عنوان مقاله [English]
This paper addresses the problem of locating Vehicle-ID sensors on the arcs of the transportation network to recognize the traffic flows along a given set of routes. This problem has received great attention from researchers and existing studies can be partitioned into two categories, namely flow-observation and flow-estimation. In the first category, the location of sensors is determined so that the flow of all routes can be determined exactly while minimizing the number of sensors. The second category is used when the number of available sensors is limited and the aim is to maximize the number of routes whose flow can be determined uniquely.
Since the number of available sensors is usually limited, the amount of flow along some routes cannot be determined uniquely; further, the set of routes, covered by at least one sensor, is partitioned into some clusters where each cluster contains the routes with the same sensor pattern. Generally, the size of clusters obtained by current optimization models is very big; however, the smaller the size of clusters, the better the estimation of flow along the routes belonging to the same cluster. To overcome this shortcoming, we present a new multi-objective model in which every route is covered by at least one sensor and the objective functions are considered in the order of priority. Indeed, the first objective is to minimize the size of the largest cluster. Then, assuming that the optimal value of the size of the largest cluster is L ,
the second objective is to minimize the number of clusters with the size L ; the third objective is to minimize the number of clusters with the sizeL-1 ; and finally, the last objective is to minimize the number of clusters with the size
2. The evaluation of the proposed model on two real-world networks, taken from the literature, confirms its importance.