Abstract
The optimal sensor placement problem arises in many contexts for the identification of optimal “sensing spots”, within a network, for monitoring the spread of “effects” triggered by “events”. There are usually different and conflicting objectives as cost, time and reliability of the detection In this paper sensor placement (SP) (i.e., location of sensors at some nodes) for the early detection of contaminants in water distribution networks (WDNs) will be used as a running example. The best trade-off between the objectives can be defined in terms of Pareto optimality.
The evaluation of the objective functions requires the execution of a simulation model: to organize the simulation results in a computationally efficient way we propose a data structure collecting simulation outcomes for every SP which is particularly suitable for visualization of the dynamics of contaminant concentration and evolutionary optimization.
In this paper we model the sensor placement problem as a multi objective optimization problem with boolean decision variables and propose a Multi Objective Evolutionary Algorithm (MOEA) for approximating and analyzing the Pareto set.
The key element is the definition of information spaces, in which a candidate placement can be represented as a matrix or, in probabilistic terms as a histogram.
The introduction of a distance between histograms, namely the Wasserstein (WST) distance, enables to derive new genetic operators: the new algorithm MOEA/WST has been tested on a benchmark problem and a real world network. The computational metrics used are hypervolume and coverage: their values are compared with NSGA-II’s in terms of the number of generations.
The experiments offer evidence of a good relative performance of MOEA/WST in particular for relatively large networks and low generation counts.
The computational analysis has been limited in this paper to WDNs but the key aspect of the method, that is the representation of feasible solutions as histograms, is suitable for problems as the detection of “fake-news” on the web where the problem is to identify a small set of blogs which catch as many cascades as early as possible and more generally Multi-objective simulation optimization problems which are also amenable to the probabilistic representation of feasible solutions as histograms.
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Acknowledgements
This study has been partially supported by the Italian project “PERFORM-WATER 2030” – programma POR (Programma Operativo Regionale) FESR (Fondo Europeo di Sviluppo Regionale) 2014–2020, innovation call “Accordi per la Ricerca e l’Innovazione” (“Agreements for Research and Innovation”) of Regione Lombardia, (DGR N. 5245/2016 - AZIONE I.1.B.1.3 – ASSE I POR FESR 2014–2020) – CUP E46D17000120009.This study has also been partially supported by the Italian project ENERGIDRICA co-financed by MIUR.We greatly acknowledge the DEMS Data Science Lab for supporting this work by providing computational resources (DEMS – Department of Economics, Management and Statistics).
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Ponti, A., Candelieri, A., Archetti, F. (2021). Optimal Sensor Placement by Distribution Based Multiobjective Evolutionary Optimization. In: Simos, D.E., Pardalos, P.M., Kotsireas, I.S. (eds) Learning and Intelligent Optimization. LION 2021. Lecture Notes in Computer Science(), vol 12931. Springer, Cham. https://doi.org/10.1007/978-3-030-92121-7_25
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