本論文主要以高斯過程模型（Gaussian Process Model）應用在電腦實驗的研究方向上，主要探討的問題同時包含定量因子（Quantitative Factors）及定性因子（Qualitative Factors），並考慮反應變數不具噪聲（Noiseless）的情境下進行多目標最佳化（Multi-objective Optimization）的研究。
我們將此研究應用於電子元件散熱鰭片之散熱效果分析，由於散熱鰭片的配置包含定量及定性因子，因此選用定量及定性型之高斯過程（Gaussian Process with Quantitative and Qualitative Factors，簡稱QQGP）為替代輔助模型，並將其延伸至多反應變量模型。實驗基本流程為利用拉丁超立方體抽樣（Latin Hypercube Sampling，簡稱LHS）取得初始實驗點（Initial Design Points），應用QQGP建構反應曲面，並以期望超容積改進量（Expected Hypervolume Improvement，簡稱EHVI）作為填充準則（Infill Criteria）進行序列設計（Sequential Design），兩步驟依序重複迭代，直至滿足停止條件為止，進而達到在控制成本的情況下，從少許實驗樣本找出使得散熱效果較佳之鰭片配置。

This thesis mainly focuses on surrogate-assisted approach for multi-objective optimization problems with qualitative and quantitative factors. Basically, the approach iterates the following two steps until a stop criterion is met. To begin with, we construct a surrogate surface based on the current explored points, and then a suitable infill criterion is adopted to identify the next explored points. Finally, we identify the solution from all explored points.
To implement our surrogate-assistant approach, first we choose a Latin hypercube sampling to get initial explored points. Since qualitative and quantitative variables are all considered in the multi-output scenario, the multi-task QQGP (MTQQGP) is adopted for surrogate construction and a maximum expected hypervolume improvement is used to identify the next explored points.
To demonstrate the performance of the proposed method, numerical experiments are conducted. Here in addition to the MTQQGP, the multi-objective QQGP (MOQQGP) is also considered due to the comparison purpose. The difference among the MOQQGP and MTQQGP is the different correlation structure assumptions. Finally due to the numerical results, MTQQGP has the better performance for our surrogate-assistant approach.
In our real case study, we focus on the performance of the heat dissipation fins in electronic components. Here there are a 4-level factor and two quantitative factors, and the two responses are the maximum and mean temperature of the grid point. Overall, the proposed surrogate-assistant approach can find good factor setups with the limited explored points.

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