Partial Outer Convexification for Traffic Light Optimization in Road Networks

Abstract. We consider the problem of computing optimal tra c light programs for urban road intersections using tra c flow conservation laws on networks. Based on a Partial Outer Convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or di↵erential algebraic equations, we develop a computationally tractable two-stage solution heuristic. The two-stage approach consists of the solution of a (smoothed) Nonlinear Programming Problem with dynamic constraints and a reconstruction Mixed-Integer Linear Program without dynamic constraints. The two-stage approach is founded on a discrete approximation lemma for Partial Outer Convexification, whose grid independence properties for (smoothed) conservation laws we investigate. We use the two-stage approach to compute tra c light programs for two scenarios on di↵erent discretizations and demonstrate that the solution candidates cannot be improved in a reasonable amout of time by global state-of-the art Mixed-Integer Nonlinear Programming Solvers. In addition, the two-stage solution candidates are better than results obtained by global optimization of piecewise linearized tra c flow models, in addition to being computed faster.