ARTICLE | doi:10.20944/preprints202112.0506.v1
Subject: Computer Science And Mathematics, Data Structures, Algorithms And Complexity Keywords: multi-objective; evolutionary algorithms; Pareto optimality; Wasserstein distance; network vulnerability; resilience; sensor placement.
Online: 31 December 2021 (11:01:51 CET)
This paper is focused on two topics very relevant in water distribution networks (WDNs): vulnerability assessment and the optimal placement of water quality sensors. The main novelty element of this paper is to represent the data of the problem, in this case all objects in a graph underlying a water distribution network, as discrete probability distributions. For vulnerability (and the related issue of re-silience) the metrics from network theory, widely studied and largely adopted in the water research community, reflect connectivity expressed as closeness centrality or, betweenness centrality based on the average values of shortest paths between all pairs of nodes. Also network efficiency and the related vulnerability measures are related to average of inverse distances. In this paper we propose a different approach based on the discrete probability distribution, for each node, of the node-to-node distances. For the optimal sensor placement, the elements to be represented as dis-crete probability distributions are sub-graphs given by the locations of water quality sensors. The objective functions, detection time and its variance as a proxy of risk, are accordingly represented as a discrete e probability distribution over contamination events. This problem is usually dealt with by EA algorithm. We’ll show that a probabilistic distance, specifically the Wasserstein (WST) distance, can naturally allow an effective formulation of genetic operators. Usually, each node is associated to a scalar real number, in the optimal sensor placement considered in the literature, average detection time, but in many applications, node labels are more naturally expressed as histograms or probability distributions: the water demand at each node is naturally seen as a histogram over the 24 hours cycle. The main aim of this paper is twofold: first to show how different problems in WDNs can take advantage of the representational flexibility inherent in WST spaces. Second how this flexibility translates into computational procedures.
ARTICLE | doi:10.20944/preprints202201.0047.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Pump scheduling optimization; Bayesian optimization; Optimal sensor placement; Wasserstein distance; Robustness
Online: 6 January 2022 (09:26:55 CET)
The main goal of this paper is to show that Bayesian optimization could be regarded as a general framework for the data driven modelling and solution of problems arising in water distribution systems. Hydraulic simulation, both scenario based, and Monte Carlo is a key tool in modelling in water distribution systems. The related optimization problems fall in 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 and increasingly neural networks and an acquisition function which drives the search for new evaluation points. These modelling options make BO nonparametric, robust, flexible and sample efficient 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 the two problems: cost/energy optimization in pump scheduling and optimal sensor placement for early detection on 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 have been proposed for multi-objective detection problem using two different acquisition functions.