然而，这些子问题可能是不必要的或已解决的。对此类子问题进行操作可能会导致服务器效率低下，尤其是在昂贵的优化情况下。为了克服这个缺点，我们提出了一种自适应子问题选择 (ASS) 策略来识别最有希望的子问题以进行进一步建模。为了更好地利用子问题之间的交叉信息，我们使用协作多输出高斯过程代理对它们进行联合建模。此外，本文还研究了常用的采集函数（也称为填充标准）。我们的分析表明，这些获取功能可能会导致多目标优化场景中的开发和探索之间出现严重的不平衡。因此，我们开发了一个新的采集函数，即自适应置信下限 (ALCB) 来应对它。三组不同基准问题的实验结果表明我们提出的算法具有竞争力。除此之外，我们还定量验证了 ASS 策略、CoMOGP 模型和 ALCB 采集函数的有效性。三组不同基准问题的实验结果表明我们提出的算法具有竞争力。除此之外，我们还定量验证了 ASS 策略、CoMOGP 模型和 ALCB 采集函数的有效性。三组不同基准问题的实验结果表明我们提出的算法具有竞争力。除此之外，我们还定量验证了 ASS 策略、CoMOGP 模型和 ALCB 采集函数的有效性。