A path-free modelling approach for the traffic counting location problem

Efficient sensor placement enhances traffic management, planning, and flow control by providing real-time traffic information. Given that the quality of this information is closely linked to sensor locations, this paper aims to find the optimal location of minimum number of counting sensors to efficiently monitor all origin–destination ($OD$) trips. This problem is known as the Traffic Counting Location Problem (TCLP) in the literature. For this problem, the paper presents a path-free modelling approach, along with a search space reduction procedure. The proposed approach removes the need to explicitly track paths between all $OD$ pairs as well as excluding unnecessary route observations. This greatly reduces the solution return time and memory usage for the TCLP, showed in extensive computational experiments tested on well-known transportation networks and randomly generated networks. Specifically, the best existing method in the literature has demonstrated effectiveness only for networks with fewer than 2,000 nodes. In contrast, the proposed solution methodology in this paper successfully addresses networks exceeding 15,000 nodes, substantially extending the scalability of exact approaches in solving the TCLP. Hence, this paper fills a significant gap in the TCLP literature by introducing an efficient exact approach that rapidly generates optimal solutions for medium-scale networks, and provides, for the first time, an optimal solution of TCLP for many large-scale networks. This advancement contributes to the development of intelligent transportation systems in smart cities, facilitating better traffic management and improving overall urban efficiency