隨著科技的進步與發展，複雜的管理系統常牽涉到許多不同的面相，傳統的數
學最佳化問題難以處理過多的不確定因子，因此模擬最佳化便是另一種可用的決
策工具。而為了使模擬環境更接近真實情形，模擬技術開始考量到有隨機限制式
的環境，隨機限制式的出現使得模擬最佳化方法在求解過程中更加困難。大部分
研究專注在單一整數或是單一實數決策變數的隨機限制式環境中，有關混整數的
隨機限制式模擬最佳化方法相較起來仍為少數，藉由以上的原因，本研究將專注
在兩個部分:

第一部分將探討隨機限制式的處理方法，在三種隨機限制式處理方法中找到各
自的特點。以整數模擬最佳化搜尋法R-SPLINE作為基礎，分別加上三種隨機限制
式的處理方法:PFM、增加可行解範圍與減少可行解範圍，此三種方法將以數值實
驗的方式探討。結果發現PFM在邊界解的情況下，其目標績效值為三個方法中最
佳的方法，且可行性表現上也能快速地收斂至一個水平上。增加可行解範圍需要
在足夠樣本數地情形下才有一定的可行性表現，在目標績效值的品質上則是三者
的中間。減少可行解空間使得可行性機率大幅提升，但是其目標績效值表現為三
者最差。

第二部分則提出一個適用於具隨機限制式混整數模擬最佳化問題的搜尋
法:SD-SCM-SLIS。該演算法將混整數變數空間拆分成整數型與連續型變數，利用
梯度搜尋分別在兩個空間中進行搜索以增加搜尋效率。在處理隨機限制式方面藉
由新增緊縮值到隨機限制式中，使可行性的判定趨向保守，但搜尋到的解有較高
的機率位於真實的可行解範圍內，並且增加搜尋過程的單體路徑數以增進解的品
質。實驗結果表示多條的單體路徑有機會增加目標績效值的表現。

Due to technological development, complex systems typically involve many factors, making it impossible to use numerical optimization to solve these problems. In this situation, simulation optimization (SO) is selected as a suitable method to overcome this issue. To make the simulated environment fit a real situation, we consider an optimization problem with stochastic constraints. The challenge in this problem is the fact that the feasibility of a given solution cannot be known for certain. Most studies on this topic have focused on the discrete or continuous variables in the problem, and only a few have considered mixed-integer variables. Therefore, this article is divided into two parts.

First, we compare the performance of stochastically-constrained processing methods.
Based on the R-SPLINE searching algorithm, we add three methods: (1) Penalty Function with Memory (PFM), (2) increasing the feasible region and (3) decreasing the feasible region. When an optimal feasible solution is a boundary solution, the experimental results show that PFM has the best objective value, and the probability of a feasible solution rapidly converges to specific level. Increasing the feasible region requires more
observations to obtain a higher probability of feasible solution, and its objective value is
between that obtained using PFM and that obtained when decreasing the feasible region.
Decreasing the feasible region leads to the highest probability of a feasible solution, but
its objective value is the worst.

Second, we propose a mixed-integer optimization method, SD-SCM-SLIS, for a stochastically constrained problem. In this method, the mixed-integer solution space is separated into a discrete subspace and a continuous subspace. SD-SCM-SLIS adopts gradient-type local searches in these subspaces and uses a decreasing feasible
region in the stochastic constraints. The above features enable SD-SCM-SLIS to maintain searching efficiency while also having the feasibility of generating a solution. SD-SCM-SLIS increases the number of searching paths and improves the quality of the solution. The experimental results show that the use of multiple searching paths makes it possible to improve the objective value performance.

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