Offset optimization of signalized intersections via the Burer-Monteiro method

This paper tackles the offset optimization problem which seeks to coordinate traffic signals in a large traffic network. By assuming that all signals have a common cycle time and that the arrival/departure rates at each intersection can be approximated by sinusoids, the original non-convex offset optimization problem can be relaxed into a semidefinite program (SDP). SDP solvers unfortunately run out of memory for larger networks with thousands of intersections. The Burer-Monteiro (BM) method [1] for solving large SDPs avoids conic constraints and solves a lower dimensional problem but is non-convex. A synthetic New York City example with 1771 intersections showcases the scalability of the BM method. Another example involving 420 intersections in Los Angeles demonstrates that the BM method recovers optimal solutions of the SDP. Moreover, a detailed microsimulation of the Los Angeles network shows that the optimized offsets result in reduced delay time and smaller queues.