An Optimal Algorithm for the Sensor Location Problem to Cover Sensor Networks

We consider the sensor location problem (SLP) on a given sensor field. We present the sensor field as grid of points. There are several types of sensors which have different detection ranges and costs. If a sensor is placed in some point, the points inside of its detection range can be covered. The coverage ratio decreases with distance. The problem we consider in this thesis is called multiple-type differential coverage sensor location problem (MDSLP). MDSLP is more realistic than SLP. The coverage quantities of points are different with their distance form sensor location in MDSLP. The objective of MDSLP is to minimize total sensor costs while covering every sensor field. This problem is known as NP-hard. We propose a new integer programming formulation of the problem. In comparison with the previous models, the new model has a smaller number of constraints and variables. This problem has symmetric structure in its solutions. This group is used for pruning in the branch-and-bound tree. We solved this problem by branch-and-cut(B&C) approach. We tested our algorithm on about 60 instances with varying sizes.