Abstract
We consider the problem of computing optimal traffic light programs for urban road intersections using traffic 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 differential 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 are investigated. We use the two-stage approach to compute traffic light programs for two scenarios on different discretizations and demonstrate that the solution candidates cannot be improved in a reasonable amount of time by global state-of...
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