4,419 research outputs found
Applications of sensitivity analysis for probit stochastic network equilibrium
Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported
A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs
This work deals with a class of problems under interval data uncertainty,
namely interval robust-hard problems, composed of interval data min-max regret
generalizations of classical NP-hard combinatorial problems modeled as 0-1
integer linear programming problems. These problems are more challenging than
other interval data min-max regret problems, as solely computing the cost of
any feasible solution requires solving an instance of an NP-hard problem. The
state-of-the-art exact algorithms in the literature are based on the generation
of a possibly exponential number of cuts. As each cut separation involves the
resolution of an NP-hard classical optimization problem, the size of the
instances that can be solved efficiently is relatively small. To smooth this
issue, we present a modeling technique for interval robust-hard problems in the
context of a heuristic framework. The heuristic obtains feasible solutions by
exploring dual information of a linearly relaxed model associated with the
classical optimization problem counterpart. Computational experiments for
interval data min-max regret versions of the restricted shortest path problem
and the set covering problem show that our heuristic is able to find optimal or
near-optimal solutions and also improves the primal bounds obtained by a
state-of-the-art exact algorithm and a 2-approximation procedure for interval
data min-max regret problems
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