Every morning, water suppliers need to define their pump schedules for the next 24 h for drinking water production. Plans must be designed in such a way that drinking water is always available and the amount of unused drinking water pumped into the network is reduced. Therefore, operators must accurately estimate the next day’s water consumption profile. In real-life applications with standard consumption profiles, some expert system or vector autoregressive models are used. Still, in recent years, significant improvements for time series prediction have been achieved through special deep learning algorithms called long short-term memory (LSTM) networks. This paper investigates the applicability of LSTM models for water demand prediction and optimal pump control and compares LSTMs against other methods currently used by water suppliers. It is shown that LSTMs outperform other methods since they can easily integrate additional information like the day of the week or national holidays. Furthermore, the online- and transfer-learning capabilities of the LSTMs are investigated. It is shown that LSTMs only need a couple of days of training data to achieve reasonable results. As the focus of the paper is on the real-world application of LSTMs, data from two different water distribution plants are used for benchmarking. Finally, it is shown that the LSTMs significantly outperform the system currently in operation.

The design and operation of water supply systems is a multicriteria task; the energy efficiency should be minimized while, at the same time, respecting technical requirements, such as the balanced operation of available pumps. On one hand, the overall system can be improved by the use of variable speed pumps. They increase the number of operating options. On the other hand, they add more complexity to the operation problem. In this paper, we discuss the difficulties associated with speed control and propose a decision support system to overcome them.

This article introduces the new class of continuous set covering problems. These optimization problems result, among others, from product portfolio design tasks with products depending continuously on design parameters and the requirement that the product portfolio satisfies customer specifications that are provided as a compact set. We show that the problem can be formulated as semi-infinite optimization problem (SIP). Yet, the inherent non-smoothness of the semi-infinite constraint function hinders the straightforward application of standard methods from semi-infinite programming. We suggest an algorithm combining adaptive discretization of the infinite index set and replacement of the non-smooth constraint function by a two-parametric smoothing function. Under few requirements, the algorithm converges and the distance of a current iterate can be bounded in terms of the discretization and smoothing error. By means of a numerical example from product portfolio optimization, we demonstrate that the proposed algorithm only needs relatively few discretization points and thus keeps the problem dimensions small.