實驗設計旨在協助研究人員有效率地蒐集數據。在傳統的設定中，實驗區域通常被假設為超立方體；然而，在實際應用中，實驗區域往往會面臨各種限制條件。隨著這些限制條件變得日益複雜，實驗區域的形狀可能會隨之變得狹窄且不規則，進而大幅增加尋找最佳實驗設計的難度。為了克服這項挑戰，本研究將受限區域的最佳實驗設計搜尋問題，轉化為受限最佳化問題來處理。在求解過程中，本研究採用粒子群最佳化 (Particle Swarm Optimization, PSO) 類型的方法，並結合多種懲罰函數法，藉此在受限的區域內建構理想的實驗設計。此外，本文亦透過與最佳混合實驗及受限空間填充設計相關的數值實驗，來驗證所提方法的實際效能。最後，本研究進一步探討了一項空間填充設計中極具複雜性的實際應用案例，以作為綜合性的說明。

Design of Experiments (DOE) assists researchers and engineers in collecting data efficiently while minimizing experimental costs. While experimental regions are typically assumed to be hypercubes, practical applications sometimes impose specific constraints on these regions. As these restrictions become increasingly complex, the experimental region can be narrow and irregular, complicating the identification of optimal experimental designs. To address this challenge, this study formulates the search for constrained optimal experimental designs as a constrained optimization problem. Specifically, the research employs Particle Swarm Optimization (PSO)-type techniques, capitalizing on their derivative-free nature and robust global search capabilities. These metaheuristic algorithms are systematically integrated with various penalty methods to construct experimental designs within the constrained regions. Numerical experiments involving optimal mixture experiments and constrained space-filling designs are utilized to evaluate the performance of the proposed methods. Finally, a complex real-world application in space-filling design is examined to illustrate the approach.

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