Lost in Optimization of Water Distribution Systems: Better Call Bayes

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Abstract
The main goal of this paper is to show that Bayesian optimization can be regarded as a general framework for the data-driven modelling and solution of problems arising in water distribution systems. Scenario-based hydraulic simulation and Monte Carlo are key tools in modelling in water distribution systems. The related optimization problems fall into a simulation/optimization framework in which objectives and constraints are often black box. Bayesian optimization (BO) is characterized by a surrogate model, usually a Gaussian process but also a random forest, as well as neural networks and an acquisition function that drives the search for new evaluation points. These modelling options make BO nonparametric, robust, flexible, and sample efficient, making it particularly suitable for simulation/optimization problems. A defining characteristic of BO is its versatility and flexibility, given, for instance, by different probabilistic models, in particular different kernels, different acquisition functions. These characteristics of the Bayesian optimization approach are exemplified by two problems: cost/energy optimization in pump scheduling and optimal sensor placement for early detection of contaminant intrusion. Different surrogate models have been used both in explicit and implicit control schemes, showing that BO can drive the process of learning control rules directly from operational data. BO can also be extended to multi-objective optimization. Two algorithms are proposed for multi-objective detection problems using two different acquisition functions.

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