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Multiobjective design of water distribution systems under uncertainty

机译：不确定性下水系统的多目标设计

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摘要

The water distribution system (WDS) design problem is defined here as a multiobjective optimization problem under uncertainty. The two objectives are (1) minimize the total WDS design cost and (2) maximize WDS robustness. The WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. Decision variables are the alternative design options for each pipe in the network. The sources of uncertainty are future water consumption and pipe roughness coefficients. Uncertain variables are modeled using probability density functions (PDFs) assigned in the problem formulation phase. The corresponding PDFs of the analyzed nodal heads are calculated using the Latin hypercube sampling technique. The optimal design problem is solved using the newly developed RNSGAII method based on the nondominated sorting genetic algorithm Ⅱ (NSGAII). In RNSGAII a small number of samples are used for each fitness evaluation, leading to significant computational savings when compared to the full sampling approach. Chromosome fitness is defined here in the same way as in the NSGAII optimization methodology. The new methodology is tested on several cases, all based on the New York tunnels reinforcement problem. The results obtained demonstrate that the new methodology is capable of identifying robust Pareto optimal solutions despite significantly reduced computational effort.
机译：供水系统（WDS）设计问题在此定义为不确定性下的多目标优化问题。这两个目标是（1）最小化WDS的总设计成本，以及（2）最大化WDS的鲁棒性。 WDS的鲁棒性定义为在网络中所有节点上同时满足最小压头约束的概率。决策变量是网络中每个管道的替代设计选项。不确定性的来源是未来的用水量和管道粗糙度系数。不确定变量使用在问题制定阶段分配的概率密度函数（PDF）进行建模。使用拉丁文超立方体采样技术计算出相应的已分析节点头的PDF。基于非支配排序遗传算法Ⅱ（NSGAII）的新开发的RNSGAII方法解决了最优设计问题。在RNSGAII中，每次适合度评估都使用少量样本，与完整采样方法相比，可节省大量计算量。此处，染色体适应性的定义与NSGAII优化方法中的定义相同。在几种情况下都对新方法进行了测试，所有情况均基于纽约隧道加固问题。获得的结果表明，尽管大大减少了计算工作量，但新方法仍能够识别鲁棒的Pareto最优解。

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