Pareto Optimality for Sensor Placements in a Water Distribution System

Detection

“…One of the conclusions made by Weickgenannt et al (2010) was that there is a reasonable benefit from a small number of sensors and diminishing returns for a large number of sensors. Shen and McBean (2011) applied the sensor placement problem to the water system located in the city of Guelph, Canada (population 110,000).…”

“…Krause et al (2008) used the concept of submodularity to optimize sensor design by using the concept of penalties and solving to minimize penalties. Shen and McBean (2011) used a nondominated genetic algorithm (NSGA-II) to solve the optimization problem with a Pareto optimality methodology. Many other researchers use the Pareto front principle to aid in optimization problem solutions.…”

Greedy Algorithms for Sensor Location in Sewer Systems

“…However, when distinct fitness functions with different objectives are considered (e.g., [20][21][22]), many optimal solutions are reported in the form of a Pareto front, and then a further criterion has to been individuated to select which to implement. Differently, to obtain a single optimal solution, procedures 4, 5 and 6 use the GR_M approach with the optimization problem formulated considering one fitness function including different objectives.…”

“…The different objectives may be applied either separately (single-objective procedure) or simultaneously (multi-objective procedure) in the optimization formulation. Some multi-objective approaches consider different objectives grouped together in a single function (e.g., [12,18,19]), while in other formulations they remain distinct (e.g., [18,[20][21][22]). In the latter procedures, a group of solutions are reported in the form of Pareto front without individuating the single best solution to implement.…”

“…The methodology has been tested on the complex distribution system of Almelo, and the estimated Pareto front suggests that a reasonable level of contaminant protection can be achieved using a small number of strategically located sensors. In [22], the authors considered two competitive objectives: the minimization of the delay time and the maximization of sensor redundancy. The study applied on the distribution network of the city of Guelph shows that the evaluation of the Pareto fronts' performance indicates five as the number of sensors needed.…”