In this work, we put forward a new algorithm for minimizing the total cost of gravity-fed water distribution networks (WDN) by optimally choosing pipe diameters. Our approach is based on network theory and heuristic procedures and aims at overcoming a number of limitations found in the current scientific literature. WDN optimization problems belong to those that are discrete, non-linear and non-convex, making the use of standard optimization algorithms inefficient. Furthermore, resorting to metaheuristic search techniques to test many different solutions has an exceedingly expensive computational cost, due to the inherent complexity of the problem. Here we present an efficient heuristic algorithm that circumvents these limitations, exploiting detailed aspects, such as the specific network topology. In order to check the capability of the algorithm in a realistic setting, we have developed and analyzed a mathematical model of a water distribution network in a Spanish municipality, considerably larger than those addressed in previous works. Our numerical results indicate significant potential construction savings over current design practices, which justifies the interest of our approach in addressing this class of optimization problems.

在这项工作中，我们提出了一种通过优化选择管径来使重力供水网（WDN）的总成本最小化的新算法。我们的方法基于网络理论和启发式程序，旨在克服当前科学文献中发现的许多局限性。WDN优化问题属于离散，非线性和非凸问题，这使得标准优化算法的使用效率低下。此外，由于问题固有的复杂性，求助于元启发式搜索技术来测试许多不同的解决方案具有极其昂贵的计算成本。在这里，我们提出了一种有效的启发式算法，它利用详细的方面（例如特定的网络拓扑）来规避这些限制。为了在现实的环境中检查算法的能力，我们开发并分析了西班牙市政供水网络的数学模型，该模型比以前的工作要大得多。我们的数值结果表明，与当前的设计实践相比，可以节省大量的施工成本，这证明了我们的方法对解决此类优化问题的兴趣。