The design and operation of flood control systems are always subjected to different uncertainties. In general, uncertainty occurs due to the inherent randomness of natural events (aleatory) or the lack of information (epistemic). In this paper, the optimal design of flood control levees was considered with respect to different types of uncertainties. For this purpose, a stochastic model was developed in which the hydrologic, hydraulic, geotechnical, and economic uncertainties were considered. The probability theory and the evidence theory were utilized along with the Monte Carlo simulation for quantifying the uncertainties. A computational strategy was developed based on the Latin hypercube sampling and Cholesky decomposition to propagate the uncertainties using the real and site-specific data of the Leaf River in Hattiesburg city, Mississippi, USA. Optimization models were solved using a differential evolutionary algorithm. While the deterministic case resulted from the single value for each output such as the total cost (10.36 × 10⁵ $) and height of the levees (2.46 and 3.28 m, for left and right levees, respectively), the stochastic case results from multiple values or an interval for each output variable as a probability distribution such as CCDF or quantile curves and decision-makers could select the system layout based on their desire risk; for example, with 50% epistemic risk, the total cost of system with a 90% confidence interval falls within [12.09 × 10⁵, 28.62 × 10⁵] $, and a corresponding height of the left and right levees falls within [4.23, 4.73] m, and [4.12, 4.75] m, respectively. On the other hand, the belief and plausibility curves (CCBF and CCPF) in evidence theory provide lower and upper bounds of probabilities or equivalently lower and upper bounds of an output value with a given risk. For example, results showed that with 90% confidence interval, the total cost falls within [0.325 × 10⁵, 3.75 × 10⁵] $ and [14.13 × 10⁵, 24.47 × 10⁵] $ based on CCBF and CCPF, respectively. Several codes were developed for calculating the probability quantiles, PDF, CCDF, CCBF, and CCPF curves, and proper tables and charts to summarize the results. This study is an attempt to involve the several uncertainties in the design and analysis of flood control systems and it seems if appropriate methods and tools are used, this purpose can be achieved.

防洪系统的设计和运行总是受到不同的不确定性的影响。一般来说，不确定性是由于自然事件的内在随机性（偶然性）或信息缺乏（认知性）而发生的。本文针对不同类型的不确定性考虑了防洪堤的优化设计。为此，开发了一个随机模型，其中考虑了水文、水力、岩土和经济的不确定性。概率论和证据理论与蒙特卡罗模拟一起用于量化不确定性。基于拉丁超立方体采样和 Cholesky 分解开发了一种计算策略，以使用密西西比州哈蒂斯堡市叶河的真实和特定地点数据传播不确定性，美国。使用差分进化算法求解优化模型。而确定性情况是由每个输出的单一值导致的，例如总成本 (10.36 × 10⁵ $) 和堤坝的高度（分别为 2.46 和 3.28 m，左右堤坝），随机情况由多个值或每个输出变量的区间产生，作为概率分布，如 CCDF 或分位数曲线和决策-创客可以根据自己的意愿风险选择系统布局；例如，对于 50% 的认知风险，具有 90% 置信区间的系统总成本落在 [12.09 × 10 ⁵ , 28.62 × 10 ⁵] $，左右堤坝对应的高度分别在[4.23, 4.73] m和[4.12, 4.75] m以内。另一方面，证据理论中的置信度和可信度曲线（CCBF 和 CCPF）提供了概率的下限和上限，或者等价的具有给定风险的输出值的下限和上限。例如，结果显示在 90% 置信区间内，总成本落在 [0.325 × 10 ⁵ , 3.75 × 10 ⁵ ] $ 和 [14.13 × 10 ⁵ , 24.47 × 10 ^{5 ]}] $ 分别基于 CCBF 和 CCPF。开发了几个代码来计算概率分位数、PDF、CCDF、CCBF 和 CCPF 曲线，以及适当的表格和图表来总结结果。本研究试图在防洪系统的设计和分析中涉及几个不确定性，如果使用适当的方法和工具，似乎可以实现这一目的。