EPANET Input Files of New York tunnels and Pacific City used in a metamodel-based optimization study

Metamodels have proven be very useful when it comes to reducing the computational requirements of Evolutionary Algorithm-based optimization by acting as quick-solving surrogates for slow-solving fitness functions. The relationship between metamodel scope and objective function varies between applications, that is, in some cases the metamodel acts as a surrogate for the whole fitness function, whereas in other cases it replaces only a component of the fitness function. This paper presents a formalized qualitative process to evaluate a fitness function to determine the most suitable metamodel scope so as to increase the likelihood of calibrating a high-fidelity metamodel and hence obtain good optimization results in a reasonable amount of time. The process is applied to the risk-based optimization of water distribution systems; a very computationally-intensive problem for real-world systems. The process is validated with a simple case study (modified New York Tunnels) and the power of metamodelling is demonstrated on a real-world case study (Pacific City) with a computational speed-up of several orders of magnitude.

元模型（metamodels）已被证实具备极高的应用价值：在降低基于进化算法的优化任务的计算开销时，其可作为求解速度较慢的适应度函数（fitness function）的快速替代模型。元模型范围与目标函数（objective function）之间的关联因应用场景而异，具体而言，部分场景下元模型会替代完整的适应度函数，而在其他场景中，它仅替代适应度函数的某一组成部分。本文提出一种形式化的定性流程，用于对适应度函数开展评估，以确定最适配的元模型范围，从而提升校准高保真元模型的可能性，进而在合理时长内获得优质的优化结果。该流程被应用于配水系统的基于风险的优化——这是一类针对实际工程系统而言计算量极大的问题。研究通过一个简易案例（改造版纽约输水隧道）验证了该流程的有效性，并在实际工程案例（太平洋城）中展示了元建模的效能，实现了数个数量级的计算加速。