A Wasserstein distance based multiobjective evolutionary algorithm for the risk aware optimization of sensor placement

In this paper we propose a new algorithm for the identification of optimal “sensing spots”, within a network, for monitoring the spread of “effects” triggered by “events”. This problem is referred to as “Optimal Sensor Placement” and many real-world problems fit into this general framework. 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. Usually, we have to manage a trade-off between different objective functions, so that we are faced with a multi objective optimization problem. (MOP). The best trade-off between the objectives can be defined in terms of Pareto optimality. 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 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. This data structure enables 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, indicators of the quality of the Pareto set and criteria to choose among the Pareto solutions. The new algorithm MOEA/WST has been tested on two benchmark water distribution networks and a real world network. Preliminary results are compared with NSGA-II and show a better performance, in terms of hypervolume and coverage, in particular for relatively large networks and low generation counts.