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Partial outer convexification for traffic light optimization in road networks

Simone Göttlich(goettlich***at***uni-mannheim.de)
Andreas Potschka(potschka***at***iwr.uni-heidelberg.de)
Ute Ziegler(ziegler***at***uni-mannheim.de)

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 we investigate. 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 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 traffic flow models, in addition to being computed faster.

Keywords: Partial outer convexification, traffic networks, discretized conservation laws, optimization, mixed-integer programming

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 3: Applications -- OR and Management Sciences (Transportation )

Citation: Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 368, 69121 Heidelberg, Germany, Nov 2015

Download: [PDF]

Entry Submitted: 11/12/2015
Entry Accepted: 11/12/2015
Entry Last Modified: 11/12/2015

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