A New Evolutionary Approach to Optimal Sensor Placement in Water Distribution Networks

Abstract

The sensor placement problem is modeled as a multi-objective optimization problem with Boolean decision variables. A new multi objective evolutionary algorithm (MOEA) is proposed for approximating and analyzing the set of Pareto optimal solutions. The evaluation of the objective functions requires the execution of a hydraulic simulation model of the network. To organize the simulation results a data structure is proposed which enables the dynamic representation of a sensor placement and its fitness as a heatmap. This allows the definition of information spaces, in which the fitness of a placement can be represented as a matrix or, in probabilistic terms as a histogram. The key element in the new algorithm is this probabilistic representation which is embedded in a space endowed with a metric based on a specific notion of distance. Among several distances between probability distributions the Wasserstein (WST) distance has been selected: WST has enabled to derive new genetic operators, indicators of the quality of the Pareto set and criteria to choose among the Pareto solutions. The new algorithm has been tested on a benchmark water distribution network with two objective functions showing an improvement over NSGA-II, in particular for low generation counts, making it a good candidate for expensive black-box multi-objective optimization

Pressure Sensor Placement for Leak Localization in Water Distribution Networks Using Information Theory

“…The model of the Hanoi network is composed of one reservoir, 31 consumer nodes, and 34 pipes, as shown in Figure 1. Due to its reduced topology, this network has been used as a standarized benchmark in different works [21,27,34].…”

“…In [23], a multi-objective approach to mitigate errors both in the detection and localization of leaks, considering minimum night flow conditions, is presented. Regarding the optimization of the objective function, two approaches are usually used: deterministic methods (e.g., branch and bound [24]) and metaheuristic methods, (e.g., genetic algorithms [25][26][27] and particle swarm optimization [28]). Deterministic approaches guarantee an optimal solution, but the computation time increases exponentially with the number of nodes and possible leak scenarios.…”

BORA: Bayesian Optimization for Resource Allocation

“…Recently, the interest on the Wasserstein distance [36] and the associated Optimal Transport theory [37] have been growing due to their successful application in many domains (e.g., imaging, signal processing and analysis, natural language process/generation, human learning, optimization, etc.) [38,39,40,41,42,43,44]. Very briefly, the Wasserstein distance allows to measure the difference between two probability distributions, α and α , independently on the values and the nature of their supports (they can be both discrete, continuous, or one continuous and one discrete).…”

Selecting the best location of water quality sensors in water distribution networks by considering the importance of nodes and contaminations using NSGA-III (case study: Zahedan water distribution network, Iran)

“…Khorshidi et al (2019) used a decision support framework based on the game theory by considering the two goals of minimizing the detection time and the sensor cost for the optimal locations of quality sensors. Ponti et al (2021) proposed a novel evolutionary algorithm to estimate and analyze the optimal solutions of Pareto for sensor placement problems. Evaluation of the results of the new algorithm with the NSGA-II algorithm on a water distribution system through applying two objective functions demonstrated an improvement of this algorithm comparing with NSGA-II, especially for low iteration counts.…”