An Analysis of Multiple Contaminant Warning System Design Objectives for Sensor Placement Optimization in Water Distribution Networks

Recent events have significantly increased the level of interest in using sensors to detect the presence of contaminants in municipal water distribution systems. A key deployment issue is identifying where a limited number of sensors should be placed in order to maximize the level of protection afforded. Researchers have proposed several algorithms for generating such placements, each optimizing with respect to a different design objective. The use of disparate objectives raises several questions, in particular (1) What is the relationship between optimal sensor placements for different design objectives? and (2) Is there any risk in focusing on specific design objectives? To answer these questions, we solve the sensor placement problem using a mixed-integer programming formulation of the well-known p-median problem from facility location theory, which can express a broad range of design objectives. Using three large test networks, we show that optimal solutions with respect to one design objective are often highly sub-optimal with respect to other design objectives. In some instances, however, it is possible to construct solutions that are simultaneously near-optimal with respect to a range of design objectives. For both algorithm developers and decision-makers, the implication is that development of robust sensor placements requires careful and simultaneous consideration of multiple, disparate design objectives. ∗Discrete Algorithms and Math Department, Sandia National Laboratories, P.O. Box 5800, MS 1110, Albuquerque, NM 87185-1110; Phone: 505-845-8887; E-Mail: [email protected]. †Discrete Algorithms and Math Department, Sandia National Laboratories, P.O. Box 5800, MS 1110, Albuquerque, NM, 87185-1110; Phone: 505-844-2217; E-Mail: [email protected]. ‡Mathematics Department, University of Colorado – Denver, P.O. Box 173364, Denver, CO 80217; Phone: 303556-8464; E-Mail: [email protected].