Robust transportation network design under user equilibrium
Massachusetts Institute of Technology. Computation for Design and Optimization Program.
Dimitris J. Bertsimas and Georgia Perakis.
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We address the problem of designing a transportation network in the presence of demand uncertainty, multiple origin-destination pairs and a budget constraint for the overall construction cost, under the behavioral assumption that travelers optimize their own travel costs (i.e., the "user-equilibrium" condition). Under deterministic demand, we propose an exact integer optimization approach that leads to a quadratic objective, linear constraints optimization problem. As a result, the problem is efficiently solvable via commercial software, when the costs are linear functions of traffic flows. We then use an iterative algorithm to address the case of nonlinear cost functions. While the problem is intractable under probabilistic assumptions on demand uncertainty, we extend the previous model and propose an iterative algorithm using a robust optimization approach that models demand uncertainty. We finally report extensive numerical results to illustrate that our approach leads to tractable solutions for large scale networks.
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 59-63).
DepartmentMassachusetts Institute of Technology. Computation for Design and Optimization Program.
Massachusetts Institute of Technology
Computation for Design and Optimization Program.