(An) algorithm for the sensor location problem on grid networks

Abstract

We consider a variant of 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 a variant of SLP. The coverage intensity of a point from a sensor located in a point decreases as the distance between the two points increases. The objective of MDSLP is to minimize total sensor costs while covering every sensor field with enough intensity. 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 symmetric structure is used to facilitate pruning in the branch-and-bound tree. We solved this problem by branch-and-cut (B&C) approach. We tested our algorithm on 60 instances with various sizes and computational reports are given.