電腦實驗廣泛地應用在許多工程領域中，除了單一反應變數外，電腦實驗也可以 生成多個反應變數。針對多反應變數的情境，一個常見的目標是能同時取得所有反 應變數的最佳值，因此多目標最佳化 (Multi-Objective Optimization, MOO) 的重要性 日益增加。另一方面，在真實世界中，需要同時處理包含定量及定性因子的問題並 不少見，也已經有許多相關的研究提出相對應的架構。然而，當定性因子的水準組 合數量龐大時，常用的建模方法可能會出現過度參數化的問題。在此，我們將這兩 種情境結合在一起，討論同時考慮混合因子情境下之多目標最佳化問題。由於類別 樹高斯過程 (category tree Gaussian process, ctGP) 模型應用在混合因子的單一反應變 數問題中有不錯的表現，在本研究中將對其進行修改以適應多目標反應變數的情況， 再搭配相對應多目標最佳化之選點準則，探討類別樹高斯過程應用在多目標最佳化 問題上的可行性。我們除了嘗試數種不同情境的數值實驗，並由 ANSYS 軟體模擬的 電子元件散熱鰭片資料作為實例分析，以驗證所提方法之效能。

Computer experiments are widely used in various engineering fields. In addition to the single objective response, the corresponding computer code could generate the multiple responses. A common goal is to optimize these objectives simultaneously, and thus the multi-objective optimization (MOO) becomes more and more important. On the other hand, in practices, we might not only consider the quantitative factor but also qualitative factors. It is a mixed-input type variable structure. When the number of the level com- binations (categories) generated from the qualitative factors is huge, the commonly used modeling approaches would have the over-parameterized problem. Here we integrate these two scenarios together. That is we are interesting in the multi-task model fitting problem with mixed-inputs. Since the category tree Gaussian process (ctGP) model has been suc- cessfully used for surrogate model with mixed inputs, and thus we would modify it for the multi-objective responses. Here several numerical experiments and a cooling system design problem were used to illustrate the performance of the proposed modeling method.

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