電腦實驗如今已廣泛應用在各個工程領域當中，相較於傳統的物理實驗，
電腦實驗有更高的靈活度和效率，也能大幅降低實驗成本。電腦實驗除了單
一反應變數之外，也可處理多個反應變數的情況，而在多個目標的條件下，
往往需要考量到目標之間的相互影響，因此多目標最佳化(Multi - Objective
Optimization, MOO) 成為了重要的研究議題。另一方面，在現實生活中，常常
需要處理包含定量和定性因子的資料，已有許多現有的研究方法提出相對應的
處理方式。然而，當定性因子的類別組合數量過於龐大時，常用的建模方法可
能會出現過度參數化的問題。在本論文中，我們將針對由ANSYS 軟體模擬的
電子元件散熱鰭片資料做全面的分析，在此我們將同時考慮散熱鰭片的平均溫
及溫度的變異數為兩個目標，嘗試不同的數值實驗來尋求在這兩個目標下的最
佳化之效能。因此基於這情境，我們將此穩健設計(robust design) 問題轉換為
在混合因子情境下的多目標最佳化問題。並以類別樹高斯過程模型(category
tree Gaussian process, ctGP) 為主要模型架構，同時搭配相對應的多目標最佳化
之選點準則，來尋找散熱鰭片的最佳穩健設計。最後進行資料變數的敏感度分
析作為結尾，以了解各個變數對反應變數的影響，同時對散熱鰭片的設計給予
適當的建議和優化。

Computer experiments have been widely applied across various engineering
fields. Compared to traditional physical experiments, they offer greater flexibility
and efficiency, while significantly reducing experimental costs. In addition to
handling a single response variable, computer experiments can also manage multiple
responses simultaneously. Under multi-objective settings, the interdependence
among objectives must often be considered, making Multi-Objective Optimization
(MOO) an important research topic. On the other hand, real-world problems often
involve both quantitative and qualitative factors. Although many modeling
approaches have been proposed to handle such mixed-type inputs, they may suffer
from over-parameterization when the number of qualitative factor combinations
becomes too large. In this study, we conduct a comprehensive analysis of heat
sink data generated through simulations using ANSYS software. Specifically, we
consider both the mean temperature and temperature variance of the heat sink
as optimization objectives and perform various numerical experiments to evaluate
performance under these dual objectives. Based on this context, we reformulate
the robust design problem as a multi-objective optimization task under mixed factors.
To address this, we adopt the category tree Gaussian process model (ctGP)
as the primary modeling framework, combined with a suitable sampling criterion
for multi-objective optimization, to identify optimal robust designs. Finally, a
sensitivity analysis is conducted to assess the influence of input variables on the
responses, providing insights and recommendations for improving heat sink design.